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BARYONS 2002

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BARYONS 2002 Proceedings of the 9th International Conference on the Structure of Baryons

Jefferson Lab

Newport News, Virginia, USA March 3 - 8,2002

Editors

Carl E. Carlson College of William & Mary, Williamsburg, Virginia

Bernhard A. Mecking Jefferson Lab, Newport News, Virginia

vp p r l d Scientific

ew Jersey London Singapore Hong Kong

Published by

World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224

USA ofice: Suite 202,1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library

BARYONS 2002 Proceedings of the 9th International Conference on the Structure of Baryons

Copyright 0 2003 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereoJ may not be reproduced in any form or by any means, electronic or mechanical. including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-238-409-X

Printed in Singapore by World Scientific Printers (S)Pte Ltd

The Baryons 2002 Conference was dedicated to the memory of Nathan lsgur as a tribute to his contributionsto Nuclear and Particle Physics and especially to the Baryons Community

V


Preface This volume presents the proceedings of the g t h International Conference on the Structure of Baryons, or more compactly, Baryons 2002, which was held at Jefferson Lab, Newport News, Virginia, from March 3 to 8, 2002. The conference discussed the latest experimental results and theoretical developments in the area of three-quark systems. The last Baryons Conference was held over three years ago, so there was great interest in the field, and much progress was reported. Over 200 participants attended the conference. The stimulating atmosphere that prevailed during the conference was made possible by the enthusiastic involvement of the participants. We particularly want to thank the speakers and the organizers of the parallel sessions for their hard work. We greatly appreciate the advice of the International Advisory Committee, and the work done by the Local Organizing Committee. We would like t o thank Jefferson Lab and the Department of Energy for financial support. Allow us t o give special thanks to the Jefferson Lab Conference Services group and t o the Physics Division secretarial staff. Without their efforts the conference would not have been possible. We would also like to thank Lori Powell for the front cover design. Carl E. Carlson John J. Doming0 Bernhard A. Mecking November 2002

vii


INTERNATIONAL ADVISORY COMMITTEE University of Massachusetts Los Alamos National Lab University of Illinois University of Maryland NIKHEF TRIUMF Rutherford Lab

Ray Arnold Peter Barnes Doug Beck Betsy Beise J o van den Brand Doug Bryman Frank Close Michael Danilov Enzo DeSanctis Dieter Drechsel Ralph Eichler Brad Filippone Don Geesaman Mauro Giannini Franc0 Iachello Ken’ichi Imai Elizabeth Jenkins Gabriel Karl Jirohta Kasagi Thomas Kirk Robert Klanner Juergen Koerner Sven Kullander Jean-Marc Laget John McClelland Ulf Meissner Volker Metag Chris Michael Richard Milner Piet Mulders Takashi Nakano Dan-Olof Riska Klaus Rith Andrew Sandorfi Carlo Schaerf Berthold Schoch Hans Stroeher

ITEP INFN Frascati Universitat Mainz Paul Scherrer Institute Caltech Argonne National Lab INFN, Genova Yale University Kyoto University University of California San Diego University of Guelph Tohoku University Brookhaven National Lab DESY Universitat Mainz Uppsala University DAPNIA Saclay Los Alamos National Lab Universitat Graz Universitat Giessen University of Liverpool MIT Vrije Universiteit, Amsterdam RCNP, Osaka University of Helsingfors Universitat Erlangen Brookhaven National Lab University of Rome Universitat Bonn FZ Juelich

ix

INTERNATIONAL ADVISORY COMMITTEE (continued) Anthony Thomas Steven Vigdor Thomas Walcher Wolfram Weise

University of Adelaide Indiana University Universitat Mainz Technische Universitat Munchen

LOCAL ORGANIZING COMMITTEE Bernhard Mecking (chair) John Doming0 (co-chair) Keith Baker Volker Burkert Carl Carlson Kees de Jager Latifa Elouadrhiri Rolf Ent Jose Goity Keith Griffioen Sebastian Kuhn Anatoly Radyushkin David Richards Winston Roberts

JLab JLab JLab/Hampton University JLab College of William & Mary JLab JLab/Christopher Newport University JLab JLab/Hampton University College of William & Mary Old Dominion University JLab/Old Dominion University JLab/Old Dominion University JLab/Old Dominion University

X

CONTENTS PLENARY SESSION PRESENTATIONS Successes and Open Issues in Baryon Physics A . Thomas Baryon Spectroscopy in the Quark Model

3

17

S. Capstick Electroexcitation of Nucleon Resonances

29

V. Burkert Baryon Spectroscopy on the Lattice R. Edwards

43

Heavy Quark Physics on the Lattice C. Davies

53

Hadrons in the Nuclear Medium-Role of Light Front Nuclear Theory G. Miller

65

Polarized Structure Functions

78

G. van der Steenhoven Proton Structure Results from the HERA Collider R. Yoshida

90

Baryon Chiral Dynamics T. Becher

102

Electromagnetic Tests of Chiral Symmetry H. Merkel

115

Hadron Structure from Lattice QCD G. Schierhob

126

Xi

xii

Photoexcitation of N * Resonances A. d’Angelo et al.

140

Instantons and Baryon Dynamics D. Diakonov

153

The Strangeness Contribution to the Form Factors of the Nucleon F. Maas

165

Electromagnetic Production of Pions in the Resonance Region - Theoretical Aspects T. Sato

178

Hadronic Production of Baryon Resonances M. Sadler

189

Baryon Resonances and Strong QCD E. Klempt

198

Spin Structure Functions in the Resonance Region R. De Vita

210

Quark-Hadron Duality S. Jeschonnek and J. W. van Orden

222

First Results from SPRING-8 T. Nakano

234

Hybrid Baryons P. Page

243

Nucleon Electromagnetic Form Factors E. Brash

256

Virtual Compton Scattering H. Fonvieille

268

...

Xlll

Generalized Parton Distributions

280

M. Diehl 290

Baryons 2002: Outlook

W. Weise

SESSION ON STRUCTURE FUNCTIONS AND FORM FACTORS The Q2Dependence of Polarized Structure Functions T. A . Forest

303

Measurement of R = ( T L / ( T T in the Nucleon Resonance Region M. E. Christy

307

The Collins Fragmentation Function in Hard Scattering Processes A . Metz, R. Kundu, A . Bacchetta and P. J. Mulders

31 1

Leading and Higher Twists in the Proton Polarized Structure Function gy at Large Bjorken-x S. Simula, M. Osipenko, G. Ricco and M. Taiuti

315

Single-Spin Asymmetries at CLAS H.Avalcian

319

Study of the A(1232) Using Double-Polarization Asymmetries

323

J. Kuhn and A . Biselli CLAS Measurement of

Electroproduction Structure Functions

327

L. C. Smith Kaon Electroproduction at Large Momentum Transfer P. Markowitz

332

xiv

Are Recoil Polarization Measurements of GP,/GP, Consistent with Rosenbluth Separation Data? J. Arrington

338

Effect of Recent R, and R, Measurements on Extended Gari-Kriimpelmann Model Fits to Nucleon Electromagnetic Form Factors E. L. Lomon

342

Measurement of the Electric Form Factor of the Neutron at Q2 = 0.6 - 0.8 (GeV/c)2 M. Seimetz

346

Neutron Electric Form Factor via Recoil Polarimetry R. Madey et al.

350

The Go Experiment: Measurements of the Strange Form Factors of the Proton J. Roche

355

The Nucleon Form Factors in the Canonically Quantized Skyrme Model E. NorvaiSas, A . Acus and D. 0. Riska

359

Soft Contribution to the Nucleon Electromagnetic Form Factors R. J. Fries, V. M. Braun, A . Lenz, N. Mahnke and E. Stein

Electroweak Properties of the Nucleon in a Chiral Constituent Quark Model M. Radici, S. BOB, L. Giozman, W. Plessas, R. F. Wagenbrunn and W. Klink Nucleon Hologram with Exclusive Leptoproduction A. V. Belitsky and D. Muller Deeply Virtual Compton Scattering at Jefferson Lab, Results and Prospects L. Elouadrhiri

363

367

371

384

xv

Twist-3 Effects in Deeply Virtual Compton Scattering Made Simple C. Weiss

388

Measurements of Hard Exclusive Reactions with a Recoil Detector at HERMES R. Kaiser

392

Dispersion Relation Formalism for Virtual Cornpton Scattering off the Proton

396

B. Pasquini, D. Drechsel, M. Gorchtein, A . Metz and M. Vanderhaeghen

SESSION ON BARYON STRUCTURE AND SPECTROSCOPY Meson-Photoproduction with the Crystal-Barrel Detector at ELSA M. Ostrick

403

K-Meson Production Studies with the TOF-Spectrometer at COSY W. Eyrich

409

First Simultaneous Measurements of the T L and TL' Structure Functions in the y*p -+ A Reaction A . Bernstein

413

Photoproduction of Resonances in a Relativistic Quark Pair Creation Model

417

F. Cano, P. Gonzdez, 5'. Noguera and B. Desplanques Relationship of the 3Po Decay Model to Other Strong Decay Models B. Desplanques, A . Nicolet and L. Theussl

42 1

Do We See the Chiral Symmetry Restoration in Baryon Spectrum? L. Ya. Glozman and T. D. Cohen

425

xvi

Virtual Compton Scattering: Results from Jefferson Lab

430

L. Van Hoorebeke Virtual Compton Scattering and Neutral Pion Electro-Production from the Proton in the Nucleon Resonance Region L. Todor

434

The Hypercentral Constituent Quark Model M. M. Giannini, E. Santopinto and A . Vassallo

438

New Search for the Neutron Electric Dipole Moment P. D. Barnes

443

qq Loop Effects on Baryon Masses

448

D. Morel and S. Capstick Learning from Dispersive Effects in the Nucleon Polarisabilities

452

H. W. Grieflhammer Dynamical Baryon Resonances with Chiral Lagrangians

456

C. Bennhold, A . Ramos and E. Oset Pion Electroproduction in the Second Resonance Region Using CLAS H. Egiyan and I. Aznauryan

460

Electron Beam Asymmetry Measurements from Exclusive no Electroproduction in the A( 1232) Resonance Region K. Joo

464

r N N * (1440) and a N N *(1440) Coupling Constants from a Microscopic N N -+ NN*(1440) Potential P. Gonzdez, B. Julici-Diaz, A . Valcarce and F. Fernbndez

468

q Electro-Production At and Above the S11 (1535) Resonance Region with CLAS

H. Denizla

472

xvii r]

Photoproduction from the Proton using CLAS E. A . Pasyuk, M. R. Dugger and B. G. Ritchie

Why is the Wavelet Analysis Useful in Physics of Resonances? Example of p' and w' States V. K . Henner, P. G. Frick and T. S. Belozerova

L = 1 Baryon Masses in the 1/Nc Expansion C. L. Schat Search for Resonance Contributions in Multi Pion Electroproduction with CLAS F. Klein, V. Burkert, H. Funsten and M. Ripani

476

480

485

489

QCD Confinement and Missing Baryons P. Gonzdez, H. Garcilazo, J. Vijande and A . Valcarce

494

Photoproduction of the E Hyperons J. W. Price, J. Ducote and B. M. K. Neflcens

498

Open Strangeness Production in CLAS G. Niculescu

502

K+ Photoproduction at LEPS/SPring-8 R. G. T. Zegers

506

Kaon Photoproduction: Background Contributions and Missing Resonances S. Janssen and J. Ryckebusch

510

Dynamical Description of Nucleon Compton Scattering at Low and Intermediate Energies: From Polarisabilities to Sum Rules S. Kondratyuk and 0. Scholten

514

xviii

SESSION ON HADRONS IN THE NUCLEAR MEDIUM Nuclear Shadowing and In-Medium Properties of the po T. Falter, S. Leupold and U.Mosel Scalar- and Vector-Meson Production in Hadron-Nucleus Reactions W. Cussing Helicity Signatures in Subthreshold p" Production on Nuclei G. M. Huber From Meson- and Photon-Nucleon Scattering to Vector Mesons in Nuclear Matter M. F. M. Lutz, Gy. Wolf and B. Friman

521

525

529

533

Polarization Transfer in the 4He(2,e' $ ) 3 H Reaction S. Strauch

537

s11(1535) Resonance in Nuclei Studied with the C(y,v) Reaction H. Yamazaki et al.

541

Double-Pion Production in y J. G. Messchendorp

+ A Reactions

Quark-Hadron Duality in Inclusive Electron-Nucleus Scattering I. Niculescu, J. Arrington, J. Crowder, R. Ent and C. Keppel Neutron Structure Function and Inclusive DIS From 3H and 3He Targets at Large Bjorken-a: M. M. Sargsian, S. Simula and M. I. Strikman Hadron Formation in Nuclei in Deep-Inelastic Lepton Scattering E. Garutti

545

550

554

558

xix

Nuclear Transparency from Quasielastic A ( e ,e’p) Reactions up to Q2= 8.1 (GeV/c)2 K. Garrow

562

Nucleon Momentum Distributions From a Modified Scaling Analysis of Inclusive Electron-Nucleus Scattering J. Arrington

567

Medium Effects in A(;, e’ ’P’) Reactions at High Q2 D. Debruyne and J. Ryckebusch Study of Nucleon Short Range Correlations in A ( e ,e‘) Reaction at zg > 1 K. Egiyan, H. Bagdasarian and N . Dashyan

571

575

N N Correlations Measured in 3He(e,e‘pp)n R. A. Niyazov and L. B. Weinstein

581

Electroproduction of Strangeness on Light Nuclei F. Dohrmann et al.

585

Hypernuclear Spectroscopy of i 2 B in the ( e le’K’) J. Reinhold

Reaction

589

SESSION ON CHIRAL PHYSICS Goldstone Boson Dynamics: Introduction to the Chiral Physics Session A. M. Bernstein

595

7’Electroproduction Off Nucleons B. Borasoy

599

A Unified Chiral Approach to Meson-Nucleon Interaction E. E. Kolomeitsev and M. F. M. Lutz

603

xx

Measurement of the Weak Pion-Nucleon Coupling Constant, H:, from Backward Pion Photo-Production Near Threshold on the Proton R . Suleiman

yy to NLO in ChPT J. L. Goity

607

xo -+

61 1

The Dependence of the “Experimental” Pion Nucleon Sigma Term on Higher Partial Waves J . Stahov

615

First Beam-Target Double-Polarization Measurements using Polarized HD at LEGS A . Lehmann et al.

619

SESSION ON LATTICE QCD AND HEAVY QUARKS Lattice Calculation of Baryon Masses Using the Clover Fermion Action D. G. Richards, M. Gockeler, P. E. L. Rakow, R. Horsley, C. M. Maynard, D. Pleiter and G. Schierholz Nucleon Magnetic Moments, Their Quark Mass Dependence and Lattice QCD Extrapolations

627

631

T. R. Hemmert and W. Weise Heavy Quark Spectrum from Anisotropic Lattices X . Liao and T. Manke The Doubly Heavy Baryons in the Nonperturbative QCD Approach I. M. Narodetskii and M. A . Trusov

635

639

xxi

Excited Baryons and Chiral Symmetry Breaking of QCD F. X. Lee

643

List of Participants

651

Author Index

669


Plenary Session Presentations


SUCCESSES AND OPEN ISSUES IN BARYON PHYSICS A. W. THOMAS Special Research Centre for the Subatomic Structure of Matter and Department of Physics and Mathematical Physics Uniuersity of Adelaide, Adelaide S A 5005, Australia E-mail: [email protected] We review some of the highlights from recent work concerning the structure of baryons. We concentrate especially on those developments where the interaction with lattice QCD has led to new insights.

1

Introduction

The study of baryon structure, both in vacuum and in a nuclear medium, is currently at a very exciting stage of development. New experimental capabilities at laboratories such as JLab, are extending our knowledge of nucleon form factors, free and bound (as well as transition form factors), into new kinematic domains and with unprecedented precision. We are beginning to see the development of phenomenologically meaningful, covariant models which can be extended to incorporate chiral symmetry. With the development of improved actions, faster computers and better implimentations of chiral symmetry, lattice QCD is beginning to deliver on its promise of new insights into baryon structure. Indeed, in combination with carefully controlled chiral extrapolation, one can expect to calculate properties of the low mass baryons quite accurately within a few years. One can also hope to address some key physics issues in baryon spectroscopy. The issue of possible changes of hadron properties in-medium has generated enormous theoretical and experimental interest. We briefly outline the role of changes of nucleon internal structure within relativistic mean field theory and report on what has the potential to be a very important development in this field, namely the recent determination of GEIGMfor a proton bound in 4He. In the context of understanding nuclear structure in terms of QCD, it is the first firm evidence for a change in the structure of a bound nucleon. After describing recent advances in linking lattice QCD to covariant models of hadron structure, we summarise the crucial issue of chiral extrapolation. The recent progress in this area underpins the prospect of calculating accurate hadron properties, at the physical quark mass, in just a few years. We close the discussion with an overview of the recent progress in hadron spectroscopy. Then we turn to the issue of changes in baryon properties in-medium.

3

4

2

Baryon Structure and Lattice QCD

The non-trivial nature of the QCD vacuum is illustrated by the fact that it For a purely gluonic version contains both quark and gluon condensates is of order -0.5 (GeV/fm)3. This of QCD the vacuum energy density, c,, is an order of magnitude larger than phenomenological estimates such as B in the MIT bag model. Clearly, either the popular idea of the perturbative vaciiiim being fully restored inside a hadron is incorrect or the situation is rather more complicated than commonly assumed. Although covariant models of baryon structure are very much in their infancy, substantial progress has been made in understanding the striicture of the low-lying pseudoscalar and vector mesons within a phenomenological implementation of the Dyson-Schwinger equations '. In addition, there have been some promising developments in the baryon sector based on the Faddeev equations '. Until now the phenomenological input has been chosen to reproduce some limited set of experimental data and then applied to other problems. However, the sophistication of modern lattice gauge theory is such that one can now begin t o check key parts of these covariant calculations against lattice simulations. The natural starting point for comparisons between covariant calculations and lattice simulations are the quark and gluon propagators. For example, there have been some preliminary studies of the quark propagator in Landau gauge. For Euclidean p 2 one can write the quark propagator as Z ( p 2 ) / ( i y , p , + M ( p 2 ) ) . The lattice simulations, so far been carried out with relatively large The current quark masses, show a clear enhancement in the infrared enhancement in the infrared region, leading t o a quark effective mass of order 300 MeV in the chiral limit, is clearly consistent with the general idea of the constituent quark model. This result not only provides a firm theoretical foundation for the concept within QCD, but it also indicates where the concept breaks down. It is clear that in processes involving significant momentum transfer it will be necessary t o go beyond the simple idea of a fixed mass and, indeed, a recent study of the nucleon electromagnetic form factors by Oettel and Alkofer finds considerable sensitivity t o the momentum dependence of the quark mass function '.

'.

516.

2.1

The role of Chiral Symmetry

A central problem in performing calculations a t realistic quark masses is the approximate chiral symmetry of QCD. Goldstone's theorem tells us that chiral symmetry is dynamically broken and that the non-perturbative vacuum is

5

'.

highly non-trivial, with massless Goldstone bosons in the limit m 4 0 For finite quark mass these bosons are the three charge states of the pion with a mass m: cx m . From the point of view of lattice simulations with dynamical quarks (i.e. unquenched) the main difficulty is that the time taken goes as m-3, or worse '. The state-of-the-art for hadron masyes is above 40 MeV. Thus, an increase of computing power t o several hundred tera-flops is needed if one is t o make a direct calculation of realistic hadron properties. A major step forward in last few years has been the realization that that, in terms of tinderstanding baryon strilcture, the lattice data obtained so far represents a wealth of information. Just as the study of QCD as a function of N , has taught 11sa great deal, so the behaviour as a function of f i can give u s great insight into hadronic physics and guide our model building. We begin by summarising the conclusions which emerge from the work of the past three years. 0

0

For quark masses r?~ > 60 MeV or so ( m , greater than 400-500 MeV) hadron properties are smooth, slowly varying functions of something like a constituent quark mass, M M o cm (with c 1). Indeed, M N

-

3 M , Atp+,

-

-

+

N

2 M and magnetic moments behave like l/M.

As m decreases below 60 MeV or so, chiral symmetry leads t o rapid, non-analytic variation, with: b~%fN fi3I2, dpH m y 6 < r2 >chN In m and moments of non-singlet parton distributions m: In m,.

-

-

Chiral quark models, like the cloudy bag model (CBM) ', provide a natural explanation of this transition. The scale is set by the inverse size of the pion source - the inverse of the bag radius in the CBM. When the pion Compton wavelength is smaller than the size of the composite source chiral loops are strongly suppressed. On the other hand, as soon as the pion Compton wavelength is larger than t h e source one begins t o see rapid, non-analytic chiral corrections. The nett result of this discovery is that one has control over the chiral extrapolation of hadron properties provided one can get data a t pion masses of order 200-300 MeV. This seems feasible with the next generation of supercomputers, which should be available within 2-3 years and which will have speeds in excess of 10 tera-flops l o .

6

2.2

Chiral Loops and Non-Analytacity

A s a consequence of spontaneous chiral symmetry breaking there must be contributions t o hadron properties from Goldstone boson loops. These loops have the unique property that they give rise to terms in the functional dependence of most hadronic properties on quark mass, which are not analytic l l . As a simple example, consider the nucleon mass. The most important chiral corrections to M N come from the processes LV + N . i r -+ ,V (u”) and N + An + N ( U N A ) . Independent of the form chosen for the ultraviolet cut-off, one finds that ~ T N Nis a non-analytic function of the quark mass. The non-analytic pi of U N N is independent of the form factor and = - 3 g ~ / ( 3 2 n f ~ ) m ~m3/2. This has a branch point, as a gives ~TNN(LNA) function of m, starting at m = 0. Such terms can only arise from Goldstone boson loops. I t is natural to ask how significant this non-analytic behaviour = -5.6m:, and a t is in practice. If the pion mass is given in GeV, the physical pion mass it is just -17 MeV. However, a t only three times the physical pion mass it is -460MeV - half t h e mass of the nucleon. If one’s aim is t o extract physical nucleon properties from lattice QCD calculations this is extremely important. A s we explained earlier, to connect t o the physical 500MeV t o m, = 140MeV. Clearly world one must extrapolate from m, one must have control of the chiral behaviour. The traditional approach is t o make a fit which naively respects the presence of a LNA term:

-

-

MN

=a

+ am3 + ym,, 3

(1)

with a ,,B and y fitted to the data. While this gives a very good fit t o the data, the chiral coefficient y is only -0.761, compared with the model independent value, -5.60, required by chiral required by chiral symmetry ’. If one insists that y be consistent with QCD, one cannot fit the d a t a with Eq.(l). An alternative suggested recently by Leinweber et QZ. ’, which also involves just three parameters, is t o evaluate U N N and U N A with the same ultra-violet form factor, with mass parameter A, and to fit M N as

MN = a+,Bm~ +UNN(~,,A)+~NA(~,,A), (2) by adjusting a,,B and A. Using a sharp cut-off (u(k) = O(A - k)) these authors were able t o obtain analytic expressions for U N N and U N A which reveal the correct LNA behaviour - and next-to-leading (NLNA) in the An case, ugiNA N m: In mrr. These expressions also reveal a branch point a t m, = M A - M N , which is important if one is extrapolating from large values of m, t o the physical value. This approach does indeed produce an excellent fit t o the lattice data, while preserving the exact LNA and NLNA behaviour of QCD.

The analysis of the lattice data for MN, incorporating the correct nonanalytic behaviour, also yields important new information concerning the sigma commutator of the nucleon, which is a direct measure of chiral SU(2) symmetry breaking in QCD. The widely accepted experimental value is 45 ± 8MeV 12. Using the Feynman-Hellmann theorem one can write &N as mdM^/dm = m^dMnf/dm^, at the physical pion mass. If one has a fit to MAT as a function of m* which is consistent with chiral symmetry, one can use this expression to evaluate a

v

0.8

t

I

Figure 3. Comparison between the ratio of polarised electron quasi-elastic scattering cross sections on 4He and on the free proton 4 8 . The measured ratio is proportional to the ratio of the proton electric to magnetic form factors of a proton hound in 4 H e to the ratio for a free proton - if the other nuclear effects are correctly handled. The data favour earlier calculations within QMC which include a change in the hound nucleon form factors.

3

Nuclear Systems

The traditional view of nuclei is as a system of unperturbable (point-like) protons and neutrons. In a mean-field treatment they move in a self-consistent binding potential. Within quantum hadrodynamics (QHD) the Lorentz character of the mean-field is taken seriously, with a strong scalar attraction of order 300-400 MeV at nuclear matter density ( P O ) and an almost equally strong vector repulsion 35. On the other hand, if one starts with the aim of understanding nuclear structure in terms of QCD it is fundamental that the protons and neutrons are far from elementary. Indeed, they are quite large composite systems of quarks and gluons. Furthermore, the typical mean scalar field noted earlier is exactly the same size as the energy required to excite a nucleon (300MeV to the A or 500 MeV to the R(1440)). Far from being a surprise that nucleon structure might play a role in nuclear structure, it is difficult to see how it could fail to be significant! One of the central aims of modern nuclear physics must be to investigate this role both theoretically and experimentally. The quest for changes in the structure of hadrons in medium began in the ~ O ’ S ,with considerable attention to the problem being generated by the idea of Brown-Rho scaling 36. At about the same time, Guichon constructed a simple generalization of QHD, in which the point-like nucleon was replaced

13

by an MIT bag and the i~ and w mesons coupled to the confined quarks 37. A self-consistent solution of this problem within mean-field approximation led to a natural saturation mechanism. Rather than the (7 - ‘%1 coupling being a constant it becomes a monotonically decreasing function of the applied scalar field, g,(a). Indeed, because of the low mass of the confined quarks this mechanism is far more effective than the decrease of $ N $ N in QHD, and the mean scalar field a t po is only 50% or so of that in QHD. This model, which is generally known as QMC (the quark-meson coilpling model), has been extensively developed by Guichon , Saito, Tsushima, Exchange contributions Blunden, Miller, Jennings and many others have been considered 42 and eventually one must go to a more sophisticated theoretical treatment than simple mean field theory. Nevertheless, the model gives interesting guidance on the modification of hadron masses 43 and reaction cross sections 44 inside nuclear matter. For instance, it provides an interesting alternative to the naive explanation of J / Q suppression in relativistic heavy ion collisions in terms of a quark-gluon plasma 4 5 . From the point of view of nuclear structure the most interesting development is the application to finite nuclei 38. This leads to a deep conceptual change in our understanding. What occupies the shell model orbits are not nucleons but nucleon-like quasi-particles. These will have different masses, magnetic moments, charge radii and so on from those of free nucleons. From this point of view is less remarkable that bound nucleons shoiild have different properties from free nucleons than that such changes have proven so difficult t o establish. This is why the nuclear EMC effect which is still only partially understood, is so important. In terms of a fundamental theory of nuclear structure there can be few more important challenges than estabIishing the change in the properties of a bound nucleon. In this respect, a recent experimental result from Mainz is potentially extremely important 48. This group measured G E / G Mfor a proton bound in 4He, using the (Z,e’p3 reaction. The change in the ratio of these form factors for the bound nucleon had been studied in detail within QMC and, as shown in Fig. 3, the experimental results support such a modification. Clearly the statistical significance of the effect is not yet great. On the other hand, preliminary indications from JLab are that a similar modification is needed for Q2 u p t o 2.5 GeV2 5 1 . Furthermore, careful theoretical study of the effects of distortion, spin-orbit forces and meson exchange suggests that this particular ratio is extremely insensitive t o such corrections. This measurement is crucial in that it is really the first clear indication of a change in the structure of a bound nucleon. 38,39140,41.

47146,

49350

14

4

Concliision

This is indeed an exciting period in the development of baryon physics. We have seen that developments in lattice QCD, especially more powerfill computers and improved chiral extrapolations, should finally allow the computation of accurate baryon properties within full QCD, at the physical quark masses, within the next five years. Studies of baryon spectroscopy on the lattice will complement important new experimental studies and improved quark models. We have seen that from the point of view of QCD, it is vital to understand the changes in baryon properties that occur as a function of density as well as temperature. I n this sense finite nuclei provide a criicial testing ground for ideas that will eventually be applied at much more extreme conditions. We briefly reviewed a n experiment that gives a tant(a1izing hint of such a change and look forward to further tests of these ideas in t h e next few years.

Acknowledgements This work was supported by the Australian Research Coiincil and the University of Adelaide.

References 1. A. W. Thomas and W . Weise, “The Structure of the Nucleon,” 289 pages.

Hardcover ISBN 3-527-40297-7 Wiley- VCH, Berlin 2001. 2. V. A . Novikov et al., Nucl. Phys. B 191, 301 (1981). 3. P. C. Tandy, Prog. Part. Nucl. Phys. 36, 97 (1996) [nucl-th/9605029]. 4. M . Oettel and R. Alkofer, arXiv:hepph/0204178. 5 . S. Aoki et al. [JLQCD Collaboration], Phys. Rev. Lett. 82 (1999) 4392. 6. J. Skulleriid, D. B. Leinweber and A . G. Williams, heplat/0102013. 7. D. B. Leinweber et al., Phys. Rev. D 61, 074502 (2000). 8. T. Lippert et al., Niicl. Phys. Proc. Suppl. 83 (2000) 182. 9. S. Theberge et al., Phys. Rev. D 22, 2838 (1980) [Erratum-ibid. D 23, 2106 (1980)l; A. W . Thomas, Adv. Nucl. Phys. 13, 1 (1984). 10. Lattice Hadron Physics Collaboration proposal, J.W. Negele and N. Isgur, ftp://www-ctp.mit.edu/pub/negele/LatProp/. 11. S. Weinberg, Physica (Amsterdam) 96 A , 327 (1979); J . Gasser and H. Leutwyler, Ann. Phys. 158, 142 (1984). 12. J. Gasser, H. Leutwyler and M . E. Sainio, Phys. Lett. B 253, 252 (1991). 13. S. V. Wright et a/., Nucl. Phys. A 680, 137 (2000). 14. E. J. Hackett-Jones et al., Phys. Lett. B 4 9 4 , 8 9 (2000) [heplat/0008018].

15

19. 16. 17. 18. 19. 20. 21. 22. 23.

G. V. Dunne et al., Phys. Lett. B531,77 (2002) [hepth/0110199]. D. B. Leinweber et al., Phys. Rev. D 60,034014 (1999). E. J. Hackett-Jones et al., Phys. Lett. B 489,143 (2000). D. B. Leinweber and A . W. Thomas, Phys. Rev. D 62,074905 (2000). K. S. Kumar and P. A. Souder, Prog. Part. Nucl. Phys. 45,S333 (2000). M . Gockeler et al., Nucl. Phys. Proc. Suppl. 53,81 (1997). D. Dolgov et al., Nucl. Phys. Proc. Suppl. 94,303 (2001). A . W. Thomas et al., Phys. Rev. Lett. 85,2892 (2000). D. Arndt and M . J. Savage, nucl-th/0105045; J. Chen and X. Ji, hepph/0105197. 24. W. Detmold et al., Phys. Rev. Lett. 87,172001 (2001). 25. P. A . Guichon, Phys. Lett. B 163,221 (1985). 26. J. Speth et al., Nucl. Phys. A 680,328 (2000). 27. E. A. Veit et al., Phys. Rev. D 31,1033 (1985). 28. N. Kaiser et al., Nucl. Phys. A 594,325 (1995); E. Oset et al., arXiv:nucl-th/0109006. 29. D. B. Leinweber, Phys. Rev. D 51,6383 (1995) [nucl-th/9406001]. 30. F. X. Lee and D. B. Leinweber, Nucl. Phys. Proc. Suppl. 73,258 (1999). 31. S. Sasaki, T . Blum and S. Ohta, heplat/0102010. 32. M. Gockeler et al. [QCDSF Collaboration], heplat/0106022. 33. W. Melnitchouk et al., arXiv:heplat/0202022. 34. R. D. Young et al., arXiv:heplat/0ll1041. 35. R. J. Furnstahl and B. D. Serot, Comm. Nucl. Part. Phys. 2, A23 (2000). 36. G. E. Brown and M. Rho, Phys. Rev. Lett. 66,2720 (1991). 37. P. A. Guichon, Phys. Lett. B 200,235 (1988). 38. P. A . Guichon et al., Nucl. Phys. A 601,349 (1996) [nucl-th/9509034]. 39. K. Saito et al., Phys. Rev. C 55,2637 (1997) [nucl-th/9612001]. 40. P. G. Blunden and G. A. Miller, Phys. Rev. C 54,359 (1996). 41. X. Jin and B. K. Jennings, Phys. Rev. C 54,1427 (1996). 42. G. Krein et al., Nucl. Phys. A 650,313 (1999). 43. K . Tsushima et al., Phys. Lett. B 443,26 (1998). 44. K. Tsushima et al., J. Phys. G G27,349 (2001). 45. A. Sibirtsev et al., Phys. Lett. B 484,23 (2000). 46. D. F. Geesaman et al., Ann. Rev. Nucl. Part. Sci. 45,337 (1995). 47. J . J. Aubert et al., Phys. Lett. B 123,275 (1983). 48. S. Dieterich et al., Phys. Lett. B 500,47 (2001) [nucl-ex/0011008]. 49. D. H. Lu et al., Phys. Rev. C 60,068201 (1999). 50. A. W. Thomas et al., nucl-th/9807027. 51. S. Strauch, contribution to this conference.

16

Danielle Morel and Simon Capstick

Gerrit Schierholz and Christine Davies

BARYON SPECTROSCOPY IN THE QUARK MODEL S. CAPSTICK Department of Physics Florida State University Tallahassee, Florida 32306-4350 E-mail: capstickQcsit.fsu.edu The basis of constituent quark models of the baryon spectrum is reviewed, with a description of the effective degrees of freedom, their confinement, and various models of their short-distance interactions. It is argued that such models should not be compared with the results of analyses of hadron scattering data without considering the effects of quark-antiquark pairs on the spectrum, and a model of such effects is described.

1

Constituent Quark Models of the Baryon Spectrum

1.1 Eflective Degrees of Freedom

In the constituent quark model, baryons are made up of three quasi-particles, with effective masses significantly larger (200-300 MeV) than the currentquark masses in the QCD Lagrangian. They are also not point-like particles, having both electromagnetic1 and strong2 form factors. Although this is a popular approach, and is taken here, other approaches exist and are briefly considered below. Baryons can be described in the soft (low-Q2) regime as being made up of a diquark cluster plus a quark3, with fewer degrees of freedom at low energy and so fewer excited states. Although this can explain the small number of positive-parity excited light-quark ( N and A) baryons seen in analyses of hadron scattering data, it is more likely that such states have weak couplings to the predominant N n formation channel. Additional states, if they exist, will almost certainly be discovered in photo- and electro-production experiments with final states other than N n . A mechanism for strong diquark clustering in baryons is lacking. Algebra-based models4 of the spectrum describe baryons as collective excitations of string-like objects. Such models incorporate radial excitations from rotations and vibrations of these strings, and so have more excited states than models with constituent quarks moving in a potential. The predictions of such models for this richer spectrum are testable in experiments designed to find new baryon states. Baryons can also be described as current quarks moving in a confining bag, with pions coupled to the surface in the cloudy

17

18

bag model5. Although this description has several advantages, it is difficult to describe non-spherical excited states in this framework, and so its application has largely been limited to ground states. 1.2 Constituent Quarks

Constituent quarks have dynamically generated masses, which run with Q’. There is evidence from lattice simulations that at low Q2 this mass is of the order of A,,,, and similar results are found in covariant studies of hadron properties based on the Schwinger-Dyson Bethe-Salpeter field theoretic approach6. In principle, spectral models which use the relativistic kinetic energy operator Ki = (p; m;) could use light-quark masses anywhere from 0 to 250 MeV. However, a study of isospin-symmetry violating mass splittings in mesons7 shows that Kd - K , N 5-10 MeV, comparable to the current-quark mass difference Am = md - mu ‘v 5-10 MeV. However, if Am is much smaller than the quark kinetic energy K , we can expand

+

+

Kd - K , = (p2 [mu

+ Am]’)

+ me) ~li (?)Am,

- (p2

(1)

which together with the above observation that Kd - K , ‘v Am implies that mu ‘v Ku N A Q ~ D‘v 200 MeV. The strange quark is given a mass between 150 and 200 MeV heavier than the light quarks. As effective degrees of freedom, the constituent quarks also should have strong form factors. Such form factors are required to render finite short distance interactions between the quarks. It has also been shown’ that the constituent quarks must be given electromagnetic (EM) form factors in order to fit the nucleon (EM) form factors at moderate Q2 values, in relativistic calculations based on light-cone dynamics. It seems sensible that the strong and EM sizes of quarks should be comparable. Interestingly, the anomalous moments of the quarks are shown in a lattice simulation* to depend on the baryon in which they lie.

1.3 A Model of Confinement In a quenched lattice calculation of the potential between three static (heavy) quarksg, it is found that a good fit to the observed potential energy can be made with the form

19

where Lmin is the length of the minimum-length Y-shaped string connecting the quarks to a junction, and A, u and C are fitted constants. A parallel calculation of the potential between a static quark and antiquark was performed to compare the string tension and Coulomb strength in mesons and baryons. It is shown that U ~ Qand U ~ are Q similar, and that the Coulomb strengths are in the ratio A ~ Q : A,Q = 1 : 2 given by one-gluon exchange. A fit with the part of the potential proportional to u replaced by U A Ci,. Iri - rjl was significantly poorer. This establishes that a confining potentid given by the minimum length of a Y-shaped string between the quarks and a junction is relevant for QQQ baryons. A reasonable starting point is to assume that it is also good for light-quark baryons. Such a potential arises in the flux-tube model", based on strong-coupling lattice QCD. In the strong coupling limit the color fields are confined to narrow tubes with an energy proportional to their length. In baryons a junction is required to maintain global color gauge invariance. When the flux-tube model is combined with the adiabatic approximation, the result is a confining interaction given by V B ( r l , r 2 , r 3 ) = u ( l l + 12 Z3) = aL,i,, where the li are the lengths of the individual strings connecting the quarks to the junction, and u is the meson string tension. Note this confining potential is linear at large quark-junction separations. There is no reason why the string should not be considered dynamical. In the flux-tube model the zero-point energy of this motion should correct the static potential VB, and excited states of the string motion should define new potentials in which the quarks in hybrid baryons movell.

+

1.4

One-Gluon Exchange

The spectrum of ground-state baryons suggests flavor-dependent short-range (contact) interactions between the quarks. One simple assumption is that at short distance, or high Q2,the exchange of a single gluon dominates the interactions between the quarks. This leads to a mass formula for the ground state baryons

where (S3(r12))is a spatial expectation value of a delta function of the separation of a pair of quarks in the (symmetric) ground-state spatial wave function, and S , is the spin of quark i. This gives, for example,

ME-MA 2 = - (1 MA-MN 3

--&) mud

N

2 3(0.4) = 0.27,

(4)

20

which compares favorably with the experimental ratio (1193-1116)/(1232939)=0.26. This model of the short-distance interactions has the advantage that it also explains certain regularities in the meson spectrum, such as the evolution of the vector-pseudoscalar splitting with quark mass. It is unclear why Eq. (3), based on a non-relativistic expansion and the assumption of weak binding, should work for light-quark baryons. This model also includes a tensor interaction with a strength fixed by that of the contact interaction. The best evidence for tensor interactions is the mixings they cause between states with similar spatial wave functions but different total quark spin, which have important consequences for strong and electromagnetic decays of these states.

170 I

unperturbed level

-

160

-: -75 MeV N

150 -

(N*f-)l N*f-

A* f-

Figure 1. Isgur-Karl model predictions for the mass splittings of the negative-parity excited non-strange baryons (lines), shown with the range of central values for the masses from analyses quoted by the Particle Data Group.

The predictions12 of the model of Isgur and Karl for the splittings of the negative-parity excited non-strange baryons (the center-of-mass of the band was fit) are compared with the quoted range of central mass values from the Particle Data Group in Figure 1. The contact interaction splits the states

21

by 612 21 150 MeV, where 6 = M A - M N . The addition of a consistent tensor interaction introduces further splittings, but also causes the mixing which allows the lightest N ’ t - state, associated with the Sll(1535) in N T scattering, to have a substantial decay width to N v . This large decay width is at first surprising, given the small available phase space available, but can be explained by the constructive interference caused by the tensor mixingI2. Associated with these “hyperfine” interactions are spin-orbit interactions, which although they can be arranged to partially cancel with those arising from Thomas precession of the quark spins in the confining potential, are at a level not present in the spectrum found from analyses of data. This is best seen by examining the negative-parity excited strange baryons, where the model without spin-orbit interactions predicts a degenerate lightest A; - and AZ-, in contrast with the splitting of the states A;-(1405) and A$-(1520) seen in analyses. Models based on one-gluon exchange have been applied consistently to all mesons and baryond3 in variational calculations which use large harmonic oscillator bases. The Hamiltonians use the relativistic kinetic energy operator and have relativistic corrections in the potentials. As an example, the contact part of the hyperfine interaction takes the form

+

1

where E, = (p: m:)Z is the kinetic energy of the i-th quark, the strong coupling asis smeared by running with Q2,and ccont is a relativistic parameter fit to the spectrum. The usual delta function is smeared out by the form factors of the interacting constituent quarks. Spin-orbit interactions from both one-gluon exchange and Thomas precession in the confining potential are included with the Coulomb, contact and tensor interactions arising from one-gluon exchange, and spin-orbit interactions in baryons can be arranged to be small. This is due to the use of a smaller value of as(0),partial cancellation of the spin-orbit interactions from the two sources, and the choice of the relativistic parameters. Although reasonable agreement with the spectrum of states from analyses is seen, the problem of the mass of the A;-(1405) is not solved. In addition, the first band of negative-parity excited states is too light by about 50 MeV, and the first positive-parity band too heavy13 by 50 MeV.

22

1.5 One-Boson Exchange Another possibility for the short-distance interactions between quarks in baryons (this model cannot be applied to mesons) is that bosonic hadrons are exchanged between the quarks, and gluons are not. Originally formulated in terms of pion exchangell, this idea was extended to the exchange of an octet of pseudoscalar bosons15, and later scalar and vector bosons16. The flavor dependence of the short-distance interactions is explicit, e.g. in the model of Glozman and Riska15 the contact interaction takes the form

where the A: are flavor SU(3) Gell-Mann matrices. Glozman and Riska fit the radial matrix elements of the pion, kaon and eta-exchange potentials V ( T Q ) to the spectrum, which allows the order of the lightest negative and positiveparity states to be inverted, as illustrated in Figure 2. It is important to

-

-N(1535)-N(1520)

+ -N(1440)

+ N

N

A

A

Figure 2. Masses of low-lying positive and negative-parity excited states of N , A and A baryons in the pseudoscalar exchange model of Glozman and Riska.

note that the masses of the positive-parity excited states of the A and A extracted from analyses are quite uncertain, 155Ck1700 MeV and 1560-1700 MeV, respectively. These exchange potential matrix elements are calculated in a more constrained model using a variational harmonic-oscillator basis, a relativistic kinetic energy operator, and string confinement16. Without the freedom to fit the matrix elements, it is necessary to include the exchange of nonets of vector mesons, and scalars. The spectrum shown in Figure 3 shows that although the Roper resonance is lighter than the lightest non-strange negative

23

parity states, the first excited A:' and A$+ states are now above the lightest negative-parity states of the same flavor. Spin-orbit interactions from Thomas precession in the confining potential are not included, and the problem of the A$-(1405)-A(1520);- splitting is not solved. Y [MeV] 1800 1700 -

Ell- U 7

1600 1500 -

-

1400 -

1300 1200 1100 -

1000 900

N

I

I

1+ 12

2

I

a+ 2

A 1

I

I

I

A

l

l

I

I

I

I

3-

a+

3-

1-

a+

2-

1+ 1- p+ 3-

2

2

2

2

2

2

2

2

2

2

I

s+ 2

I

52

Figure 3. Masses of low-lying positive and negative-parity excited states of N , A and A baryons in the one-boson exchange model of Glozman et aLI6

I . 6 Instanton-Induced Interactions Another explicitly flavor-dependent interaction which has been adopted to explain the spectrum of light baryons is that of instanton-induced interactions. These interactions have the form (q2;S,L,TIWIq2;s , L , T ) = -4gbS,06L,06T,Ow,

(7)

and so act only between two quarks which are in a relative S-wave, and in an isoscalar state with total quark spin zero. The interaction W is a contact interaction. A model based on this interaction has been applied to excited baryon states by Blask, Bohn, Huber, Metsch and Petry17. The model has very few parameters, and shows reasonable agreement with the spectrum of ground states, and P-wave N and A states, although the contact splittings are too small in the P-wave C states, and positive-parity excited states are generally too heavy by about 250 MeV. There are no contact splittings between A states, where all quark pairs have T = 1. A more sophisticated version of this model is described in these proceedings18.

24

1.7 Necessity of a Decay Model It is sometimes overlooked that a model of the spectrum cannot be compared with the results of analyses of scattering data without a calculation of the strong decays of the model states. This is because analyses af hadron scattering data generally find fewer states than are present in models. An obvious explanation, which has been explicitly seen in model calc~lations'~, is that such states do not couple strongly to the T N and K N formation channels comprising most of the data. It is therefore crucial that predictions are made for which of the model states are likely to have been seen in the analyses. A popular phenomenological model of such decays is the 3Po model, which has the advantage that the emitted mesons have structure, and allows correlation of many decays with few parameters. 2

Unquenching the Constituent Quark Model

In QCD, qqq(qq) configurations are possible in baryons, and it may be that many of the outstanding difficulties encountered in model descriptions of the baryon spectrum arise from their neglect. Because of the lack of a unique color configuration, and fall-apart decays into colorless hadrons, it is not possible to solve directly for the masses and properties of baryons in the presence of such states with the usual confining and short-range interactions between the quarks (and antiquarks). Instead, it is natural and consistent with confinement to expand such configurations in a basis of baryon-meson intermediate states. Masses of baryons will be shifted by their couplings to open (and sub-threshold) channels by self energies arising from loops containing baryonmeson intermediate states. Note that calculation of these mass shifts requires a model of baryon-baryon-meson ( B B ' M ) strong vertices and their momentum dependence, and that the high-momentum (short-range) part of the loops contains one-boson exchange between the quarks. Calculation of the vertices, and of mass shifts from intermediate baryons missing from analyses, requires a model of the baryon spectrum and wave functions. The mass shifts are found by solving

self consistently to find the bare mass E at which the sum of the bare mass and self energy is the physical mass M B . Note that the self energy is a sum of self energies arising from all possible baryon-meson intermediate states, including states for which the external baryon mass is below threshold, and those containing excited mesons and baryons. The effect on the spectrum is

25

M _-.-

Figure 4. Contribution to the self energy of a baryon B from a loop containing a baryon B' and a meson M.

examined by evaluating the splittings of the bare masses required to fit the physical masses, and comparing these to model mass splittings.

2.1

Convergence

The self energies of baryons due to individual B ' M loops can be expected to be comparable to their partial widths to these channels, i.e. of the order of tens to hundreds of MeV. Because many such channels are open, due to the density of the spectrum of excited baryon intermediate states, it it not trivial that the sum over intermediate states required to form C s ( E ) converges. The best calculations of this kind20*21have been applied to N , A, A and C ground and light negative parity excited external ( B )states. The intermediate states B'M contain ground state mesons M E {a,K , q , q', p, w , K * } and baryons B' E { N , A, A, C, C*}. Zenczykowski21has shown that without the inclusion of complete sets of intermediate states related by SU(6) flavor-spin symmetry, the self energies of the ground state N and A will not be equal in the SU(6) symmetry limit. This means that any calculation which does not include all of the octet and decuplet ground-state baryons and pseudoscalar and vector ground-state mesons is necessarily incomplete. However, it not enough to include intermediate states made up only of ground state baryons. A calculation22 restricted to B'a intermediate states, but with B' taken from all N and A excited states in the N = 0 , 1 , 2 and 3 oscillator bands, shows that the A - N splitting converges once the N = 3 band states are included, but the splittings between negative-parity states have not. Clearly, the restriction to ground state intermediate baryons is a poor approximation.

26

2.2 Soft vertices In time-ordered perturbation theory, self energies from B'M intermediate states can be found by performing the loop integral

As this samples all momenta, its size depends critically on the poorly constrained size of the strong decay matrix element MB+BtM(k) at large (far off-shell) values of the loop momentum k. The usual 3 P , model gives vertices which are too hard, and the loops get large contributions from high momenta. In a calculation of such effects in mesons, Geiger and I s g ~ give r ~ ~their pair creation operator a (Gaussian) form factor proportional to exp(- fZbq -pq]'), with f = 3.0 GeVW2,which gives the pair-creation vertex a reasonable spatial size of about 0.35 fm, considering that these are constituent quarks. This has the effect of softening the strong decay vertices and making possible the convergence of the sum over intermediate states. A similar form factor is used by Silvestre-Brac and GignouxZ0in their calculation of the splittings of negative-parity excited baryons arising from baryon-meson loop effects. The convergence of the sum over intermediate states in a calculation of meson mass splittings is shown to be more rapid in a covariant, field-theoretic based on the Schwinger-Dyson Bethe-Salpeter approach, partly because the calculated form factors are softer than those found in non-relativistic models. Clearly the off-shell behavior of the strong-decay vertices is of crucial importance to such calculations. 2.3 Non-Strange Baryon Self Energies From the above, it is clear that a calculation of ground state and negativeparity excited-state baryon self energies must include a complete set of SU(6)related intermediate states, and a large set of excited intermediate baryons. Such a calculation has been performed by Danielle Morel, and is reported on elsewhere in these proceedingsz5. The results exhibit convergence of the A - N splitting, with the result that the mass splitting of the physical A and nucleon is only partly due to interactions between the quarks in the bare qqq states, with a significant contribution from these self energies. Convergence of the self energies of the negative-parity excited states in slower, but significant splittings also arise due to the differences in the self energies of these states.

27

3

Conclusions

Given the obvious importance of the effects of qqq(qq) configurations to the mass spectrum of baryons, it may be premature t o draw conclusions about the successes of various approaches to the short-distance interactions between the quarks. It seems likely that such effects may be responsible for the universal lack of agreement between a spectrum calculated with only qqq configurations and certain aspects of the spectrum of states extracted from analyses. With considerable theoretical effort, using a variety of different approaches, it may be possible to resolve these problems and come to a better understanding of the underlying degrees of freedom and their interactions in baryons.

Acknowledgments The work summarized here would not have been possible without my collaborators Nathan Isgur, Danielle Morel, Philip Page, Michael Pichowsky, Winston Roberts, and Sameer Walawalkar. This work is supported by the U.S. Department of Energy under Contract DEFG02-86ER40273.

References 1. P. L. Chung and F. Coester, Phys. Rev. D 44,229 (1991); F. Schlumpf, J. Phys. G 20, 237 (1994); F. Cardarelli, E. Pace, G. Salme and S. Simula, Phys. Lett. B 357, 267 (1995). 2. D. P. Stanley and D. Robson Phys. Rev. D 21, 3180 (1980); J. Carlson, J. B. Kogut and V. R. Pandharipande, Phys. Rev. D 28, 2807 (1983). 3. G. R. Goldstein, TUFTS-TH-G88-5, presented at Workshop on Diquarks, Turin, Italy, Oct 24-26, 1988. 4. R. Bijker, F. Iachello and A. Leviatan, Annals Phys. 236, 69 (1994). 5. S. Theberge, A. W. Thomas and G. A. Miller, Phys. Rev. D 22, 2838 (1980). 6. See, for example, C. D. Roberts and S. M. Schmidt, Prog. Part. Nucl. Phys. 45, S1 (2000). 7. S. Godfrey and N. Isgur, Phys. Rev. D 34, 899 (1986). 8. D. B. Leinweber, R. M. Woloshyn and T. Draper, Phys. Rev. D 43, 1659 (1991). 9. T. T. Takahashi, H. Matsufuru, Y. Nemoto and H. Suganuma, Phys. Rev. Lett. 86, 18 (2001). 10. N. Isgur and J. Paton, Phys. Rev. D 31, 2910 (1985).

28

11. Philip R. Page, these proceedings; see also S. Capstick and P. R. Page, Phys. Rev. D 60,111501 (1999). 12. N. Isgur and G. Karl, Phys. Rev. D 20,768 (1979). 13. S. Godfrey and N. Isgur, Phys. Rev. D 32,189 (1985); S. Capstick and N. Isgur, Phys. Rev. D 34,2809 (1986). 14. D. Robson, Proceedings of the Topical Conference on Nuclear Chromodynamics, Argonne National Laboratory (1988), Eds. J. Qiu and D. Sivers (World Scientific), pg. 174. 15. L. Y. Glozman and D. 0. Riska, Phys. Rept. 268,263 (1996). 16. R. F. Wagenbrunn, L. Y. Glozman, W. Plessas and K. Varga, Nucl. Phys. A 666,29 (2000). 17. W. H. Blask, U. Bohn, M. G. Huber, B. C. Metsch and H. R. Petry, Z. Phys. A 337,327 (1990). 18. Ulrich Loring, these proceedings. 19. R. Koniuk and N. Isgur, Phys. Rev. D 21,1868 (1980); S. Capstick and W. Roberts, Phys. Rev. D 47, 1994 (1993). 20. W. Blask, M. G. Huber and B. Metsch, Z. Phys. A 326 (1987) 413; B. Silvestre- Brac and C. Gignoux, Phys. Rev. D 43,3699 (1991); Y.Fujiwara, Prog. Theor. Phys. 90,105 (1993). 21. P. Zenczykowski, Annals Phys. 169,453 (1986). 22. M. Brack and R. K. Bhaduri, Phys. Rev. D 35,3451 (1987). 23. P. Geiger and N. Isgur, Phys. Rev. Lett. 67,1066 (1991). 24. M. A. Pichowsky, S. Walawalkar and S. Capstick, Phys. Rev. D 60, 054030 (1999). 25. Danielle Morel, Florida State University PhD thesis, and in these proceedings.

ELECTROEXCITATION OF NUCLEON RESONANCES VOLKER D. BURKERT Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA23606 Recent elcctroproductiori results in the domain of schaniiel nucleon rcsoriaricc excitation arc prcsentcd. and preliminary data in the search for missing states will be discussed. I also address a ncw avenue to pursue N * physics using exclusive decply virtual Compton scattering. recently measured for the first time at JLab and DESY.

1

Why N”s are important

Nucleon physics today is focussed on understanding the details of the nucleon spin and flavor structures at varying distances, and on the systematics of the baryon spectrum which reveals properties of the underlying symmetry structure. R.esonance electroproduction has rich applications in nucleon structure studies at intermediate and large distances. Resonances play an important role in understanding the spin structure of the nucleon 2,3. More than 80% of the helicity-dependent integrated total photoabsorption cross section difAt ference (GDH integral) is a result of the excitation of the A(1232) Q2= 1GeV2 about 40% of the first moment rf‘(Q2) =J : gl(s,Q2)dx for the proton is due to contributions of the resonance region at W < 2GeV 5 , 6 . Conclusions regarding the nucleon spin structure for Q2 < 2GeV2 must therefore be regarded with some scepticism if contributions of baryon resonances are not taken into account. The nucleon’s excitation spectrum has been explored mostly with pion beams. Many states, predicted in the standard quark model, have not been seen in these studies, possibly many of them decouple from the N K channel ’. Electromagnetic interaction and measurement of multi-pion final states, may then be the only way to study some of these states. While photoproduction is one way 8, electroproduction, though harder to measure, adds additional sensitivity due to the possibility of varying the photon virtuality. Electroexcitation in the past was not considered a tool of baryon spectroscopy. CLAS is the first full acceptance instrument with sufficient resolution to measure exclusive electroproduction of mesons with the goal of studying the excitation of nucleon resonances in detail. This feature is illustrated in Fig. 1, where the invariant mass W of the hadronic system is plotted versus the missing mass of the e p -+ e p X , where X represents the undetected 412.

29

30 1969-1981: 1995-2000:

I

mm-l

-2oL 0

"I

0.5

CEA 0 DESY 0 NINA 0 ELSA0 JLAB 0 LEGS A MAU

BONN 0

LO

I

I

EATES

1.5

'

2

"

2.5

3

'

3.6

0

1

1

b(GeV/d'

Figure 1. Left panel: Invariant mass M7*,versus missing mass M X for y ' p -+ p X , measured in CLAS. Right panel: REnr and Rskr before the year 2001.

system. The no, 71, and w bands are correlated with enhancements in the invariant mass, and indicate resonances coupling to pro prl, and possibly pw channels. Some of the lower mass states are already well known. However, their photocouplings and the Q2 evolution of the transition form factors may be quite uncertain, or completely unknown. 2

Quadrupole Deformations of the Nucleon and A

An interesting aspects of nucleon structure at low energies is a possible this quadrupole deformation of the nucleon. In the interpretation of ref. would be evident in non-zero values of the quadrupole transition amplitudes El+ and Sl+ from the nucleon to the A(1232). In models with SU(6) spherical symmetry, this transition is due t o a magnetic dipole MI+ mediated by a simple spin flip from the J = f nucleon ground state to the Delta with J = $. Non-zero values for El+ would indicate deformation. Dynamically such deformations may arise through interaction of the photon with the pion cloud or through the one-gluon exchange mechanism '. At asymptotic momentum transfer, a model-independent prediction of helicity conservation requires REhf = El+/M1+ + + l . An interpretation of REhf in terms of a quadrupole deformation can therefore only be valid at low momentum transfer. The data before 2001 ( Fig. 1) show large systematic discrepancies. Taken together no clear trend is visible. At the photon point recent data from MAMI

31 1.22 GeV

W= 1.20 GeV

5,

I

1.24 GeV

I

K O

Y

2 GeV. The recoiling baryonic system clearly shows the excitation of resonances, the A(1232), N*(1520), and N*(1680). While these are well known states that are also excited in the usual s-channel processes, the DVCS process has the advantage that it decouples the photon virtuality Q2 from the 4-momentum transfer to the baryon system. Q2 may be chosen sufficiently high such that the virtual photon couples to an elementary quark, while the momentum transfer to the nucleon system can be varied independently from small to large values. In this way, a theoretical framework employing perturbative methods can be used to probe the "soft" N N ' transition, allowing t o map out internal parton correlations for this transition. 6

Conclusions

Electroexcitation of nucleon resonances has evolved to an effective tool in studying nucleon structure in the regime of strong QCD and confinement. The new data from JLab in the A3/2+(1232) and N;,2- (1535) regions give a consistent picture of the Q2 evolution of the transition form factors. Large data sets in different channels including polarization observables will vastly improve the analysis of states such as the "Roper" Nil,+(1440), and many other higher mass states. A strong resonance signal near 1.72 GeV, seen

41

R

14+

JLubKLAS ep -> ey(X+ll) E = 4.3GeV W>2GeV Q2> I GeV2

I

1

12

1.4

16

18

2

22

I,

2.4

I

I

I

I I I

26

I ,

28

,I 3

M(x+n),GeV Figure 9. Inelastic deeply virtual Compton scattering measured in CLAS. The rccoiling (n~') system clearly shows the excitation of several resonances, the A(1232), N*(1520). and "(1680).

with CLAS in the p.lr+.lr- channel, exhibits hadronic properties which are incompatible with any of the known states in this mass region. While schannel resonance excitation will remain the backbone of the N * program for years to come, inelastic deeply virtual Compton scattering is a promising tool in resonance physics at the elementary parton level, which allows the study of parton-parton correlations within a well defined theoretical framework. The Southeastern Universities Research Association (SURA) operates the the Thomas Jefferson National Accelerator Facility for the United States Department of Energy under Contract No. DEAC05-84ER40150.

References

1. N. Isgur, in: Excited Nucleons and Hadron Structure, World Scientific, 2001, eds.: V. Burkert, L. Elouadrhiri, J. Kelly, R. Minehart. 2. V.D. Burkert, and Zh. Li, Phys.Rev.D47:46-50,1993 3. V.D. Burkert and B.L. Ioffe, Phys.Lett.B296:223-226,1992; J .Exp.T heor .Phys. 78:619-622,1994 4. J. Ahrens et al., Phys.Rev.Lett.87:022003,2001 5. R. De Vita, this conferences 6. V.D. Burkert, Nucl.Phys.A699:261-269,2002 7. R. Koniuk and N. Isgur, Phys.Rev.D21:1868,1980 8. A. d'Angelo, this conference

42

9. A. Buchmann and E. Henley, Phys.Rev.D65:073017,2002 10. T. Sat0 and T.S. Lee, T. Sato, this conferences 11. S.S. Kamalov and S.N. Yang, Phys.Rev.Lett.83:4494-4497,1999 12. R. Beck et al., Phys.Rev.C61:035204,2000 13. G. Blanpied et al., Phys.Rev.C64:025203,2001 14. V.V. Frnlov et al., Phys.Rev.Lett.82:45-48,1999 15. G. A. Warren, C.E. Carlson, Phys.Rev.D42:3020-3024,1990 16. A. Silva et al., Nucl.Phys.A675:637-657,2000 17. M. Warns, H. Schroder, W. Pfeil, H. Rollnik, Z.Phys.C45:627,1990 18. I.G. Aznaurian, Z.Phys.A346:297-305,1993 19. D. Leinweber, T. Draper, R.M. Woloshyn, Phys.Rev.D48:2230-2249,1993 20. K. .loo, et al, Phys. Rev. Lett. 88, 122001,2002; L.C. Smith, this conferences 21. Z.P. Li, V. Burkert, Zh. Li; Phys.Rev.D46, 70, 1992 22. F. Can0 and P. Gonzales, Phys.Lett.B431:270-276,1998 23. 0. Krehl, C. Hanhart, S. Krewald, J. Speth, Phys.Rev.C62:025207,2000 24. H. Egiyan, this conference 25. S. Sasaki, T. Blum, S. Ohta Phys.Rev.D65:074503 26. R. Thompson et al., Phys.Rev.Lett.86, 1702 (2001), H. Denizli, this conference 27. C.S. Armstrong et al., Phys.Rev.D60:052004,1999 28. M.Q. Tran et al., Phys.Lett.B445:20-26,1998 29. M.M. Giannini, E. Santopinto, A. Vassallo, Nucl.Phys.A699:308311,2002; E. Santopinto, this conference 30. N. Kaiser, P.B. Siegel, W. Weise, Phys.Lett.B362:23-28,1995 31. W.N. Cottingham and I.H. Dunbar, Z.Phys.C2, 41, 1979 32. M. Ftipani, Nucl.Phys.A699:270-277,2002 33. S. Capstick and W. Roberts, Phys.Rev.D49:4570-4586,1994 34. V.I. Mokeev, et al., Phys.Atom.Nucl.64:1292-1298,2001 35. S. Capstick, P.R. Page, Phys.Rev.D60:111501,1999 36. D.E. Groom et al., EL1r.Phys.J. C15, 1-878, 2000 37. L.A. Copley, G. Karl, E. Obryk, Nucl.Phys.B13:303-319,1969 38. G. Niculescu, this conferences; R. Feuerbach, private communications. 39. H. Fnnvieille, this conferences 40. A. Airapetian et al., Phys.Rev.Lett.87, 182001-l(2001) 4 1. S. Stepanyan et al., P hys.Rev.Lett .87,182002- 1(2001) 42. M. Guidal, private communications (2002)

BARYON SPECTROSCOPY ON THE LATTICE ROBERT G . EDWARDS Jefferson Lab 12000 Jeflerson Avenue Newport News, Virginia 23606, U S A E-mail:[email protected] Recent lattice QCD calculations of the baryon spectrum are outlined.

1

Introduction

Quantum Chromodynamics (QCD) provides an excellent description of nature; however, the theory suffers from divergences that must be removed to render it finite. Lattice QCD provides an apriori non-perturbative regularization of QCD that makes it amenable to analytic and computational methods. No model assumptions other than QCD itself are needed to formulate the theory. This review surveys the rapidly evolving work in using Lattice QCD for calculations of baryon spectroscopy. Along the way, sources of systematic uncertainties in calculations are described and future directions are outlined. 1.1

Regularization of QCD on a lattice

As the starting point for lattice QCD, the path integral formulation in Euclidean space is used'. The usual continuous space-time of 4-dimensional continuum QCD are approximated with a discrete 4-dimensional lattice, with derivatives approximated by finite differences. Quarks are put on sites, gluons on links. Gluons are represented as 3 x 3 complex unitary matrices U,(z) = exp(igaA,(z)) elements of the group SU(3) with vector potential A,(z), coupling g , and lattice spacing a. The vacuum expectation value of operators involves path integration over gauge and fermion fields

-+

2'

1

dU, 0 (U,M-' ( U ) ) det ( M ( U ) )CSc(').

The Gaussian integration over the anti-commuting fermion fields $ result&l in the det(M(U)) and M - ' ( U ) factors with M ( U ) a lattice form of the Dirac operator. The gauge action & ( U ) approximates the Yang-Mills action of the continuum. The quenched approximation neglects the fermion determinant.

43

44

The choice of working in Euclidean space resulted in no factors of i in the exponent multiplying the gauge and fermion actions. The path integral therefore resembles a 4-dimensional statistical mechanical model making it amenable to analytic as well as Monte Carlo methods for evaluation. Numerical predictions from lattice QCD are in principle exact (to some precision) after systematic errors are controlled. The statistical uncertainties go like 1/mfor N configurations of gauge fields in a Monte Carlo ensemble average. Systematic uncertainties include: (1) Finite volume - the lattice 2fm or more is box must hold a hadron state, typically a lattice size of L needed. Several pion Compton wavelengths are needed m,L 4 . ( 2 ) Chiral extrapolations - calculations with small quark masses are expensive - extrapolate observables to physical quark mass region (delicate!). (3) Discretization effects: inherent O ( a ) or O(a’) lattice uncertainty. One must extrapolate to continuum limit ( a -+ 0) to recover physical quantities. N

2

Confinement and Model Predictions Potentials

-

- Static Quark

A particularly useful r61e of lattice QCD is model testing. There is significant recent activity in the study of 3 quark potentials which provide phenomenological insight into the forces inside a baryon. By gauge invariance, the quarks must be joined by 3 glue strings. These strings meet at a “gluon junction”, which has been conjectured to be a non-perturbative excitation of the QCD vacuum’. What is the area law behavior? One can test two ansatze. The Y-ansatz predicts the potential grows linearly like V,,, 0: o,,Ly where L y is the minimal length of the 3 flux tubes necessary to join the 3 quarks at the Steiner point. It is derived from strong coupling arguments3, and is consistent with the dual superconductivity confinement scenario. At large distances, the A-ansatz predicts instead that the potential grows linearly with the perimeter L a of the quark triangle, e.g. V,,, 0: a,,-La/2. It is derived from a model of confinement by center vortices using a topological argument4. ~ ? ~ Recent work6 claims There is controversy as to which a n ~ a t zholds. that at short distances the potential approaches the A-ansatz but rises like the Y-ansatz at large distances. Departures from the A-ansatz appear above d,, 0.7fm hence the A model is more appropriate inside a hadron. However, recently Simonov7claims there is a field strength depletion near the Y-junction which lowers the potential and could disguise the true behavior. Tests using adjoint sources could help reconcile the various claims. N

45

3 3.1

Hadron Spectrum Chiral Symmetry

As mentioned before, for accurate lattice calculations systematic uncertainties need to be controlled. The discretization of the Dirac operator has been particularly troublesome since lattice QCD’s inception and can significantly affect continuum and chiral extrapolations. The “doubling” problem is easily demonstrated by examining the lattice momentum representation of the free r,a, -+ $ C , 7, sin(up,). The propagator has Dirac operator, namely additional zeros at the momentum corners, e.g. up, = 0 , n so there are 16 species of fermions in general. Originally, Wilson lifted the doublers by adding a Laplacian term that breaks chiral symmetry. In fact, the Nielson-Ninornia no-go theorems state one cannot avoid both doubling and chiral symmetry breaking with a local, hermitian action analytic in the gauge fields. This major theoretical problem has been solved with the recent advent of chiral fermion actions8 (e.g., Domain-Wall or Overlap fermions) and their use is crucial for matrix elements. How important is chiral symmetry for spectroscopy studies? Renormalization theory tells us that breaking a symmetry leads to induced quantum terms in an action. The Wilson fermion action has U ( u ) scaling from the breaking of chiral symmetry. One can add a dimension 5 operator (hyper-fine term) and rigorously improve scaling from U ( u ) to O ( u 2 ) .Scaling violations are dramatically reduced - mostly from improving chiral symmetry. Scaling violations are comparable with chiral fermion formulations. The conclusion is that chiral symmetry is important for accurate spectrum calculationsg at comparatively heavy quark masses. However, the benefits of chiral fermion actions with exact chiral symmetry are now being dramatically demonstrated as near physical quark masses are approached as will be shown below.

c,

3.2

Quenched Pathologies in Hadron Spectrum

Clearly, precisely controlled lattice calculations come with the inclusion of the fermion determinant. However, because of their vastly reduced computational cost quenched calculations are quite prevalent and one can gain important phenomenological insight into QCD, but the potentially large systematic errors induced in this approximation should be carefully ascertained. Suppressing the fermion determinant leads to well known pathologies as studied in chiral perturbation theory”. There are missing vacuum contributions to

46

the disconnected piece of singlet correlators

These effects are manifested in the 7’ propagator missing vacuum contributions with new double pole divergences arising of the form 1

.

How dramatic are these quenched effects and to what extent do they affect the extraction of physical observables? One idea is to incorporate knowledge of quenched divergences in calculations and then attempt to extract useful information.

3.3 Decay in the Quenched Approximation The m; in Eq. (1) is the mass shift needed to recover the pseudoscalar sinthe unique piece of the 7’corglet mass from the non-singlet pion. In relator - the hairpin - was computed directly. The parameter m; was extracted and one sees the lattice data is well described by the xPT prediction. With the shift, the 7’ mass (at non-zero lattice spacing) is determined to be 820(30)MeV with possibly large O(a) scaling uncertaintities. A recent Domain Wall calculation” gives 940(4)MeV. Further dramatic behavior is seen in the isotriplet scalar particle ao. There is an 7’ - 7r intermediate state with missing contributions in the quenched approximation as shown in Fig. (1). In fact, the a0 correlator . xPT, one can goes negative - a clear sign of violations of ~ n i t a r i t y ’ ~From construct the a0 correlator by including couplings between 7’ - 7r states and rescattering states which can be resummed. The lightest a0 correlator is fairly well described by a 1-loop resummed bubble term with 7’ mass insertion fixed. A mass ma”= 1.34(9)GeV was found. The new Domain Wall calculation12 gives mat,= 1.04(7)GeV. The latter results does not exclude the possibility of aO(980) being a qq state.

’’,

3.4

Quenched and Full QCD Hadron Spectrum

The quenched low-lying hadron spectrum has been extensively studied by the CPPACS collaboration using Wilson fermions14. Masses were computed at four lattice spacings and extrapolated to the continuum limit. Lattice sizes

47

ICl

1,ms (lame

unnq

Figure 1. Left: contributions t o the a0 propagator from an q - 7r intermediate state. Right: comparison of scalar a0 propagator with the bubble sum formula fitted t o the interval t=1-6 (Ref. 13).

ranged up to 643 x 112 for a 3.2fm box. At each lattice spacing, the lightest pseudoscalar mass obtained was about 500 to 6OOMeV. Hadron masses were extrapolated in the quark mass via an ansatz motivated by the quenched xPT prediction

+

m $ ~= ,A(m1 ~ ~ m2){1- 6 [In ( 2 A m / A i ) ] m2/ (m2 - ml) ln ( m 2 / w ) }+ B ( m l + m2)2+ 0 (m3) (2) mH (mps) = mo Clpmps + C1m2,~ + C3pm3pS , C l p 0; 6 . The constants A , B , and Ci are fixed in the fits. Quenching effects were more clearly seen in the pseudoscalar channel. The calculation shows the basic hadron spectrum is well determined even in the quenched approximation t o within 10% accuracy. The computational cost was roughly 50 Gigaflop-years. A subsequent two-flavor dynamical calculation was made with four quark masses at 3 lattice spacings15. Box sizes range up to about 2.5fm. In the meson sector, the results are consistent with the original quenched calculations and now agree to within 1%of experiment. Systematic deviations of the quenched calculation from experiment are seen demonstrating that sea quark effects are important. The vector meson masses are increased after unquenching. This increased hyperfine splitting is consistent with the qualitative view that the spin-spin coupling in quenched QCD is suppressed compared to full QCD due to a faster running of the coupling constant. In the baryon sector, two-flavor dynamical sea quark effects are not as apparent. As seen in Fig. (2). The N and A masses are higher than experiment, but other masses are consistent. With only a 2.5fm box, finite-volume effects could well be large. Another concern is that the octet and decuplet chiral extrapolations have many parameters resulting in possibly underestimated er-

+

+

48

1.4

1.1

0.0

0.5 a p?t']

1

1.o

Figure 2. Baryon masses in twc-flavor (filled symbols) and quenched (open symbols) QCD. Both graphs have the same lattice spacing scale. (Ref.15).

rors and will be discussed more next. However, this is a significant calculation involving roughly one Teraflop-year of computations and well demonstrates the efficacy of lattice methods. 3.5 Improved Chiral Extrapolations The Adelaide group has been extensively studying higher order xPT effects on hadronic quantities16. The basic upshot is that the na'ive chiral extrapolations in use are just too na'ive! In particular, they incorporate leading non-analytic behavior from heavy baryon xPT arising from B + B'T B intermediate states with B = N , A ---f

n/r, = ( Y B +

P B ~ :+ C B ( m T , A )

(3)

where C B is a self-energy term. The coefficient of the m; term is actually known analyticl!ly in contrast to Eq. (2). The basic argument is since xPT has a zero radius of convergence (or certainly not a well defined radius), a simple leading order approximation to Eq. (3) is quite a bad approximation at moderate m,. They use a simple regularization of the self-energy term. Fig. (3) shows a comparison of a recent quenched and 2+ 1 dynamical calculation of the low lying hadron spectrum for a variant of staggered fermions at the same (physical) lattice spacing16. The various lines are from fits using Eq. (3). One can see that the self energy term becomes significant for small lattice quark masses. The intriguing result is that the fit parameters ( Y B and PB agree very well between the quenched and dynamical calculations. This

49 0.2 I

I

I

0.1

0.2

I

I

2.0

I

0.8 0.0

I

I

0.1

-203 0

0.0

-0.1 -0.2 -nn

. 1

I

0.0

0.3

m,,’ (CeV’)

0.4

0.5

0.6

‘

I 0.1

0.2

0.3 0.4 m,,’ (GeV’)

0.5

0.6

Figure 3. Left: contributions from various intermediate states to the quenched and unquenched self-energy term C. Right: fit (open squares) to lattice data - quenched (open A) and dynamical (filled A) with adjusted self-energy expressions accounting for finite volume and lattice spacing artifacts. The continuum limit of quenched (dashed lines) and dynamical (solid lines) are shown. The lower curves are for N and upper for A. (Ref. 16.)

result can be used to justify the claim that the dominant effects of quenching is attributed to first order meson loop corrections. While quite intriguing it is fair to say there is some controversy over these results. At issue is the concern that once one uses any model to directly interpret lattice results, one has lost predictably. However, in defense once one used a chiral extrapolation at all one has chosen a model. Ultimately, the Adelaide’s group work has shown that their is interesting structure in the “pion cloud” around a hadron and going to light quark masses is essential. 3.6 Excited Baryons

Understanding the N* spectrum gives vital clues about the dynamics of QCD and hadronic physics. Some open mysteries are what is the nature of the Roper resonance? Why is the ordering of the lowest-lying states - the positive and negative parity states - inverted between the N , A and A channels? The history of lattice studies of excited baryons is quite brief. Recently, new calculations are starting to appear using improved gauge and fermion actions. The nucleon channel is the most studied and work has focussed on two independent local interpolating fields

Ni = Eijk (uTCY.=jdj)U k

,

N2 = E i j k ( U T C d j ) 7 5 U k

.

(4)

Both interpolating fields couple to positive and negative parity states, so in practice parity projection techniques are used. Making the lattice anisotropic with finer discretization in time allows the behavior of the correlators to be

50 3.5

"."

,

I

0.0

I

I

0.8

0.4

0.6

0.8

m, (GeV.)

Figure 4. Left: effective masses for correlators with fields Eq. (4) corresponding to the nucleon (circles), its parity partner (diamonds) and tentatively the lowest positive parity excitation (cross) with an anisotropic clover action (Ref.17). Right: masses in physical units obtained with the isotropic Overlap action (Ref.l8). Solid symbols denote N ( 4 ' ) states: ground lowest

(0)

and 1st-excited (*). Empty symbols denote N ( $ - ) states: lowest (A) and 2nd

(a). The experimental points (*) are taken from PDG.

examined over many more time slices than on isotropic lattices. Additional tuning of the fermion action is needed to recover hypercubic symmetry. The left side of Fig. (4) shows the effective mass for the nucleon and its parity partner on an anisotropic lattice using the clover action" - an action improved to have reduced discretization uncertainties. Long plateaus (clean extraction of a mass) are seen demonstrating the efficacy of the method. For this quark mass, there appears to be the expected ordering of the states Nt1j2+ > N112- > N1/2f. However, there is difficulty in approaching small quark masses, and the mass extracted with the N2 operator appears too large. A recent quenched calculation" using Overlap fermions (a chiral fermion action) going to much smaller quark masses reveals a dramatic decrease in the nucleon masses extracted only with the N1 interpolating field as seen in the right side of Fig. (4). The authors claim the apparent crossing of the first excited N1/2 and lowest N1/2- states is the demonstration of the physically correct ordering of states. However, it is also possible that at such light quark masses a decay threshold has been crossed and the mass observed is affected by missing dynamical effects via the mechanisms described in Sec.3.3. If so, a finite volume check via shrinking the lattice box can reveal this. It is clear lattice calculations are really beginning to probe interesting excited state phenomena. With judicious use of finite volume techniques, physically relevant mass information can be extracted.

51

4

Conclusions

First generation lattice calculations of excited baryon spectroscopy are a p pearing. State of the art calculations require roughly 100 Gigaflop-year in quenched QCD and roughly 1 to 10 Teraflop-years in full QCD. The required resources are not available to the US lattice community. The Dept. of Energy’s SciDAC program is addressing this shortcoming and a large effort is ongoing in the U S . to meet future computational needs. Acknowledgments RGE was supported by DOE contract DEAC05-84ER40150 under which the Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility (TJNAF). References 1. I. Montvay and G. Miinster, Quantum Fields on a Lattice, (Cambridge Univ. Press, 1994). 2. D. Kharzeev, Phys. Lett. B 378,238 (1996). 3. N. Isgur and J. Paton, Phys. Rev. D 31,2910 (1985). 4. J. M. Cornwall, Phys. Rev. D 54,6527 (1996). 5. T. T. Takahashi, et.al., Phys. Rev. D 65,114509 (2002). 6. C. Alexandrou, P. De Forcrand and A. Tsapalis, hep-lat/0209062. 7. D.S. Kuzmenko, Yu.A. Simonov, hep-ph/0202277. 8. D.B. Kaplan, Phys. Lett. B288, 342 (1992). R. Narayanan and H. Neuberger, Nucl. Phys. B443,305 (1995). 9. R.G. Edwards, U.M Heller, T.R. Klassen, Phys. Rev. Lett. 80, 3448 (1998). 10. B. Bardeen, et.al., Phys. Rev. D 62,114505 (2000). 11. C. Bernard and M. Golterman, Phys. Rev. D 46,853 (1992). S. Sharpe, Phys. Rev. D 46,3146 (1992). 12. S. Prelovsek and K. Orginos, heplat/0209132. 13. B. Bardeen, et.al., Phys. Rev. D 65,014509 (2002). 14. S. Aoki, et.al., Phys. Rev. Lett. 84, 238 (2000). 15. A. Ali Khan, et.al., Phys. Rev. D 65,054505 (2002). 16. R.D. Young, et.al., hep-lat/0111041. 17. R.G. Edwards, U. Heller, D. Richards, proceedings of Lattice 02. 18. F.X. Lee, et.al., heplat/0208070.

52

______

._

Lucy Collins, Rachel Harris, Linda Ceraul, Mary Fox, and Heather Ashley

Coffee break at CEBAF Center

HEAVY QUARK PHYSICS ON THE LATTICE C. T.H. DAVIES Department of Physics and Astronomy, University of Glasgow, Glasgow, GI2

uf(

SQQ, E-mail: [email protected]. Irk I describe methods for dealing with b and c quarks within the lattice QCD approach and summarise recent results for phenomenologically important quantities.

1

Introduction

Lattice QCD is a well-established numerical approach to evaluating the Feynman path Integral for QCD, renderred finite by the discretisation of space-time into a Cdmensional lattice. A recent pedagogical review is given in RRf. 1. One of the main aims of this field is to calculate quantities for comparison to, or as predictions for, experiment. There is a long history of such calculations and the methods we use mean that there are systematic and st;b tistical uncertainties associated with the results. These uncertainties have improved steadily over the years, helped particularly by recent approaches to the improvement of systematic errors from discretisation. In many cases the largest remaining source of systematic error is that from the failure so far to include dynamical quarks in the vacuum with realistically low masses. We are now on the threshold of being able to overcome this source of uncertainty with new Teraflops computing power coming onstream in the next three years. This will mean an improvement of lattice systematic errors down to the level of a few percent (depending on the quantity calculated) and then lattice results can have a big impact on experiment. In particular I am concerned with calculations in heavy quark physics and there the determination of the sides of the CKM triangle w i l l be dominated by theoretical uncertainties unless these are improved to a few percent. Below I elaborate on heavy quark results &om current lattice Calculations. Most of these are still &om the quenched approximation, but the methods being developed are directly applicable to configurations which include dynamical quarks once we have them. 2

Heavy quarks on the lattice

Heavy (b or c) quarks present special challenges to lattice QCD because the quark mass in units of the lattice spacing, .mga 2 1. (on typical lattices,

53

54

mba M 2 - 3?m,a w 0.5 - 1. This means that relativistic momenta ji M TTZQ are very distorted by the lattice discretisation and the use of a naive relativistic lattice action (Wilson or clover quarks) will give large errors that depend on mga or ( T T Z Q U ) ~However, . one glance at the spectrum of bound states of b or c quarks shows that they are non-relativistic (the radial and orbital excitation energies are much smaller than the meson masses) and therefore it is possible to control these errors if we take a non-relativistic approach to the physics. Then b and c quarks can be treated accurately on the lattice and indeed heavy quarks physics is one of the most successful areas of lattice phenomenology. There are several ways to proceed, each with its differentproponents: Static quarks. This is the mg = 00 limit. Then the heavy quark is spinless and flavourless and the quark propagator becomes a string of gluon fields in the time direction '. This is a useful limit for comparison to continuum Heavy Quark EffectiveTheory. NRQCD. This is a non-relativistic effective theory with a 2-component heavy quark field 3.

The ci are h e d by matching to full continuum QCD. They represent the effect of states with momenta above the lattice cut-off, n / a , (missingfrom the lattice theory) and so this matching can be done in perturbation theory for large enough d u e s of the lattice cut-off. It may also be done non-perturbatively. The value of the bare mass,~ Q U is, tuned non-perturbatively by requiring one hadron mass to be correct (the standard method for tuning lattice masses). The lattice spacing, a, cannot be taken to zero in this approach to get to the continuum limit; instead we must systematically improve the matching to full continuum QCD by adding higher order terms to remove discretisation errors. We can also improve by adding higher order terms in the non-relativistic expansion and, in general, these two improvements go together. As m ~ -+a 00 we get the static limit. Heavy Wilson @arks (FNAL method). This approach uses the standard relativistic lattice quark action, but interprets the quark propagator in a non, remove a large part of the errors that relativistic way when fixing ~ Q U to this would otherwise give 4.

LQ = &?9

+ mga +

Fop)$

where the first two terms represent the lattice (Wiion) discretisation of the Dirac Lagrangian and the last term is the clover term. A systematic matching to full QCD is possible in this approach with wedependent coefficients. In

55 4.8

4.4

3.2

2.8

Figure 1. The charmonium spectrum from lattice QCD 7. Experimental results are giwn by dotted lines.

the small ~ Q limit U this approach yields standard light quark results. In the large ~ Q limit U it goes over essentially to NRQCD. Wdsson/clouer quarks. This uses the standard clover light quark action (as above), improved to remove the leading discretisation errors. The residual errors are O ( m ~ aand ) ~ may not be large for c quarks. HQET-inspired extrapolations to the b quark can be done provided that care is taken to untangle physical and unphysical (discretisation) dependence on the quark mass 5. These extrapolations tend to give large errors. Improvements to this method may be possible using anisotropiclattice techniques. Then the lattice spacing in the temporal direction is much smaller than that in the spatial direction and m ~ can & be small on manageable lattice volumes even for heavy quarks 7 .

3 The spectrum Extensive calculations of the heavyonium spectrum have been done with the NRQCD and heavy Wilson approaches and, more recently, with anisotropic clover. The static method gives the heavy quark potential which can then be solved within a potential model framework. Several of the radial and orbital excitation energies can be extracted if care is taken to use several different ‘sm&ngs’ to excite dif€erent states from the vacuum. Figure 1shows the charmonium spectrum obtained by the Columbia

56

group using the anisotropic clover action in the quenched approximation. In addition to the standard S, P and D states they find a signal for ‘hybrid’ gluonic excitations, some with exotic quantum numbers. It is important to fix the mass of these more precisely in the presence of dynamical quarks so that they c a be ~ found ~ in the next generation of experiments.

MeV

4

i

-**T

0

-20

t ___ : 0

:

4

:

Fxpaiment.

LatticeQuenchedapprmimatjon. Lattice N f = 2 dyn. quarks at m, from UKQCD.

: : IMrapolate to light d p .

ma6s and

Nf = 3.

Figure 2. Fine structure in the bottomonium spectrum from lattice QCD 8.

Figure 2 focusses on the fine structure in the bottomonium spectrum using NRQCD for the b quarks and comparing results in the quenched a p proximation to those including two flavours of clover dynamid quarks with severd masses dawn to a mass around the strange quark mass *. The hyperh e splitting, between the T and the q b , is obtained quite precisely on the lattice and there is a clear increase on including dynamical quarks and as the dynamical quark mass decreases. If the results are extrapolated linearly in

57

the dynamical quark mass to m,/3 and the number of dynamical flavours is extrapolated linearly to 3, a hypedine splitting of 60 f 15 MeV is obtained. A much more precise result should be possible on configurations with 2+1 flavours of lighter d y n d d quarks with improved detennination of the y codcients in the NRQCD Lagrangan. This will then provide a prediction for the mass of the q b , yet to be seen experimentally. The most complete determination of the spectrum of heavy-light bound states is based on using NRQCD for the b quark and the clover action for the light quark. Propagators for light quarks and heavy quarks are combined to make heavy-light mesons. Since it is not possible to generate light quark propagators with masses close to mU,deven in the quenched approximation, the results must be extrapolated to the chird (light quark) limit to reach the B. Figure 3 shows the spectrum from ref. in the quenched approximation. In common with results for the charmonium spectrum the hyperfine splitting, here between the B and the B' mesons, is underestimated. This is believed to be, at least partially, a result of the quenched approximation. Another source of underestimation is the coefficient, a,which multiplies the coupling of the quark spin to the chromomagnetic field in a non-relativistic treatment of heavy quarks. More precise determinations of this coefficient are underway lo.

B

B'

Figure 3. The spectrum of blight mesons from lattice QCD g .

58 Figure 4 shows results for the heavy-light-light baryon spectrum obtained in a similar way u. T

5.0

Figure 4. The spectrum of blight-light baryons from lattice QCD ”.

3.1 The b mass

Lattice QCD provides a non-perturbative method for fixing the bare quark mass in the lattice QCD Lagrangian. It can be adjusted until a particular hadron mass is correct. This bare m a s can then be converted ta any other mass desired, e.g. the quark mass in the MS scheme. In fact the best current determinationsof the b quark mass use, rather than the bare mass,the binding energy in the static limit. Then

& is the lattice energy ‘offset’ and is known in the quenched approximation, in the static limit, to O(lr:) 12. Z,,,,,t is the continuum renormalisation from h f to ~ mb in ~ the M S scheme and is also known to (?(a:) 13. New non-perturbative methods are also aalso being developed to fix & 14. The ‘world average’ for mb(mb) is currently 4.30(10) GeV in the quenched approximation l5. using the heavy Wilon and light clover methods Recent results on agree on a d u e of 1.26(13) GeV in the quenched approximation 16.

59

4 4.1

Matrix elements fB

The simplest matrix element to calculate is that for the leptonic decay of the B, mediated by the heavy-light axial vector current. The decay rate can be determined experimentally in principle but is difficult in practice so a precise lattice determination is useful.

B

Figure 5. Leptonic B decay.

'888891 '9294

'W97

'98

'99

Figure 6. A time history of lattice rasults for fB in the quenched approximation.

f~ is determined on the lattice from the matrix element of A, between the m u m and a B meson.

< OIApIB >= P p f B We must match A, on the lattice to full continuum QCD. This has been done to O(a,, l/mg, a) for NRQCD and heavy Wilson quarks, and these give

60

currently the most precise results, in agreement with each other 17. For light clover quarks the matching has been done non-perturbatively in the ma 4 0 limit and this cafl be used to obtain a result for fD and extrapolate to fB I*. Results for f~ have improved steadily over the yeass (see Figure 6) as improved techniques have given us more confidence in them. Table 1 gives the typical error budget for a current calculation of fB in the quenched approximation. World averages quoted at the recent Lattice Conferences are: = 173 rt 23 MeV = 203 f 14 MeV fB,/fB= 1-15(5);fD./fD = 1-16(4) 15319

fAQA' fh!A)

Table 1. A typical enor budget for a calculation of j~ in the quenched approximation.

source statistical + interp. disc. O((aA)2) Pert. aQ.2 4/(aM)) NRQCD O ( ( A / M ) 2cr,A/M) , light quark mass a-' (mp) Total

percent 3 4 7 2 +4 4 10

There is evidence that including dynmical quarks gives an increased d u e (by 20%) for fB depending on how the overall scale is determined 19.

The matrix elements for the Cquark operators of the effective weak Hamiltonian appropriate to Bo - B" mixing c i ~ nbe evaluated on the lattice. It is conventional to take the ratio of this to fg and call the answer BB. This is a somewhat harder calculation than f~ but the matching to the continuum has n m been improved to the same level as that for fB and the results from different methods are converging. World averages from recent Lattice Conferences l5>l9 are:

EB&= 1.30(12)(13); fBd&

= 230(40) MeV.

61

Figure 7. l%e box diagram for B0 operator.

mixing becoma the.matrix element of a kquark

1 ' ' ' ' 1 1.6 'T

a"

1.4

sE'dPfPL&kr: I&=& ' 1 ' 'APE extrap to B X Iellouchkln ,'3=6.Z + LeI!ouch&ii~~extrep ta li 0 JLQCD @=5.9 0 Gimenez&Reyes,UKQCD@=6.2+ Gimenez&Reyes,APE,9=6.0 Christensen et al. @=a.O , x m y fit, interp. of 0 ,00 X

m

-

1.2

-r

0.0

0.2

1/M,

0.4 0.6 (GeV)-'

0.8

Figure 8. A summary of results for BB from different methods in lattice QCD 19.

Figure 8 l9 plots a summary of results for BB at different values of the heavy quark mass, indicated by the inverse of the pseudoscalar heavy-light

62

meson mass. It shows clearly the different regions in which different methods work best, and indicates general agreement between the methods in the overlap regions. 4.3 B Semi-leptonic decay

B mesons decay semi-leptonically through the weak decay of the b quark to either a c quark or a u quark, and the decay of the virtual W particle to a lepton pair. The associated dements of the CKM matrix Vcb and Vub can be determined by a compaxison of the theoretical rate (proportional to the square of the unknown CKM element) with the experimental result. They are important inputs to constraints on the self-consistency of the Standard Model through the CKM triangle.

Figure 9. Semi-leptonic decay of a B meson.

B decay to D or D*mesons citn usefully be discussed within a framework in which we consider both the b and the c quarks as heavy and determine corrections to the infinite mass limit in terms of inverse powers of mb and m,. In the infinite mass limit, heavy quarks are spinless and flavorless, as discussed above. Then the form factors for decay B to D and B to D* and elastic B to B scattering all become the same, when plotted against the variable w v', where w is the initial meson and w' the final meson Cvelocity. This form factor is then known as the Isgur-Wise function and calculations on the lattice have been done using a variety of methods m. Of more direct use is a calculation of the form factor at the physical b and c masses in the zemrecoil limit (when V B - V D = 1). There are a number of theoretical simplifications in this limit and the experimental results can be extrapolated to this point for the case of B 4 D*.A direct comparison of the two yields Vcb. At last year's lattice conference there were new results from the FNAL

63

group on the B + D ' form factor at zero recoil using the Heavy Wilson method 21- After perturbative matching to the continuum they obtain a value for the form factor at zero recoil of 0.929(11) in the quenched approximation, X with an error significantly smaller than the experimental errors on V ~ this form factor. Unquenching affects the discrepancy of the theoretical result from unity and so is unlikely to change the result by more than one percent. B semi-leptonic decay to light hadrons is harder to tackle on the lattice because most of the experimental rate occurs where the 7~ or p meson has large momentum. When jh is large, there is the possibility of large discretisation errors. A number of groups have calculated the form factors for B 3 ?r decay but the results are still somewhat uncertain, depending markedly on how the extrapolation to physical light quark masses is done 15. There is also some dispute about how well the soft pion theorem j 0 ( h a z )= fB/ fm is satisfied 19. 5 Conclusions New calculations with much lighter dynamical quarks than before are on the horizon and this will result in significantlyimproved lattice results, to combine with improved experimental results over the next few years. Acknowledgments

I thank my collaborators,particularly S. Collins, J. Hein, G. P. Lepage anf J. Shigemitsu for many useful discussions. This work was supported by PPARC and the EU under HPRN-200@00145 Hadrons/Lattice QCD. References 1. C. T. H. Davies, Proceedings of the 55th Scottish Universities Summer School in Physics, St. Andrews, Scotland, August 2001, hepph/0205181. 2. E. Eichten, Nucl. Phys. B (Proc. Suppl. 4) (1988) 170. 3. B. A. T h d e r and G . P. Lepage, Phys. Rev D43 (1991) 196. 4. A. X. El-Khadra et al, Phys. Rev.D55 (1997) 3933. 5. C. Maynard: LATO1, Nucl. Phys. B (Proc. Suppl. 106) 388, h e p lat/0109026. 6. T. Klassen, Nucl. Phys. B533 (1998) 557. 7. P. Chen et alNucl. Phys. B (Proc. Suppl. 94) (2000) 342. 8. L. Marcantonio et 02 Nucl. Phys. B (Proc. Suppl. 94) (2000) 363. See also N. Eicker et d Phys. Rev.D57 (1998) 4080; T. Manke et al Phys. Rev. D62 (2000) 114508.

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9. J. Hein et 01 Phys. Rev. D62 (2000) 074503. 10. H. Trottier and G. P. Lepage: Nucl. Phys. B (Proc. Suppl. 63 (1998) 865. 11. A. Ali Khan et al Phys. Rev. D62 (2000) 054505. 12. F. Di %nu, and L. Scorzato, JHEP 0102 (2001) 020; G. P. Lepage et a1 Nucl. Phys. B (Proc. Suppl. 83 (2000) 866. 13. K. Melnikov and T. v;tn Ritbergen, Phys. Lett. B482 (2000) 99. 14. J. Heitger and R. Sommer, LATO1, Nucl. Phys. B (Proc. Suppl.l06), 358, heplat/0llOO16. 15. S. Ryan, LATO1, Nucl. Phys. B (Proc. Suppl.l06), 86. 16. D. Becirevic et al hepph/0107124; J . Juge, LATO1, Nucl. Phys. B (Proc. Suppl.106) 847, heplat/O110131. 17. JLQCD, Phys. Rev. Lett. 80 (1998) 5711; Phys. Rev. D61 (2000) 074501; A. Ali Khan et al Phys. Lett. B427 (1998) 132; A. El-Khadra et al Phys. Rev. D58 (1998) 014506. 18. D. Becirevic et 01 Phys. Rev. D60 (1999) 074501; K. Bawler et a1 heplat /0007020. 19. C. Bernard, Nucl. Phys. B (Proc. Suppl. 94)(2000) 159. 20. See, for a m p l e , G. Lacapha, LATO1, Nucl. Phys. B (Proc. Suppl.106) 373, heplat/O109006. 21. J. Simone, LATO1, Nucl. Phys. B (Proc. Suppl.), 394.

HADRONS IN THE NUCLEAR MEDIUM- ROLE OF LIGHT FRONT NUCLEAR THEORY GERALD A. MILLER Department of Physics, University of Washington Seattle, WA 98195-1560 E-mail: [email protected] The problem of understanding the nuclear effects observed in lepton-nucleus deepinelastic-scattering (the EMC effect) is still with us. Standard nuclear models (those using only hadronic degrees of freedom) are not able to account for the EMC effect. Thus it is necessary to understand how the nuclear medium modifies quark wave functions in the nucleus. Possibilities for such modifications, represented by the quark meson coupling model, and the suppression of point-like-configurations are discussed, and methods to experimentally choose between these are reviewed.

1

Introduction

When the organizers asked me to give a talk entitled “Hadrons in the Nuclear Medium” I thought about what the title might mean. Since the nuclear mass M A M [ N M , Z M p ] ( l - 0.01), and nucleons are hadrons, maybe the title should be “Hadrons are the Nuclear Medium!”. On the other hand, the modern paradigm for the strong interaction is QCD and QCD is a theory of quarks and gluons. Maybe the title should be “Are Hadrons the Nuclear Medium?”. We have known, since the discovery of the EMC effect in 1982, that the structure functions measured in deep inelastic scattering from nuclear targets are not those of free nucleons. So one theme of this talk is to try to understand, interpret and use the EMC effect. Despite the age of this effect, no consensus has been reached regarding its interpretation, importance and implications. The second theme of this talk arises from the kinematic variables used to describe the data. The Bjorken x variable: x = Q 2 / 2 M v is, in the parton model, a ratio of quark to target momenta pz/Pz, where the superscript refers the plus-component of the four-momentum vector. This in turn can be written as: ( p $ / p $ ) (pZ/P;), so that one needs to know how often a nucleon has a given value of plus-momentum, p Z . Conventional nuclear wave functions are not expressed in terms of this variable, so one needs to derive nuclear wave functions which are expressed in terms of plus-momenta. Therefore, I assert that light front nuclear theory is needed.

+

+

65

66

2

Outline

I turn towards a more detailed outline. The first part of the talk is concerned with what I call the “Return of the EMC effect”. This is the statement that conventional nuclear physics does not explain the EMC effect. The physics here is subtle, so I believe that some formal development involving the construction of nuclear wave functions using light front nuclear theory is needed. I try to answer the simple queries: “light front theory- what is it? why use it?”. A partial answer is reviewed in Ref. The saturation of infinite nuclear matter using the mean field approximation is discussed here. The result is that there is no binding effect which explains the EMC e f f e ~ t ~ This ,~. statement is a natural consequence of the light version of the Hugenholtz-Van Hove Theorem4: the pressure of a stable system vanishes. If one goes beyond the mean-field calculations and includes correlations by using a Hamiltonian which involves only nucleon degrees of freedom, there is again no binding effect. Furthermore, I’ll argue that using mesons along with nucleons probably won’t allow a description of all the relevant data. It is therefore reasonable, proper and necessary to examine the subject of how the internal structure of a nucleon is modified by the nucleus to which it is bound. To see how the medium modifies the wave function of nucleon, a particular model of the free proton wave function5 is used. This allows the examination of two different and complementary ideas: the quark meson coupling model6 and the suppression of point-like-configurations7. A quick summary is that the goal is to explain EMC effect and then predict new experimental consequences. This god is not attained but is within reach.

’.

3

Return of the EMC effect

It is necessary to use nuclear wave functions in which one of the variables is the plus-momentum of a nucleon, &. Thus the use of light front quantization, or light-front dynamics, which I now try to explain, is necessary. 3.1 Light R o n t Quantization Lite Light-front dynamics is a relativistic many-body dynamics in which fields are quantized at a time"=^ = zo+z3 z+.The T-development operator is then - P3 G P-.These equations show the notation that a four-vector given by AP is expressed in terms of its f components A* E A’ f A3. One quantizes at z+ = 0 which is a light-front, hence the name “light front dynamics”. The

67

canonical spatial variable must be orthogonal to the time variable, and this is given by x- = xo - x3. The canonical momentum is then P+ = Po P 3 . The other coordinates are as usual XI and PI. The most important consequence of this is that the relation between energy and momentum of a free particle is given by:

+

a relativistic formula for the kinetic energy which does not contain a square root operator. This feature allows the separation of center of mass and relative coordinates, so that the computed wave functions are frame independent. The philosophy, for the beginning of this talk, is to use a Lagrangian density, L: which is converted into an energy-momentum tensor T P ” . The total-four-momentum operator is defined formally as

‘S

PP = -2

d2zldx-T+’,

(2)

with P+ as the “momentum” operator and P- as the ‘Lenergy”operator. We then need to express T+P in terms of independent variables. In particular, the nucleon, usually described as a four-component spinor, is a spin 1/2 particle and therefore there are only two independent degrees of freedom. I’ll start with the well-known Walecka model in which L(4,V P N , ) is expressed in terms of nucleon N , vector meson V p , and scalar meson 4 degrees of freedom. The plan is to first carry out calculations using the mean field approximation, and then include the effects of N N correlations using other Lagrangians. 3.2

Light Front Quantization

The mode equation for nucleons in infinite nuclear matter nuclear matter is given by

( I t - S U Y - ( M + 984))1c,= 0, (3) within the mean field approximation of the Walecka model. The quantity of relevance for understanding deep inelastic scattering is the nuclear plus component of momentum given by3 = (i@ + guV+) $+!A), (4) where $+ = $yay+$, the independent component of the nucleon field. Furthermore

68

In the rest frame we must have P i = MA, P i = MA = E A , a result not obvious from the above equations. However, if we minimize Pi subject to the constraint that the expectation value of ( P i - P i ) vanish, we indeed get the same EA as Walecka and more! The more refers to information about the plus momenta. The result P i = P i means P i = 0, which is a statement that pressure vanishes for a stable system. According to a venerable 1958 theorem by Hugenholtz & Van Hove, a vanishing pressure, plus the definition that the nucleon Fermi energy EF gives EF = = MA A = . Th'1s has important consequences now because we may express the result (4) as

9

P i = MA = A

J

Next we use a dimensionless variable y

d k + f N ( k + ) k+. E

a

(6)

5+ to find that (7)

which means that nucleons carry all of the plus momentum. The relevance of this can be seen by calculating the effects of nucleons in deep inelastic lepton nucleus scattering using a manifestly covariant calculation of the handbag diagram. One finds*

where

The quantity ~ ( kP,) is the nuclear expectation value of the connected part of the nucleon Green's function. This can easily be calculated for our light front nuclear wave functions. The result is

or

69

s

which obeys the baryon d y f N ( y ) = 1 and momentum (7) sum rules, so that nucleons carry all of the plus momentum. This is important because f ~ ( y is) narrowly peaked at y = 1 , so that F Z A ( Z AX) A F ~ N ( Z A )and , there is almost NO Binding Effect. One can see this more directly by expanding FZ(z/y)in Taylor seriesQ about y = 1 to find:

where c = 1 - fil?/MN M 161940. The resulting figure is shown as Fig. 2 of Ref.3, but Eq. ( 1 2 ) shows clearly that F Z N ( Z A ) / F 2 N ( Z ) is too large. Similar calculations can now be done for finite nuclei lo. Although being able to do these calculations is a major technical achievement (according to me), the results also show a huge disagreement with experiment. 3.3

Beyond the Mean Field Approximation

Suppose one assumes nucleons are the only degrees of freedom in the Hamiltonian, so that i

i<j

i<j 0.003, in line with the expectation of Equat,ion (3), if xg(s, Q 2 )has the form x P x and only a slow dependence on Q 2 . The value of Q 2 ,or x, where the slope of the derivatives changes sign can be read off from Figures 9a and 9b. This transition, for values of W above 85 GeV, happens a t a relatively high Q2 of 2-6 GeV2 a t the corresponding z of 5.10-4 to $loP3. The dashed lines in Figure 9 are the predict,ion of t,he GB&W model, which explicitly incorporates the transition between the behaviors described in Equations (10) and (3) as a transition between the pQCD region and the saturation region of the dipole cross-section. The lines are drawn only at x < 0.01 where the model is applicable. The solid line is the result of a DGLA4P fit by the ZEUS collaboration. The line is drawn only above Q2 > 2.7 GeV2, where data have been fit,. In case of the DGLAP fit, the peaking behavior of Figure 9 is related t o the rapid decrease of the gluon density at low x bet,ween Q2 of 10 GeV2 and 1 GeV2 15930.

4

Discussion and Outlook

The measurements of the proton structure a t small z at HERA are now very precise. However, in spite of the expectation that these measurements should show some manifestation of dynamics beyond that incorporated in the (In Q 2 ) expansion of the DGLAP formalism, the DGLAP fits t o the data give a good description above Q2 of about 1 GeV2. The question of whether the success of DGLAP fits merely indicates the flexibility of the parton parameterizations and the still-limited (In Q 2 ) range of the measurement a t small-z is not likely to be answered by looking a t F 2 alone, at least in the currently available kinematic range. While the qualitative features of F2 at small-a: (and necessarily small Q 2 ) ,show some characteristics expected by a saturation model, the DGLAP fits can reproduce those same features without any parton saturation. One of the most promising ways of investigating the small-z proton structure is t o look at the inclusive DIS measurements together with t,he diffractive DIS reactions. While the theoretical understanding of the relation of small-x and diffraction is not yet very rigorous, the data sets from HERA provide many interesting indications of the underlying dynamics.

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References

1. L. N. Lipat,ov, Sou. J . Nucl. Phys. 20, 94 (1975); V. N. Gribov and L. N. Lipatov, Sou. ,I. Nucl. Phys. 15, 438 (1972); G. -4ltarelli and G. Parisi, Nucl. Phys. B 126, 298 (1977); Y. L. Dokshitzer, Sou. Phys. JETP46, 641 (1977). 2. C. Adloff et al. [Hl Collaboration], Eur. Phys. C 21, 33 (2001). 3. ZEUS Collaboration, paper 412, XXXt,h International Conference on High Energy Physics, July 27-August 2, 2000, Osaka, .Japan. 4. C. Adloff et al. [Hl Collaboration], Nucl. Phys. B 497, 3 (1997). 5. J . Breitweg et al. [ZEUS Collaboration], Eur. Phys. J. C 7, 609 (1999). 6. K. Prytz, Phys. Lett. B 311, 286 (1993). 7. V. S. Fadin, E. A . Kuraev and L. N. Lipatov, Phys. Lett. B 60, 50 (1975); E. -4.Kuraev, L. N. Lipatov and V. S. Fadin, Sou. Phys. J E T P 4 4 (1976) 443; E. A . Kuraev, L. N. Lipatov and V. S. Fadin, Sou. Phys. JETP45 (1977) 199; I. I. Balitsky and L. N. Lipatov, Sou. J. Nucl. Phys. 28, 822 (1978). 8. V. S. Fadin and L. N. Lipatov, Phys. Lett. B B429, 127 (1998); M. Ciafaloni and G. Camici, Phys. Lett. B 430, 349 (1998). 9. J. Blumlein and A . Vogt, Phys. Rev. D 57, 1 (1998). J. Blumlein, V. Ravindran, W.L. van Neerven and PI. \logt, hep-phf9806368. 10. M. Ciafaloni, Nucl. Phys. B 296, 49 (1988); S. Catani, F. Fiorani and G. hlarchesini, Nucl. Phys. B B336, 18 (1990); S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B 234, 339 (1990). 11. L. V. Gribov, E. hl. Levin and hl. G. Ryskin, Phys. Rep. 100, 1 (1983). 12. J . Bartels, G. -4.Schuler and J. Blumlein, Z. Phys. C 50 (1991) 91. 13. R. S. Thorne, Nucl. Phys. B512, 323 (1998). 14. H. Jung, Nucl. Phys. Proc. Suppl. 79, 429 (1999). 15. J. Breitweg et al. [ZEUS Collaboration], Eur. Phys. J. C6, 43 (1999). 16. C. A4dloffet al. [Hl Collaboration], 2. Phys. C 76,613 (1997). 17. H1 Collaboration, paper 571, XXIXth International Conference on High Energy Physics, July 23-29, 1998, Tampere, Finland. 18. J. C. Collins, Phys. Rev. D 57, 3051 (1998). 19. G. Ingelman and P. E. Schlein, Phys. Lett. B 152, 256 (1985). 20. C. Adloff e t al. [Hl Collaboration], hep-ex/0012051. 21. K. Golec-Biernat and M. Wusthoff, Phys. Rev. D 59, 014017 (1999). 22. K . Golec-Biernat and M. Wusthoff, Phys. Rev. D 60, 114023 (1999). 23. E. Gotsman, E. Levin and U. Maor, Nucl. Phys. B 493, 354 (1997);

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24. 25. 26. 27. 28.

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E. Gotsman, E. Levin and U. Maor, Phys. Lett. B 425, 369 (1998); E. Got,sman, E. Levin, U. Maor and E. Naftali, Nucl. Phys. B 539, 535 (1999); N. Nikolaev and B. G. Zakharov, 2.Phys. C 49, 607 (1992); N. Nikolaev and B. G. Zakharov, 2.Phys. C 53, 331 (1992); V. Barone, PI.Genovese, N. N. Nikolaev, E. Predazzi and B. G. Zakharov, Phys. Lett. B 326, 161 (1994); J. R. Forshaw, G. Kerley and G. Shaw, Phys. Rev. D 60,074012 (1999); \%’. Buchmuller, T. Gehrmann and A. Hebecker, Nucl. Phys. B 537, 477 (1999); -4. H. Mueller and B. Patel, Nucl. Phys. B 425, 471 (1994); -4. H. hlueller, NU^. Phys. B 415, 373 (1994); \V. Buchmuller and A. Hebecker, N7lcE. Phys. B B476, 203 (1996); \%’.Buchmuller, M. F. McDermot,t and -4. Hebecker, Nucl. Phys. B 487, 283 (1997). -4. H. Mueller, hep-ph/9911289. J . Bartels, J. Phys. G 26, 481 (2000). M. F. McDermott,, hep-ph/0008260. ZEUS Collaborat,ion, paper 416, XXXt,h Int,ernational Conference on High Energy Physics, July 27-August 2, 2000, Osaka, Japan. &I. R. Adams et al. [E665 Collaboration], Phys. Rev. D 54, 3006 (1996); M. Arneodo et al. [New Muon Collaboration], Nucl. Phys. B 483, 3 (1997). H. Abramowicz, E. &I. Levin, A . Levy and U. hlaor, Phys. Lett. B 269, 465 (1991). H. Abramowicz and A. Levy, hep-ph/9712415. -4. D. Martin, R. G. Roberts, \%’. J. Stirling and R. S. Thorne, Eur. Phys. J. C 4, 463 (1998).

BARYON CHIRAL DYNAMICS THOMAS BECHER Stanford Linear Accelerator Center Stanford University, Stanford, CA 94309, U S A E-mail: [email protected] After contrasting the low energy effective theory for the baryon sector with one for the Goldstone sector, I use the example of pion nucleon scattering to discuss some of the progress and open issues in baryon chiral perturbation theory.

1

Higher, faster, swifter?

Many of the constraints of chiral symmetry on the interaction of pions and nucleons at low energies were worked out long before the advent of QCD (Current algebra, PCAC). Later it was realized that the corrections to these symmetry relations can be obtained by implementing the chiral symmetry and its breaking by the quark masses into an effective Lagrangian describing the interaction of mesons and baryons. This method is called chiral perturbation theory (CHPT).l It allows one to compute the expansion of QCD amplitudes and transition currents in powers of the external momenta and quark masses; it has become one of the standard tools to analyze the strong interactions at low energy. Over the last few years, the progress in this field in the baryon sector has been twofold: on one hand, we have reached a new level of precision in many of the classical applications: by now, the full one loop result for the nucleon form factors and the pion-nucleon scattering amplitude in the isospin limit is k n ~ w n Even . ~ ~ the ~ first two-loop result has been obtained: the chirai expansion of the nucleon mass has been worked out to fifth order.4 On the other hand, the framework has been extended and applied to a whole range of new processes: the effective Lagrangian has been extended to include electromagnetism, making it possible to disentangle strong and electromagnetic isospin ~ i o l a t i o nThis . ~ effective theory of QCD+QED has been used to calculate next-to-leading order isospin violating effects in the pion-nucleon scattering amplitude6 and to study the properties of the r - p bound state.7 Another extension of the framework incorporates the A-resonance as an explicit degree of freedom into the effective Lagrangian, thereby summing up the potentially large higher-order terms in the chiral expansion associated with this resonance.a Despite all of this impressive progress, we are still short of having the answers to some very old questions, like, for example, what is the value of the

102

103

a-term, and the agreement with data in many cases is not quite as satisfactory as in the Goldstone sector. In my talk, I will contrast the baryon with the meson sector and illustrate some of the peculiarities that arise, once the baryon field is included into the effective Lagrangian. I will illustrate my discussion with the example of 7rN-scattering and conclude that the low energy theorems for this amplitude hold to high accuracy. Chiral symmetry governs the amplitude in a small region around the Cheng-Dashen point. However, the momentum dependence of the chiral representation for the amplitude is not accurate enough t o make direct contact with experimental data. After discussing some of the difficulties associated with the extrapolation of the experimental results to the low energy region, I show how the simple structure of the result in the low energy theory can be implemented into a dispersive analysis of the data. As I focus the discussion mostly on 7rN-scattering, I will fail t o report on many important developments over the past few years. Fortunately, my sense of guilt for omitting electromagnetic probes of the nucleon was relieved by the plenary talks of Ed Brash, Helene Fonvieille, Frank Maas and Harald Merkel as well as a number of interesting talks on these matters in the parallel sessions. Unfortunately, there were no talks covering the few nucleon sectorg, nor about the recent work on quenchedlO and partially quenched" baryon CHPT. 2

Baryons versus mesons

While this is not the place t o give an introduction to CHPT12, it is instructive t o point out some of the differences between CHPT in the baryon and the Goldstone sector. All in all, the inclusion of the baryon field leads to three complications: i) in general, one has t o deal with a larger number of low energy constants than in the vacuum sector, ii) from the viewpoint of the low energy theory, the physical region is a t higher energies, iii) the singularity structure of the amplitudes is more complicated. On the upside, there are much more and more precise data available than in the meson sector. 2.1

Effective Lagrangian

For vanishing up- and down-quark masses, the pions are the Goldstone bosons associated with the spontaneous breaking of chiral symmetry. The interactions between Goldstone bosons tend t o zero at low energies and they decouple from matter fields. Accordingly, the effective Lagrangian is organized in pow-

104

ers of derivatives on the Golstone fields. At low energies, the terms with higher powers of derivatives on the meson field are suppressed by powers of the meson momenta. Because of decoupling, the interactions of the baryon and the meson involve at least one derivative on the meson field. The lowest-order, effective Lagrangian for the pion-nucleon interaction reads

The ellipsis stands for terms which involve higher powers of the pion field. Their coefficients are fixed by chiral symmetry. At second order, the effective Lagrangian also contains terms proportional to the quark masses. The fact that the lowest-order Lagrangian is fully determined by the nucleon mass and the matrix element of the axial charge shows how chiral symmetry constrains the interactions of mesons and baryons. However, the rapid increase in the number of parameters at higher orders makes it evident that it is not nearly as restrictive as in the meson sector. The number of parameters entering at each order is shown in brackets:

The larger number of low energy constants arises from the spin-; nature of the nucleon and because it stays massive in the chiral limit, so that the effective Lagrangian involves odd as well as even powers in the chiral expansion. In a given process only a handful of the outrageous number of terms in the fourth-order Lagrangian will contribute. The fact that the effective Lagrangian contains 118 terms a t fourth order,13 however, means that the chances that the same combination enters two different observables are rather dim: there will hardly be any symmetry relations valid to fourth order in the chiral expansion. 2.2

The low energy region and the role of resonances

The strongest constraints from chiral symmetry on the 7rN-scattering amplitude are obtained a t unphysically small values of Mandelstam variables, a t the Cheng-Dashen point s = u = m:, t = 2M:. In figure 1 the Mandelstam triangles for m r - and 7rN-scattering are compared. The figure makes it evident that the physical threshold for 7rN-scattering is a t higher energies: the

105

increase in s from the Cheng-Dashen point to the threshold is of O ( M T )for rN-scattering, while it is O(M:) for mr scattering. At threshold, higher-order

Figure 1. Comparison of the Mandelstam triangles for mr-and rrN-scattering.

terms in the chiral expansion will therefore be more important in n N - than in mr-scattering. This observation is confirmed by looking at the position of the first resonance. The increase in s from the Cheng-Dashen point to the first resonance is roughly the same in both cases: mz - m$ M m:. The relevant expansion parameter for the resonance contributions at threshold is, however, much larger for 7rN-scattering: 2mNM,/(m: x 0.4 >> 4M,/mE x 0.1. While the effective theory for the mcson sector will still yield meaningful results well above threshold, the A-resonance must be included into the Lagrangian if one wants to arrive at an accurate description of the meson nucleon amplitude above threshold. This can be done in a systematic way by counting the mass difference S = m, - mN as a small quantity of the same order as M,. This procedure is referred to as “small scale expansion” and allows one to resum the potentially large corrections associated with the resonance.8 While it is certainly important to get a handle on the resonance contributions, a few words of caution are appropriate: we are still performing a low energy expansion and there are higher-order terms not associated with the resonance. In particular, the inclusion of the A has so far only be performed in the non-relativistic

mt)

106

framework for baryon CHPT (to be discussed in the next subsection) and the higher-order kinematic corrections are important already in the threshold region. Furthermore, the effective theory which includes the A is not unique: recently it has been claimed that the effective Lagrangian is compatible with different counting schemes; it seems in general not possible to decide from first principles at which order a given operator enters. l4 The 7rN-scattering amplitude has been calculated to third order in this combined expansion in 6 and the meson momenta.15 The calculation confirms that the bulk of the A contribution stems from the resonance pole term. According to the authors, the energy range in which their results reproduces the existing data is only slightly larger than for the fourth-order calculation in pure CHPT. 2.3 Formulation of the eflective t h e o y In the low energy expansion, the baryon four momentum Pp has to be counted as a large quantity, since P 2 = rn; is of the size of the typical QCD scale squared. If we choose a frame, where the baryon is initially at rest and let it interact with low energy pions, the nucleon will remain nearly static, its three momentum being of the order of the meson mass. The chiral expansion of the corresponding amplitudes in the momenta and masses of the mesons therefore leads to an expansion of the nucleon kinematics around the static limit. This expansion is implemented a b initio in the framework called heavy baryon chiral perturbation theory (HBCHPT).l' However, the expansion of the kinematics fails t o converge in part of the low energy region. The breakdown is related t o the fact that the expansion of the nucleon propagator in some cases ruins the singularity structure of the amplitudes. This makes it desirable to perform the calculations in a relativistic framework. In doing so, the correct analytic properties of the amplitudes are guaranteed, and one can address the question of their chiral expansion in a controlled way. In the relativistic formulation of the effective theory a technical complication arises from the fact that in a standard regularization prescription, like dimensional regularization, the low energy expansion of the loop graphs starts in general at the same order as the corresponding tree diagrams.17 Since the contributions that upset the organization of the perturbation expansion stem from the region of large loop momentum of the order of the nucleon mass, they are free of infrared singularities. In d-dimensions, the infrared singular part of the loop integrals can be unambiguously separated from the remainder, whose low energy expansion to any finite order is a polynomial in the momenta and quark masses. Moreover, the infrared singular and regular parts of the amplitudes separately obey the Ward identities of chiral sym-

107

metry. This ensures that a suitable renormalization of the effective coupling constants removes the infrared regular part altogether, so that we may drop the regular part of the loop integrals and redefine them as the infrared singular part of the integrals in dimensional regularization, a procedure referred to as infrared regularization. l8 The representation of the various quantities of interest obtained in this way combines the virtues of HBCHPT and the relativistic formulation: both the chiral counting rules and Lorentz invariance are manifest at every stage of the calculation. In the meantime, this relativistic framework has been used to calculate the scalarls, axiallg and electro-magnetic form factors20 as well as the elastic pion-nucleon amplitude3 to fourth order in the chiral expansion. Recently, the Gerasimov-Drell-Hearn sum rule has been reanalyzed and it was found that the recoil corrections, which are summed up in the relativistic approach, are rather large.21 3 3.1

Pion-nucleon scattering

Low energy theorems

Chiral symmetry constrains the strength of the 7rN-interaction as well as the value of the scattering amplitudes at the Cheng-Dashen point. The fourthorder result for the scattering amplitude allows us to analyze the corrections to the low energy theorems that arise at leading order in the expansion and we find that the symmetry breaking corrections are rather small. As a first example, let us consider the Goldberger-Treiman relation

If the masses of the up- and down-quarks are tuned to zero, the strength of the .rrN interaction is fully determined by gA and F,: ACT = 0. Up to and including terms of third order in M,, the correction has the form

ACT = cM:

+ O(M:).

It is remarkable that the correction neither involves a term of the form M: In(%) (a “chiral logarithm”) nor a correction of order M,. Such inm N frared singular terms are present in the chiral expansion of g,N, QA, F, and m,, but they cancel out in the above relation. To this order, the correction is thus analytic in the quark masses. If the low energy constant c is of typical size, c M 1/GeV2, the correction to the Goldberger-Treiman relation is 2%. If one evaluates the above relation with value for the coupling constant given in Hohler’s comprehensive review of .rrN-scattering22,one finds ACT = 4%. The

108

data accumulated since then seems t o favor a smaller value of g,N reducing the correction t o 2-3%. Another well known low-energy theorem relates the value of the isosymmetric amplitude D f at the Cheng-Dashen pointa C = F,D 2 -+ ( s = m t , t = 2M:) to the scalar form factor

(N‘I mu Uu

+ m d dd IN) = a ( t )U’U .

The relation may be written in the form C = a(2M:)

+ A,,

.

The theorem states that the term A,, vanishes up t o and including contributions of order M,”. The explicit expression obtained for C when evaluating the scattering amplitude t o order q4 again contains infrared singularities proportional to M: and M: lnM,”/m;. Precisely the same singularities, however, also show up in the scalar form factor at t = 2M;, so that the result for AGO is free of such singularities:

A,,

= d M,“

+ O(M,).

A crude estimate like the one used in the case of the Goldberger-Treiman relation indicates that the term A,, must be very small, of order 1 MeV. Unfortunately, the experimental situation concerning the magnitude of the amplitude at the Cheng-Dashen point leaves much t o be desired. The inconsistencies between the results of the various partial wave analyses need to be clarified in order t o arrive at a reliable value for g , N . Only then it will be possible t o extract a small quantity like the C-term from data.’ 3.2

M o m e n t u m dependence: analyticity and unitarity

To obtain the amplitudes in the region around the Cheng-Dashen point, the experimental results need to be extrapolated to the subthreshold region. The extrapolation can only be performed reliably, if the correct structure of the singularities of the amplitude is implemented into the data analysis. Having to deal with functions of two variables, this is not a simple task and while all aThe bar indicates that the pseudwvector Born term has been subtracted. *Jugoslav Stahov has reported a t the conference that discrepancies in the higher partial waves of different partial wave analyses can explain the inconsistencies between different determinations of the C-term.23

109

modern partial wave analyses incorporate some of these constraints, subsequent analyses have not kept up with the high level of sophistication reached by the Karlsruhe-Helsinki collaboration in the eighties. Because of the complexity of a dispersive analysis, it is tempting to use the representation obtained in chiral perturbation theory to perform the extrapolation to the unphysical region, since the use of a relativistic effective Lagrangian guarantees the correct analytic properties in the low energy region. The problem with this approach is that unitarity is not exact in the chiral representation, but only fulfilled to the order considered. At one loop level, the imaginary part will be given by the current algebra amplitudes squared. Since the corrections to the current algebra result become sizeable above threshold, the violation of unitarity will prevent an accurate extrapolation to the subthreshold region in this framework. This is illustrated in figure 2, where we compare the result obtained in CHPT with the KA84 solution.24 The parameters in the chiral representation have been adjusted t o the KA84 solution a t the threshold and we want to check the energy range in which we reproduce the KA84 solution. For the amplitude D+, the deviation in the region around the Cheng-Dashen point would translate into a 10 MeV uncertainty in the C-term. The accuracy is better in the case of the amplitude D - , but also in this case the chiral representation starts to deviate soon after threshold. There are various prescription^^^ t o fix the problem by hand: one can, e. g. ,use the K-matrix formalism to unitarize the amplitudes found in CHPT. Once some resonances are added in, these unitarized amplitudes usually fit the data very nicely, however, this “solution” has its price: the unitarizations usually ruin crossing symmetry and analyticity, by introducing unphysical singularities into the results, making their use for an extrapolation to lower energies doubtful. We have set up a framework that combines the analytic structure found in CHPT with the constraints from ~ n i t a r i t y one : ~ starts by writing a dispersive representation for the result found in the low energy effective theory. This representation splits the amplitude into a polynomial part and nine functions of a single variable, which are given by integrals over the imaginary parts of the amplitude. In the elastic region, unitarity then leads a set of coupled integral equations for these functions, similar to the Roy equations in m-scattering. Replacing the imaginary parts found in CHPT by the experimental imaginary parts in the inelastic region and solving the equations iteratively one arrives at a representation of the amplitude that fulfills both the constraints from unitarity and analyticity. In addition to the imaginary parts, this system of equations also needs four subtraction constants as an input. One of them can

110

- CHPT O(g4) I

1-80 1

02

04

06

v

I

OX

%l?!D0.7 1 I

70 60

0.2

0.1

0.6

0.8 Y

1

1.:

1.4

Figure 2. Real part of the pion-nucleon amplitude at zero momentum transfer. The variable v denotes the lab. energy of the incoming pion. The reaction threshold is at v = M,. The red line is the result obtained at the fourth order in the chiral expansion. The black curve corresponds to the KA84 solution.

be expressed as an integral over the total cross section, while the other three need to be pinned down from the experimental information at low energies. The results from the study of pionic hydrogen, to be discussed below, should subject these constants to stringent bounds. 3.3 Isospin violation, pionic hydrogen

To study strong isospin breaking, one needs to disentangle it from electromagnetic isospin violation. Since both are of similar magnitude, they need to be treated simultaneously, making it necessary to incorporate the photon field as an additional degree of freedom into the low energy effective Lagrangian. In

111

-

the baryon sector, the corresponding Lagrangian has been worked out to third order5 in a simultaneous expansion in m, q2 e2 and the result for the pion-nucleon scattering amplitude has been worked out to the same order.6 An important application of the low energy effective theory of QCD+QED is the extraction of the hadronic scattering length from the measurements of the strong interaction width and level shifts of hadronic atoms. The goal of the experiments with pionic hydrogen (the bound state of a T- with a proton) at PSI 26 is to measure these quantities at the level of one per cent. In order to extract the pure QCD scattering lengths from the measurements, one needs to remove isospin breaking effects with high precision. The framework for the calculation has been set up and by now, the calculation of the strong energy shift has been carried out to next-to-leading order in isospin breaking.7 The results differ significantly from earlier potential model calculations which fail to consistently incorporate all of the interactions present even at the leading order. At present, the main uncertainty in the result of the effective theory is the value of the low energy constant fi , whose value is as yet unknown. 4

Conclusions

We have a good understanding of how chiral symmetry manifests itself in the baryon sector. Chiral symmetry breaking effects, on the other hand, are small and their determination from measurements is nontrivial. The reason being that, in many cases, we cannot directly confront the low energy theorems of the symmetry with the experimental data taken at higher energies. In this situation, the precise extrapolation of the data to lower energies becomes a central issue. While the representations obtained in CHPT are not suitable for this purpose, their analytic structure can be implemented into a dispersive analysis.

Acknowledgments I would like to thank the organizers for this stimulating and pleasant conference. This work has been sponsored by the Department of Energy under grant DE-AC03-76SF00515. References 1. J. Gasser and H. Leutwyler, Annals Phys. 158,142 (1984), J. Gasser and H. Leutwyler, Nucl. Phys. B 250, 465 (1985)

112

2. N. Fettes and U. G. Meianer, Nucl. Phys. A 676, 311 (2000) [hepph/0002162]. 3. T. Becher and H. Leutwyler, JHEP 0106, 017 (2001) [hep-ph/0103263]. 4. J. A. McGovern and M. C. Birse, Phys. Lett. B 446, 300 (1999) [ h e p ph/9807384]. 5. G. Muller and U. G. Meianer, Nucl. Phys. B 556, 265 (1999) [hepph/9903375]. 6. U. G. MeiBner and S. Steininger, Phys. Lett. B 419, 403 (1998) [hepph/9709453], N. Fettes and U. G. Meifher, Phys. Rev. C 63, 045201 (2001) [hepph/0008181], N. Fettes and U. G. MeiOner, Nucl. Phys. A 693, 693 (2001) [hepph/0101030]. 7. J. Gasser, M. A. Ivanov, E. Lipartia, M. MojiiS and A. Rusetsky, Groundstate energy of pionic hydrogen to one loop, hep-ph/0206068. 8. T. R. Hemmert, B. R. Holstein and J. Kambor, J. Phys. G 24, 1831 (1998) [hep-ph/9712496]. 9. For a recent review, see H. W. Griesshammer, An Introduction to Few Nucleon Systems in Effective Field Theory, nucl-th/0108060. 10. J. N. Labrenz and S. R. Sharpe, Phys. Rev. D 54, 4595 (1996) [heplat/9605034]. 11. J. W. Chen and M. J . Savage, Phys. Rev. D 65, 094001 (2002) [heplat/0111050]. 12. Two recent reviews are H. Leutwyler, Chiral dynamics, in Shifman, M. (ed.): At the frontier of particle physics, vol. 1, 271-316 [hep-ph/0008124], U. G. Meifher, Chiral QCD: B a y o n dynamics, ibid. , 417-505 [hepph/0007092]. 13. N. Fettes, U. G. Meifher, M. MojiiS and S. Steininger, Annals Phys. 283, 273 (2000); Erratum-ibid. 288, 249 (2001), [hep-ph/0001308]. 14. T. R. Hemmert and W. Weise, hep-lat/0204005. 15. N. Fettes and U. G. Meifher, Nucl. Phys. A 679, 629 (2001) [hepph/0006299]. 16. E. Jenkins and A. V. Manohar, Phys. Lett. B 255, 558 (1991). V. Bernard, N. Kaiser, J. Kambor and U.-G. MeiBner, Nucl. Phys. B 388, 315 (1992). 17. J . Gasser, M. E. Sainio and A. Svarc, Nucl. Phys. B 307, 779 (1988). 18. T. Becher and H. Leutwyler, Eur. Phys. J . C 9, 643 (1999) [hepph/9901384].

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19. J. Schweizer, Low energy representation for the axial f o r m factor of the nucleon, diploma thesis, Bern 2000. 20. B. Kubis and U. G. MeiBner, Eur. Phys. J. C 18, 747 (2001) [hepph/0010283]. B. Kubis and U. G. Meiher, Nucl. Phys. A 679, 698 (2001) [hepph/0007056]. 21. V. Bernard, T. R. Hemmert and U. G. Meifher, hep-ph/0203167. 22. G. Hohler, in Landolt-Bornstein, 9b2, ed. H. Schopper (Springer, Berlin, 1983). 23. J. Stahov, The dependence of the experimental pion-nucleon sigma term o n higher partial waves, hep-ph f0206041. 24. R. Koch, Z. Phys. C 29 (1985) 597. 25. For recent work along those lines, see e. g. U. G. MeiOner and J. A. Oller, Nucl. Phys. A 673, 311 (2000) [nuclth/9912026], M. F. Lutz and E. E. Kolomeitsev, Nucl. Phys. A 700, 193 (2002) [nuclth/0105042], S. Kondratyuk, Pion nucleon amplitude near threshold: The sigma-term and scattering lengths beyond few loops, nucl-th/0204050. 26. G.C. Oades et al. , Measurement of the strong interaction width and shijl of the ground state ofpionic hydrogen, PSI Proposal R-98-01, H. C. Schroder et al. , Eur. Phys. J. C 21, 473 (2001).

114

Harald Griesshammer and Harald Merkel

Leonid Gloman and Yuri Simonov

ELECTROMAGNETIC TESTS OF CHIRAL SYMMETRY HARALD MERKEL for the A1 COLLABORATION Institut f i r Kernphysik, Johannes Gutenberg-Universitat, 55099 Mainz, Germany E-mail: [email protected] An overview of recent results in threshold pion production is given. While the photoproduction data are in impressive agreement with calculations in the framework of Chiral Perturbation Theory, electroproductiondata at low four-momentum transfer shows severe deviations from these calculations.

1

Introduction

Chiral Perturbation Theory is a consistent scheme to utilize the symmetries of QCD to predict observables at the confinement scale. An overview of the theoretical status of this field is given by the contribution of Th. Becher in these proceedings. In this talk, the current status of the neutral pion photo- and electroproduction experiments near threshold is discussed. Since the pion is the Goldstone Boson of the chiral symmetry breaking, these experiments are well suited to test the predictions of Heavy Baryon Chiral Perturbation Theory (HBChPT)l. 2

Neutral Pion Photoproduction

First experiment^^>^ on threshold pion photoproduction were aimed to test the predictions of Low Energy Theorems4 for the threshold value of the s wave multipole amplitude Eo+. The severe disagreement between these theorems and the experiments was resolved in the following years by refined calculations in HBChPT5, which also gave predictions for the p wave multipole combinations

Pi P2 P3

Mi+ - M i = 3&+ - Mi+ + M i = 2M1+ + Mi-. = 3E1+ -j-

(1)

(2)

(3) The calculations showed, that the s wave amplitude is only slow converging in the chiral expansion, while the p wave combinations Pi and P2 are strong predictions in this framework. P3 is given by a low energy constant of HBChPT and has to be determined by the experiment.

115

116

4.5

.

A. Schmidtetal.

4.0 . 0 M.Fuchsetal. 0 J.C. Bergstrom et al. 3.5 .n

am

3.0

a 2.5

\

2.0 1.5 1.o

0.5 0.0 144

147

150

153

156

159

162

165

168

E, I MeV Figure 1. The total cross section for neutral pion photoproduction a t threshold. Data from SAL6 and MAMI

2.1

Differential Cross Section

The first experimental access to the multipoles is the measurement of the differential cross section. With the assumption, that only s and p waves contribute at threshold, the angular structure of the cross section is given by c(O) = -9( A + B . c o s O + C . c o s 2 0 )

k with the phase space factor f and three angular coefficients A = Ei+

+ 51 (Pz2+ P32)

(4)

B = 2 . Re (EO+Pl') c = P12- -21 (P22+ P32) Fig. 1 summerizes the quality of the existing data sets by the total cross section versus the incoming photon energy. The SAL data6 and the new MAMI data7 agree, while the old MAMI data set8 seems to have some systematic errors at higher energies.

117

0.4

0.3 0.2 0.1

W 0.0 -0.1

I

1

1

.....,..... HBChF'T

--- DR

-0.2

-0.3

' 0

- fit to the data

H A. Schmidt et al.

20

40

60

80

100 120 140 160 180

Figure 2. Polarized photon asymmetry measured a t MAM17 in comparison with calculations in ChPT5 and in Dispersion Relations formalismg.

2.2 Polarized Photon Asymmetry From unpolarized cross section experiments, the s wave multipole IEo+l and the p wave combinations PI and P23 = i(P2' P3') can be extracted. To further decompose all multipoles, a further observable has to be measured. A convenient choice is the polarized photon asymmetry C with the multipole decomposition

+

Such an experiment was performed at MAM17 at the tagged photon beam of the A2 collaboration with the TAPS detector for the detection of the 7ro decay photons. The polarized photon beam was produced by coherent Bremsstrahlung from a diamond crystal. Fig. 2 shows the asymmetry C, averaged over the energy range of the experiment. With this experiment, for the first time a complete separation of the p waves is possible. The results are given in table 1, in comparison with the predictions of Chiral Perturbation Theory (CHPT)5 and Dispersion Relati~ns(DR)~. Within the error bars, the two existing high resolution ex-

118 Table 1. Experimental multipole amplitudes for photoproduction from MAMI' and SAL6 in comparison with Chiral Perturbation Theory (CHPT))5 and Dispersion Relations (DR).

(10-~/""

MAMI SAL ChPT

-1.31f0.08 -1.321t0.05 -1.16 -1.22

(qlc. 1 0 - ~ / ~ : ) (qlc. 1 0 - ~ / ~ : ) ( q k .1 0 - ~ / ~ 9 )

10.02f0.2 10.26f0.1 10.33k0.6 10.54

-10.5f0.2

13.1f0.1

-11.Of0.6 -11.4

11.7f0.6 10.2

periments and the quoted calculations agree. The deviation for p% of ChPT can be removed by re-fitting the low energy constants to the new data set.

3

Electroproduction at low Q2

Additional information on the pion production mechanism can be extracted from electroproduction experiments. While e.g. the multipole combination flj is basically a fit parameter in the description of the photoproduction data, the extention of this quantity to virtual photons is given in ChPT without further degrees of freedom. In addition, the longitudinal s wave amplitude LO+and two further p wave combinations can be extracted. First experiments at a photon virtuality of Q2 = 0.1 (GeV/c)2 aimed to extract the s wave amplitudes at threshold'0:''.12. These experiments were in reasonable agreement with calculations'3, but the value of Q2 = 0.1 (GeV/c)2 is somewhat to high for the convergence of ChPT. Therefore, a further experiment at an intermediate value of Q2 = 0.05 (GeV/c)2, half way between photoproduction and the existing data was performed at MAMI14. The results were surprising, as can be seen in fig. 3, which shows the differential cross section for the virtual photon polarization E = 0.72. In this figure, the cross section at four different values of the center of mass energy W is compared with CHPT and the phenomenological model MAID15. To show the consistency of the data, a fit with the assumption of only s and p waves contributing to the cross section is also included. As can be seen, the magnitude of the cross section is nearly half the prediction of ChPT and MAID. To illustrate the discrepancy further, figure 4 shows the total cross section as function of Q2. In this observable, the statistical error of all data points is very small and only systematic errors play a role. Thus, the clear discrepancy between data and calculations, but also the increasing discrepancy between ChPT and MAID is visible.

119

-

AW = 1.5 MeV

30

L

cn

\

a

d 20 *n

& = 10 13 0 0"

45"

90" 135" 180" 0"

45"

90" 135" 1E 3"

Figure 3. Differential cross sections for the first 4MeV above threshold for the virtual photon polarization 6 = 0.72. The solid line represents a fit with the assumption of only s and p waves contributing, the dashed and dash-dotted lines represent the predictions of ChPT13 and MAIDIS.

Table 2 tries to compare all existing data of pion production from the proton by using the same kind of fit for all experiments. The extracted multipoles deviate from the quoted values in the corresponding publications, since most of them were extracted in the past with further model assumptions to reduce the error bars. As can be seen, the deviation seems to be burried in the multipole combination P23, which is already fixed by photoproduction and can not be adjusted in the calculation to describe the data. Since the discrepancy is large and surprising, this subject urgently needs further investigation. An experiment at MAMI is planned to cover a continuous range in Q2, while an independent experiment is planned at JLab16 with extended kinematical coverage using a large acceptance spectrometer.

120

2.0-

1.o

-

-

--

AW = 0.5 MeV

*

L

v)

\

a

A0.5 -

1.5:

AW = 1.5 MeV

--

1.0-

c

d

0.00

0.05

0.10

0.00

0.05

0.1

Figure 4. The total cross section utot versus Qz, at a value of E = 0.8. The solid (dashed) line is the prediction of ChPT13 (MAID"), data points a t Q2 = 0 and 0.1 GeV2/c2 from 7,12.

4

Electroproduction from the Deuteron

The low energy constants of ChPT were adjusted, as shown above, to describe the existing pion photo- and electroproduction data from the proton. By this, one looses some of the predictive power of CHPT, since in threshold experiments the complete amplitude is already given by only few parameters. On the other hand, from the description of the proton amplitudes one can extract predictions for the pion production from the neutron without introducing further degrees of freedom.

121 Table 2. Extracted multipole amplitudes in comparison with the threshold values of ChPT13 and MAID". The AmPSll value for JLo+l was extracted from their value for a0 x e ~ l L o + I ~For . the AmPS lo fit LO+ was fixed, since no Rosenbluth separation was performed

MAM17 ChPT MAID

MAMI12 AmPSlO ChPT MAID

-1.33 -1.14 -1.16

-1.70 -1.29

0.58 f0.18 1.99 f0.3 1.42 2.2

Q2 = 0.1 GeV2/c2 573 -1.38 fll fO.O1 526 -1.33 fixed f 7 -1.33 571 -1.12 315

111 105 95

9.5 9.3 9.3

15.1 50.8 16.4 f0.6 20.1 17.1

-0.6 -3.0

-2.3 f0.2 -1.0 f0.4 -0.6 -1.1

-0.2 2.2

.

0.1 f0.3 -1.0 f0.4 -0.1 1.4

Despite this theoretical advantage, the experimental access to the free neutron amplitude is, as usual, quite difficult. The most promising access seems to be the coherent pion production from a deuteron target. In impulse approximation, the production amplitude is basically given by the coherent isescalar sum of the free proton and free neutron amplitude, corrected by form factors as parameterization of the deuteron structure. In this formalism, special care has to be taken for the rescattering contribution by charged pions in the intermediate state. Current calculations for photo17 and electroprod~ction~~ are restricted to predictions of the threshold s wave amplitudes, since the mixing of the free p wave amplitudes in the re-

122

gion of the breakup of the deuteron to the coherent p wave amplitude from the deuteron requires a substantial extension of the formalism. A first measurement of the photoproduction amplitude was performed at SAL20. The IGLOO detector was used to detect the decay photons of the T O decay in coincidence. By this technique, the missing mass resolution is not sufficient to separate the coherent channel from the deuteron breakup. By calculating this contribution in a simple model the authors were able to extract the threshold value of the s wave amplitude to Ed = (-1.45f0.09) x lO-"/m,. This value falls about 20% below the prediction of ChPT17 of Ed = (-1.8 f0.6) x 10-'/m, but the agreement seems reasonable within the error bars. The extension of this experiments to finite Q2introduces further experimental difficulties. Due to the background conditions for electroproduction the detection of the pion decay photons has to be replaced by the detection of the recoil deuteron, which suffers at the low energies at threshold from energy loss and multiple scattering. On the other hand, by this technique the coherent channel is clearly separated from the deuteron break up reaction and can be extracted without model assumptions. A first threshold measurement of d(e, e'd).rrO was performed at MAMI18. The detection of the deuteron limited this experiment to a four momentum transfer of Q2 = 0.1 (GeV/c)2. As for the similar experiments from the proton, the full center of mass angle was covered up to 4 MeV above threshold and a Rosenbluth separation was performed. While the complete angular structure was measured, only for the s wave threshold multipoles existed a prediction from ChPT. To extract these amplitudes, a fit with the assumption of only s and p wave contributions was performed (fig. 5). Since the electric s wave contribution to the cross section is very small, only an upper limit could be extracted for Ed:

5 0.42. w 3 / m , lLdl = (0.50 f 0.11) ' 10-'//m,. Fig. 6 shows this result in comparison with the calculations of ChPTlg. The dash-dotted curve shows the calculation without rescattering contributions while the solid curve shows the full calculation. The dashed lines are the full calculation with the contribution of the free neutron amplitude varied by f10-3/m, to picturize the sensitivity to this amplitude. As can be seen from this comparison, the electric multipole E d is in agreement within the error bars with the calculations, while the longitudinal multipole Ld is clearly overestimated by theory. In terms of the s wave cross section 00 = €LILd12 the discrepancy is an order of magnitude.

+

123

CMS Energy AW [MeV] Figure 5. The total cross section for three different values of the photon polarization E. The lines show the result of a least squares fit with the assumption of only p and s waves contributing t o the cross section near threshold.

An attempt to explain this huge discrepancy was made by Rekalo and Tomasi-Gustafsson21. They argued, that the contribution of the rescattering terms with an intermediate pion should be suppressed by the Pauli principle and parity conservation. Omitting these graphs would lead to an agreement between the ChPT calculations and the MAMI data.

Acknowledgments This work was supported by the Deutsche Forschungsgemeinschaft(SFB 441) and the Federal State of Rhineland-Palatinate.

124

Ewald et al. Bergstrom et al.

I 0

I

0.05 2 2 -q2 [GeV / c ]

0.

2.01

Figure 6. The extracted 3 wave multipoles from MAMI's(circles) in comparison with the prediction of ChPTXg.The photon point of SAL2' is plotted as a square. For the explanation of the curves see text.

125

References 1. 2. 3. 4.

5.

6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

V. Bernard et al., Nucl. Phys. B 383 (1992) 442 E. Mazzucato et al., Phys. Rev. Lett. 57, 3144 (1986). R. Beck et al., Phys. Rev. Lett. 65, 1841 (1990). P. de Baenst, Nucl. Phys. B24, 633 (1970); I. A. Vainshtein and V. I. Zakharov, Nucl. Phys. B36, 589 (1972). V. Bernard, N. Kaiser, J. Gasser, and U.-G. MeiBner, Phys. Lett.B268, 291 (1991); V. Bernard, N. Kaiser, and U.-G. MeiBner, Z. Phys. C 70,483 (1996). J. C. Bergstrom et al., Phys. Rev. C 53, R1052 (1996). A. Schmidt et al., Phys. Rev. Lett. 87, 232501 (2001). M. Fuchs et al., Phys. Lett. B 368, 20 (1996); A. M. Bernstein et al., Phys. Rev. C 55, 1509 (1997). 0. Hanstein et al., Phys. Lett. B 399 (1997) 13 H. B. van den Brink et al., Phys. Rev. Lett. 74, 3561 (1995). T. P. Welch et al., Phys. Rev. Lett. 69, 2761 (1992). M. 0. Distler et al., Phys. Rev. Lett. 80, 2294 (1998). V. Bernard, N. Kaiser, and U.-G. MeiBner, Nucl. Phys. A607, 379 (1996); A633, 695(E) (1998). H. Merkel et al., Phys. Rev. Lett. 88, 012301 (2002) D. Drechsel et al., Nucl. Phys. A645, 145 (1999); S. S. Kamalov et al., Phys. Lett. B 522, 27-36 (2001). R. Lindgren et al., Experiment E01-014, JLab, 2001. S.R. Beane et al., Nucl. Phys. A 618, 381 (1997) I. Ewald et al., Phys. Lett. B 499, 238-244 (2001) V. Bernard, H. Krebs, U.-G. MeiBner, Phys. Rev. C 61, 58201 (2000) J. C. Bergstrom et al., Phys. Rev. C 57 6, 3203 (1998) M. Rekalo and E. Tomasi-Gustafsson, nucl-th/Ol12063

HADRON STRUCTURE FROM LATTICE QCD* G. SCHIERHOLZ John won Neumann-Institut fur Computing NIC, Deutsches Elektronen-Synchrotron DESY, 0-15738 Zeuthen, Germany and Deutsches Elektronen-Synchrotron DESY, D-22609 Hamburg, Germany E-mail: [email protected] I present an overview of both the technical issues involved and the progress made so far in the study of hadron structure using lattice QCD.

Introduction

1

Understanding the structure of hadrons in terms of quark and gluon constituents, in particular how quarks and gluons provide the binding and spin of the nucleon, is one of the outstanding problems in particle physics. While perturbative QCD has been crucial in extracting quark, gluon and helicity distributions of the nucleon from experiment, it is inadequate for the more fundamental challenge of calculating them from first principles. The lattice formulation of QCD, combined with numerical simulations, is the only known way of addressing the non-perturbative properties of the theory without any model assumptions. Lattice calculations of hadron matrix elements are rather complex and progress has been slow. However, continuing advances in computing power, and recent theoretical developments, such as - O(a) improvement of the action and the operators, to reduce finite cut-off

effects and to facilitate the extrapolation to the continuum limit, - (non)-perturbative renormalization and matching of the (bare) lattice

operators, -

chiral perturbation theory, to extrapolate reliably from the masses where the lattice calculations are performed to the physical pion mass,

have now brought lattice QCD to the point that definitive quantitative calculations of a host of hadron observables are becoming possible. *This talk is largely based on work done by the QCDSF Collaboration: S. Capitani, M. Gockeler, R. Horsley, B. Klaus, W. Kiirzinger, H. Perk, D. Petters, D. Pleiter, P. W o w , S. Schaefer, A. Schafer, G. Schierholz and A. Schiller.

126

127

In this talk I will highlight recent developments in lattice calculations of hadron structure functions. Special attention will be devoted to higher twist contributions. Due to lack of space I will not be able to cover recent results on nucleon form factors, and I refer the interested reader to the 1iterature.l 2

Theoretical developments

Before I present any results, let me briefly comment on the theoretical developments. There are various choices of discretizing the QCD action, and here the fermion action is of particular interest. The original, unimproved Wilson action S F has discretization errors of O ( a ) , which can be as large as 20% at typical lattice spacings of a M 0.1 fm.2 On top of that it breaks all chiral symmetries. The most promising action is Neuberger's a ~ t i o nwhich , ~ has discretization errors of O ( a 2 )only and possesses an exact chiral ~ y m r n e t r y But .~ numerical simulations of this action take a factor of O(100) more computer time, which limits it to exploratory studies at the moment. A fair compromise is the non-perturbatively improved Wilson action

which, likewise, reduces discretization errors to O ( a 2 )in on-shell quantities, such as masses and matrix elements, if the operators are improved as well:

+

0 + (1 co a m p

+a

c

ci Oi.

i2l

The condition is that the coefficients CSW, cot c1, . . . are computed to nonperturbative precision. The improvement program can be extended to off-shell quantities ~ o o . Furthermore, ~ , ~ the axial Ward identities can be satisfied to so that a systematic restoration of chiral symmetry is possible. The coefficient csw is known non-perturbatively,' while the improvement coefficients of the operators are largely known in one-loop perturbation theory,6910 and to a lesser extent non-perturbatively.ll But the list of non-perturbatively known coefficients is steadily increasing. l2 Another important theoretical issue is renormalization. The lattice operators are, in general, divergent (in the limit a -+ 0) and need to be normalized, O S ( p )= Z@(a),

S : scheme,

(3)

where S must match the normalization condition of the corresponding, perturbatively calculated Wilson coefficient. Usually this is the scheme. As

m

128

5.0 4.0

~

t

1.o

1

#

10

100

(r,d Figure 1. The non-perturbative renormalization constants Z R G r (solid symbols) for quenched Wilson fermions at ,B = 6.0 as a function of ( r ~ p(where ) ~ TO = 0.5 fm), compared with the perturbative results (dashed lines).

long as there are at most logarithmic divergences present, a perturbative calculation of the renormalization constants is possible, and many results have been reported in recent years, both for unimproved l 3 and improved Wilson fermiom6 Because the coupling constant is large, perturbative results are not always reliable, and non-perturbative techniques have been developed. 14,15716 In Fig. 1 I show a comparison of perturbative and non-perturbative renormdization constants for the operators that give the first three moments of the unpolarized structure function of the nucleon, (z), (z2) and (z3).The renormalization constants have been converted to the renormalization group invariant ( R G I ) form ZRG' = AZsZs, using tadpole improved, renormalization group improved, boosted perturbation theory.I7 For the lower two moments the agreement is surprisingly good. The lattice data show distinct discretization errors at larger p2 values though, which grow with the size of the operators (in lattice units) involved. We have made the observation that most of the discretization errors are perturbatively calculable,'8 which should help to remove this source of error and find more convincing plateau values from our simulations. The lattice calculations are currently limited to quark masses that are equivalent to pion masses of m, 2 400 MeV in the quenched case, and to m, 2

129

500 MeV in full QCD. As a result, the lattice data have to be extrapolated to the chiral limit before they can be compared with experiment. Such an extrapolation is far from trivial and must respect the constraints imposed by chiral symmetry, in particular as the existence of Goldstone bosons leads, in general, to a behavior which is non-analytic in the quark mass. At small pion masses hadronic observables can be systematically expanded in a series in m, using chiral perturbation theory. Recently, one-loop formulae became available for the moments of the unpolarized and polarized structure functions of the nucleon, as well as for the tensor charge:”

analytic terms, analytic terms, analytic terms, where NS stands for the non-singlet or valence quark contribution, g A is the axial vector coupling of the nucleon, and A is a phenomenological parameter which determines the scale above which pion loops no longer yield rapid variation. Similar formulae are available for singlet contributions 2o and nucleon form factors.21 The message is that the pion loop (cloud) results in a large deviation from linearity at small m,. This suggests that important physics is omitted by a naive (linear) extrapolation, and even though one need not calculate at the physical pion (quark) mass, the pion mass must be small enough that the parameters of the chiral expansion are well determined by the lattice calculations. 3

Structure functions

Basics

The nucleon has four structure functions, zF1, F2, g1 and g2. The operator product expansion (OPE) relates moments of them to nucleon matrix elements. For the unpolarized structure functions this reads

130

where the Wilson coefficients c are independent of the target, and vi2)are the leading, twist-two reduced matrix elements of the nucleon defined by

and being renormalized at the scale p. I will return to higher-twist contributions in the next section. In parton model language @ =: ( p - l

(8)

where qT (z, p ) (qI (z, p ) ) , the parton distribution function, measures the probability of finding a quark q (= u, d, . . . ) with fractional momentum 2 and helicity + (-) inside the nucleon. Similarly, for the polarized structure functions we have

In parton model language 1

-2 an

=: An4 =

1'

dsz"

(dZ,p ) - a(",P ) )

where Au - Ad = QA

7

131

o'6 h

0

II

s PI

t

1

0.4

A

x v

0.2

0

Figure 2. The lowest non-singlet moment (z)against (m.rro)2 (where TO = 0.5 fm) for improved quenched Wilson fermions, together with the phenomenological value (*). 0.a

0.6

h

0

0.2

0

Figure 3. The same as Fig. 2, but for improved N f = 2 dynamical Wilson fermions.

132

(A := A'), while d,, has twist three and no parton model interpretation. The structure of the nucleon is not completely described by the parton distributions (8) and (10). In addition we have22

where q l ( x , p ) (qT(Z,p)) measures the probability of finding a quark in an eigenstate $Iy5 = +1/2 (-1/2) in a transversely polarized nucleon, and g T ( p ) = 6u - 6d

(13)

is the tensor charge of the nucleon. The moments (12) are obtained from H H . . . Dp,,$, and reduced matrix elements of operators of the form i&,,ysDpl q L ( z ,p ) and q ~ ( ~ ,can p )be measured in Drell-Yan processes. The expressions given above refer to the continuum and chiral limit. The moments must not depend on the scale parameter p. In principle one could compute the Wilson coefficients in lattice perturbation theory ( p = l / u ) . This would save us from having to renormalize the operators (and the Wilson coefficients). But lattice perturbation theory converges badly, and it is extremely hard to do calculations beyond one (fermion) loop. At first sight it seems that all one has to do now is compute the reduced matrix elements on the lattice and renormalize the operators within the class of operators stated. However, the matter is complicated by the fact that current lattice fermions break chiral symmetry, which gives rise to mixing with lower dimensional operators of opposite chirality not showing up in the (continuum) OPE. I will restrict myself to a few highlights now. Among them are the chiral extrapolation of (sn), which is a hot subject right now, the axial vector coupling and the tensor charge, the former being a benchmark calculation of QCD, and the twist-three contribution d2 to the lowest moment of g2, which is of considerable phenomenological interest and a theoretical challenge as well.

Moments of unpolarized structure function In Figs. 2 and 3 I show the lowest non-trivial moment of the unpolarized parton distribution function for improved quenched 23 and improved N f = 2 dynamical Wilson fermions. (For a very recent calculation with unimproved Wilson fermions see Ref. 25.) Both quenched and dynamical results have been extrapolated to the continuum limit. (In the dynamical case the lever arm is very short though.) The quenched and dynamical results hardly differ. The lines are linear extrapolations to the chiral limit. They overestimate the phenomenological result 26 by approximately 40%. I estimate that 17324

133 0.6

0.4

om

ZZ

x

v

0.2

fl

X 0 Chiral MRS extrapol. 0

Chiral extrapol.

i1 0

Figure 4. The non-singlet moment (2)for quenched Wilson fermions at 0 = 6.0. The two leftmost points with larger error bars are obtained on 323 48 lattices, the other points on 243 32 and 163 32 lattices.

the renormalization constants have a systematic uncertainty of a few per cent only and, hence, cannot account for this discrepancy. The higher moments, which I cannot show here, show a similar effect. The arrows on the right-hand side of the figures point to the non-relativistic result. It is important to understand the origin of this deviation. It has been argued l9 that the light pion cloud is not adequately represented by a linear extrapolation in the quark mass. To test that, we are currently doing simulations at pion masses of 300 MeV and smaller on large lattices (m,L > 4, L being the linear extent of the lattice) for quenched Wilson fermions. (In the quenched approximation one encounters a pion cloud as well with slightly reduced coupling^.^^) In Fig. 4 I show some very preliminary results, which indicate that the data indeed bend down towards the phenomenological value, though it is too early to jump to conclusions. The curve shows an (unconditioned) fit of (4) to the lattice data, which reproduces the phenomenological number and gives A M 350MeV. If true, this means that one will have to do simulations at pion masses of m, 5 300 MeV in order to determine the parameters of the non-linear expansion reasonably well.

134

Axial vector coupling and tensor charge Before one can make contact with chiral perturbation theory, one has to extrapolate the lattice data not only to the continuum limit, but also to the infinite volume. In the unpolarized case we did not see significant finite volume effects in quenched and full QCD. For gA this is different. In the dynamical case g~ increases by x 10% if the lattice size is increased from L = 1.5 fm to L = 2.2 fm. In Fig. 5 I show Q A extrapolated to the infinite volume for improved dynamical f e r m i o n ~ The . ~ ~ data points lie on a straight line, as before. However, this time a linear extrapolation gives good agreement with experiment, while a non-linear extrapolation of the form (5), with A = O(400 MeV), would undershoot the experimental value by 30-40%. It should be noted that the amount of curvature depends crucially on the value of A, which is a phenomenological parameter and can vary from process to process. A different finds a rather flat dependence of gA on mT,combining chiral perturbation theory with Pad6 techniques. The arrow on the righ-hand side of the figure shows again the non-relativistic result. ~' In Fig. 6 I show our prediction for the tensor charge gT = ( 6 ~ - 6 d ) ~for improved dynamical fermions. It appears that it saturates Soffer's inequality 29

2gT 5 1 + g A .

(14)

Twist-three matrix element In our first paper3' on g2 we computed operator

d2

from the matrix element of the

and the corresponding renormalization constant Z 5( u p ) was computed perturbatively. The operator (15) has dimension five. This calculation has been copied by other authors25. It misses the point though that for Wilson-type fermions the operator (15) mixes with the operator

which has dimension four and opposite chirality to (15). Thus, the correct renormalization condition reads

The renormalization constant Z 5 ( a p ) and the mixing coefficient Z " ( a p ) have been computed recently.31 At p2 = 5GeV2 we find Z"/Z5 M -0.2, which

135

Figure 5 . The axial vector charge gA against ( r n , r ~ for ) ~ improved Nf = 2 dynamical Wilson fermions, together with the experimental value (*). 2

1.5

0.5

0

Figure 6 . The tensor charge ( b ~ - b d ) ~against ~' ( r n , r ~for ) ~improved Nf = 2 dynamical Wilson fermions.

136

0.00

.

-0.01.

zigure 7. The reduced matrix element dz a t p2 = 5GeV2 against the lattice spacing a for )roton (open symbols) and neutron (solid symbols), together with the experimental values at a = 0).

ias a big effect on the result of d 2 . In Fig. 7 I show d2 for quenched Wilson ermions and three /? values. The numbers have been extrapolated linearly o the chiral limit. Now, with mixing effects taken properly into account, we ind good agreement with experiment.

L

Higher twist contributions

'ower corrections to structure functions provide insight into the mechanism hat binds quarks and gluons to hadrons. Phenomenological determinations Nf quark and gluon distribution functions msume that power corrections are .egligible down to Q2 5 1 GeV'. But that has never been testified. The evaluation of power corrections is a very difficult task.32. Let us reonsider the lowest moment of F2, now including the twist-four contribution:

general, the twist-four matrix element v P ' ( p ) has an UV renormalon amiguity in any soft renormalzation scheme, which must be cancelled by a xresponding IR renormalon ambiguity in the Wilson coefficient c p )(Q 2 ,p ) . I

137 0.12,

,

I

I

I

,

I

O . 0O 4 5L - - - - - J

10

,

I

Q2

I

I

,

I

[G e15V ]

I

I

I

,

I

I

I

,

20

Figure 8. The non-singlet moment M 2 ( Q 2 )against Q2 in the quenched approximation at /3 = 6.0, compared with the phenomenological (parton model) result. T h e nucleon matrix elements have been extrapolated linearly t o the chiral limit.

To achieve this, one will have to compute the Wilson coefficient to very high orders in perturbation theory. The problem is unambiguously defined and amenable to calculation if operators and Wilson coefficients are regularized on the lattice:

Due to the hard cut-off (- l/a) "?)(a) has no renormalon ambiguity. Kowever, it will develop a quadratic divergence, which has to be cancelled by exactly the same singularity in the Wilson coefficient. This is only possible if c?)(Q2,p ) is computed non-perturbatively, i.e. on the lattice, as well. The moments (7) and (9) are obtained from the OPE

bIJp(dJv(-dlP)

+ '.= '

c

c ~ " p l . . . p , ,a( )~bl"E...pn l lP)

(20)

m,n

after Nachtmann i n t e g r a t i ~ n where ~ ~ , q is the euclidean photon momentum (q2 = Q2). On the lattice the left-hand side will receive contributions from seagull terms, which are denoted by dots. We truncate the series at spin > 4, which amounts to neglecting power corrections cx l/Q4. To determine the Wilson coefficients, we compute (plJ,(q)J,(-q)lp) . . and ( p I c 3 ~ . , , p , z Ifor p) a large set of quark states lp) of different momenta. This then defines a linear set of equations, which we can solve for ~ ~ ~ ~ ~ . by . ,a singular ~ ~ ( qvalue , ~ ) d e c o m p o ~ i t i o nTo .~~ obtain the moments of the nucleon structure function, we

+.

138

finally have to combine this calculation with a calculation of the appropriate nucleon matrix elements. A bonus of the calculation is that we do not have to renormalize the operatots. We encounter strong mixing effects between the twist-four matrix element "?)(a) and the Wilson coefficient c?)(Q2,a ) , as was to be expected. The net power corrections turn out to be small though. In Fig. 8 I show our results for the moment M2(q2)of proton minus neutron structure functions. The errors originate almost entirely from the nucleon matrix elements (which are independent of Q 2 ) , and so are highly correlated. We thus may conclude that power corrections are small down to Q2 values of a few GeV2. A recent experimental analysis comes to the same c o n c l u ~ i o n . ~ ~ 5

Conclusions

The precision of numerical results is steadily improving, due to increasing computer power, the use of improved actions and improved operators, and non-perturbative renormalization. The price is high though. For a modest calculation one needs to determine O(20) parameters to non-perturbative precision. First results on nucleon structure functions (and form factors) including the effects of dynamical quarks are available now. We do not see big differences between quenched and dynamical results in non-singlet quantities. By and large we find good agreement with experiment, except for (xn). Whether (z) will eventually approach the phenomenological value at small m,, as suggested by chiral perturbation theory, is currently being investigated. To estimate the range of applicability of chiral perturbation theory, and in particular to understand why it fails in the case of g A , a two-loop calculation would be very helpful. We were able to compute higher-twist contributions to nucleon structure functions in a completely non-perturbative setting. The resulting power corrections to the lowest moment of F2 turn out to be small, which I consider an important prediction.

References 1. M. Gockeler et al. [QCDSFCollaboration], Nucleon electromagnetic form factors from lattice QCD, to be published shortly. 2. M. Gockeler et al., Phys. Rev. D57 (1998) 5562. 3. H. Neuberger, Phys. Lett. B417 (1998) 141. 4. M. Luscher, Phys. Lett. B428 (1998) 342.

139

5. B. Sheikholeslarni and R. Wohlert, Nucl. Phys. B259 (1985) 572. 6. S. Capitani et al., Nucl. Phys. B593 (2001) 183. 7. G. Martinelli et al., Nucl. Phys. B611 (2001) 311. 8. S. Capitani et al., Nucl. Phys. (Proc. Suppl.) 63 (1998) 871. 9. K. Jansen and R. Sommer, Nucl. Phys. B530 (1998) 185; pvl. Guagnelli et al., Phys. Lett. B459 (1999) 594. 10. S. Sint and P. Weisz, Nucl. Phys. B502 (1997) 251. 11. For a summary of results see: T. Bhattacharya et al., Phys. Rev. D63 (2001) 074505. 12. R. Horsley, Nucl. Phys. (Proc. Suppl.) 94 (2001) 307. 13. G. Martinelli and Y.-C. Zhang, Phys. Lett. B123 (1983) 433; S. Capitani and G. Rossi, Nucl. Phys. B433 (1995) 351; G. Beccarini et al., Nucl. Phys. B456 (1995) 271; M. Gockeler et al., Nucl. Phys. B472 (1996) 309; S. Capitani et al., Nucl. Phys. B570 (2000) 393. 14. K. Jansen et al., Phys. Lett. B372 (1996) 275. 15. G. Martinelli et al., Nucl. Phys. B445 (1995) 81. 16. M. Gockeler et al., Nucl. Phys. B544 (1999) 699. 17. S. Capitani et al., Nucl. Phys. (Proc. Suppl.) 106 (2002) 299. 18. M. Gockeler et al. [QCDSF Collaboration], in progress. 19. W. Detmold et al., Phys. Rev. Lett. 87 (2001) 172001; D. Arndt and M. Savage, Nucl. Phys. A697 (2002) 429; J.-W. Chen and X. Ji, Phys. Lett. B523 (2001) 107. 20. D. Arndt and M. Savage, Ref. 19. 21. B. Kubis et al., Phys. Lett. B456 (1999) 240. 22. R.L. Jaffe and X. Ji, Phys. Rev. Lett. 67 (1991) 552. 23. M. Gockeler et al. [QCDSF Collaboration], in preparation. 24. M. Gockeler et al. [QCDSF-UKQCD Collaboration], in preparation. 25. D. Dolgov et al., hep-lat/0201021. 26. A.D. Martin et al., Phys. Lett. B354 (1995) 155. 27. J.W. Chen and M. Savage, nucl-th/0108042. 28. T.R. Hemmert, private communication. 29. J . Soffer, Phys. Rev. Lett. 74 (1995) 1292. 30. M. Gockeler et al., Phys. Rev. D53 (1996) 2317. 31. M. Gockeler et al., Phys. Rev. D63 (2001) 074506. 32. G. Martinelli and C.T. Sachrajda, Nucl. Phys. B478 (1996) 660. 33. 0. Nachtmann, Nucl. Phys. B63 (1973) 237. 34. S. Capitani et al., Nucl. Phys. (Proc. Suppl.) 73 (1999) 288; M. Gockeler et al. [QCDSF Collaboration], in preparation. 35. C.S. Armstrong et al., Phys. Rev. D63 (2001) 094008.

PHOTOEXCITATION OF N* FtESONANCES ANNALISA D'ANGEL0'i2i* FOR THE GRAAL COLLABORATION 0. BARTALIN13p4,V. BELLIN15, J.P. BOCQUET', M. CASTOLD17, ANNALISA D'ANGELO',', ANNELISA D'ANGELO'>', J.P. DIDELEZ', R. DI SALVO'>', A. FANTINI'>', G. GERVINOg, F. GHIO", B. GIROLAMI", A. GIUSA5, M. GUIDAL', E. HOURANY8, V. KOUZNETSOV'~", R. KUNNE', A. LAPIK", P. LEV1 SANDR14, A. LLERES', D. MORICCIANI', V. NEDOREZOV", L. NICOLETT15i6, C. RANDIER15, D. REBREYEND', F. RENARD', N.V. RUDNEV", C. SCHAERF'?', M. L. SPERDUT05, C. M. SUTERA5, A. TURINGE'3, A. ZABRODIN1', A. ZUCCHIATT17 Universitci degli Studi d i Roma "Tor Vergata", Via della Ricerca Scaentifica,l I-00133 Rome, Italy

' INFN, Sezione d i Roma 11, Italy Universita d i T k n t o , Italy INFN, Laboratori Nmionali d i fiascati, Italy Universitci d i Catania and INFN, Sezione LNS, Italy

' INZP3, Institut des Sciences Nuclbaire, Grenoble, fiance INFN, Sezione Genova, Italy IN2P3, Institut de Physique Nucl6aaire, Orsay, Fmnce INFN, Sezione d i Torino, Italy lo

Istituto Superiore d i Sanitci and INFN Sezione d i Roma I, Italy

'' Institute for

'' Institute for l3

Nuclear Research, Moscow, Russia

Theoretical and Experimental Physics, Moscow, Russia

L. Kurchatov Institute of Atomic Energy, Moscow, Russia * E-mail: annalisa.dangeloQmma2.infn.it

We present an overview of most recent experimental results of photonuclear reactions in the resonance energy region. High precision and polarization obsenables are the key issues in the study of N ' resonance properties.

140

141

1

Introduction

The excited states of the nucleon were observed for the first time in n-- N scattering experiments, as clear peaks in the cross-section. Partial-wave analysis of n- - N elastic scattering data and charge exchange reactions have provided quantum numbers, masses and widths of most of the baryonic (N and A) resonances . Smaller sets of data are available for pion induced reactions with Nq, A K , AE or N m produced in the final state. They have provided information on the branching fraction for the N' decaying into different baryon-meson channels. Meson photoproduction reactions have been used to extract the electromagnetic transitions amplitudes (the A1i2 and the A3/2 helicity amplitudes), providing complementary dynamical information on the composite structure of the baryons. It is very difficult to eliminate the model dependence in the extraction of baryonic parameters from experimental results. For example a model independent multipole analysis of meson photoproduction would require precise measurements of cross section and polarization observables for a complete set of results. These must include a minimum of eight single and double polarization observables, in the case of pseudoscalar meson photoproduction. The minimum number of independent observables increases to 23 in the case of vector meson photoproduction. In lack of such complete information, the extraction of resonance parameters relays on both the choice of a theoretical model and on the quality of data. At energies above the &3(1232) the task is complicated by the overlapping of several broad resonances. Having these resonances fixed quantum numbers, their contribution to a scattering process appears only in specific multipoles. However the values of resonance parameters extracted in a multipole analysis depend on the procedure used to discriminate the resonant from the background contribution. Recently a new generation of precise data on meson photoproduction, including single and double polarization measurements, has become available. This is due to the advent of high quality, polarized and tagged electron and photon beams (MAMI-B, ELSA, LEGS, GRAAL, LEPS, JLAB, BATES), coupled with large solid angle detectors and, in some cases, also with polarized targets. At the same time these results have stimulated the theoretical community to refine the models and t o increase their efforts to understand and quantify the theoretical uncertainties of resonance parameters, by comparing results obtained by different procedures on the same data set. This is the case of the Baryon Resonance Analysis Group (BRAG) that is promoting the collaboration among theoretical and experimental physicists to work towards a commonly accepted review of the resonance parameters, extracted from modern electromagnetic and hadronic facilities.

'

142

2

The First Resonance Region and the A(1232) EMR

In the energy region corresponding to masses up to 1400 MeV, the excitation of the A(1232) resonance dominates the reaction mechanisms. It is therefore possible to extract its parameters with high precision, not yet achieved at higher energies. The yN + A transition proceeds mainly through magnetic dipole (M1 or M:?), due to a quark spin flip. The presence of a d-wave admixture in the nucleon wave-function allows for a small contribution from the electric quadrupole (E2 or E:c) transition amplitude. The origin of the d-wave component, that breaks the spherical symmetry of the nucleon, differs in various models of the nucleon. In constituent quark models (CQM), inspired to Quantum Cromo-Dynamics (QCD), the d-wave component arises from the introduction of an effective color-magnetic tensor interaction, while in chiral bag models the nucleon deformation is ascribed to the asymmetric coupling of the meson cloud to the nucleon spin. The ratio of resonant E2 to M1 transition strengths (EMR) is the experimental quantity of interest. Its value has been extracted from a large amount of available data, using different analysis procedures. The decomposition of amplitudes into a resonant and a background term is model dependent and not unique. Most analysis do not explicitly calculate the influence of non-resonant mechanisms on the resonance properties, such as interference contributions from Born terms and meson rescattering. It is not the bare value of the EMR to be extracted in such analysis, but the value the EMR dressed by the meson cloud. Precise measurements, including polarization observables, on 7 p -+ 7ro p , 7 p -+ 7r+ n and Compton scattering have been provided by the Mainz and Legs laboratories. Because the A decays into TRN final states with 99.4% branch and back to the yN state with 0.6% branch, the analysis of simul-

Table 1. Values of the dressed A(1232) resonance EMR and helicity amplitudes extracted by the most recent multipole analysis by Legs and Mainz groups. Results are compared with the latest edition of the Review of Particle Physics.

Mainz analysis Legs analysis PDG

REM (%)

AlI2 ( 1 0 - ~ / a

All2 ( 1 O r 3 / m

-2.5 f 0.1 f 0.2 -3.07 f 0.26 f 0.24 -2.5 f 0.5

-( 131 f 1) -(135.7 f 1.3 f 3.7) -(135 f 6)

-(251 f 1) -(266.9 f 1.6 f 7.8) -(255 f 8)

143

220 240 260 280 300 320 340

220 240 260 280 Mo 320 340 360

Figure 1. Differential cross sections and beam polarization asymmetries for the reactions T p + y p , T p -+ xop and q p -+ x+n, measured by the mainz (open circles) [2,4] and the Legs (full circles)[3,5] laboratories.

taneous measurements of previous channels has the potential to extract A properties with high accuracy. Figure 1 shows results obtained for the dif-

144

Table 2. Results for M1, E2 and EMR from the analysis of various groups belonging to BRAG [6,7].Values for M1 and E2 are expressed in units those for EMR are given in %.

REM

Effective Lagrangian RPI Partial wave anal. GWU SAID Multipole anal. fixed-t disp. relations H A Multipole anal. unitary isobar mod. MAID Dynamical mod. by Yang & Kamalov KY Fixed-t disp. relations by Aznauryan AZ Multipole anal. by Omeiaenko O M Average

-

281

-6.6

278

-5.3 -6.2 -6.3

281.3 & 4.5

-6.6 f 0.8

-2.55 -2.57 -2.35 -1.93 -2.24 -2.28 -2.77 -2.38 f0.27

&

ferential cross section and the beam polarization asymmetries for Compton scattering and no photoproduction, at polar angle equal to 90" in the center of mass. Also data at 85" in the center of mass for the n+n reaction channel are plotted. Full circles are Legs measurements, empty circles are those from Mainz. Very high precision results and good agreement among data are obtained for the beam polarization asymmetries C. While Compton scattering differential cross section data nicely agree, a 10% overall scaling factor is necessary t o reconcile the differential cross section results of pion photoproduction reactions. Table 1 shows results obtained for A resonance parameters extracted by multipole analysis performed by the two laboratories on their own measurements. Results are compared with the latest Review of Particle Physics' evaluation. The differance between the two laboratories results may be ascribed to the disagreement among measured differential cross sections. The Baryon Resonance Analysis Group (BRAG) 6,7 has performed the analysis of a "bench-mark" data set of 1287 points on photoreactions and pion induced reactions, not including the latest results from Mainz and Legs, using several theoretical approaches to study the model dependence in the extraction of the dressed values of the M1 and E2 strengths. Results were published in and are reported in Table 2. The average result should not be taken as a final value, because it is based on the chosen data set, which does not include all recent experiments. However the results fluctuation is very small and the extraction of a 2% effect may be obtained with a 0.3% percent model dependence.

145

t

I 0

200

:140

101)

500

6(w)

70(1

,yno

E, (MeV) Figure 2. Measured values of the total absorption cross section difference between the two relative helicity states of the proton and the longitudinally polarized photon. Results are from Mainz (open and full circles). Data are compared with predictions by Hanstein et al. (dot-dashed curve), rnultipole analysis by SAID (solid curve) and the Unitary Isobar Model (MAID) (dotted curve).

3

Double polarization measurements and the GDH sum-rule

The first measurements obtained with a polarized photon beam on a polarized target represent an important break through in the study of photonuclear reactions. First data on photoabsorbtion cross sections on the proton have been obtained at Mainz using a longitudinally polarized beam on a frozen spin butanol target in the energy range 200 < E, < 800 MeV. The difference between the total cross section measured in the two relative spin configurations of photons and protons in the initial state, namely 0312 is plotted in Figure 2. Open and full circles are experimental results, compared with predictions by Hanstein et al.” (dot-dashed curve), multipole analysis by SAID12 (solid curve) and the Mainz Unitary Isobar Model (MAID)I3 (dotted curve). Only the last calculation includes multi-pion and 9 photoproduction 879910

146

contributions and predictions fail to reproduce the full strength of the cross section difference in the second resonance region. These first measurements may be used to experimentally verify the GDH14 sum-rule, defined as follows: (0312

- 0112)-

du u

2x2a =-IC~

M2

= 204pb

where u is the photon energy, uo is the pion photoproduction threshold, a is the fine-structure constant, M is the proton mass and IC is the anomalous magnetic moment of the proton. The experimental contribution to the integral appearing on the left side of the sum-rule, in the measured energy range, is 226 f 5 f 12pb. The combination of this result with estimations of the contributions in the missing energy ranges, provides a total result which is consistent with the GDH sum-rule within the experimental errors. The extension of this measurement to higher energies is underway at the Bonn laboratory15. First results using a polarized Compton backscattered ?-ray beam on a frozen spin HD target, have been obtained at Legs16. Very promising measurements have been obtained in three days of data taking, only. The beam polarization was changed regularly among six states: circular polarization parallel or antiparallel to the proton polarization, linear polarization with the polarization vector oriented vertically, horizontally or at an angle of f45". For the first time it was possible to extract all double polarization asymmetries involving beam and target. More data taking is expected in the near future. 4

Single and double pion photoproduction

New precise results on the differential cross section and C have been obtained at GRAAL for the 7 p -+ xo p reaction, in the energy range from 600 to 1100 MeV17, and for the beam asymmetry C for the T p -+ x+n reaction at energies from 600 to 1500 Comparison with existing well established results provided excellent confidence on the quality of the data. The inclusion of these results in the latest GWU-SAID data base12 has produced significant modifications in some of the partial cross section of the SAID Partial Wave Analysis. The new solution (FAO1) requires a stronger contribution of the Pl3(1720) resonance and a suppression of the &,(1620), with respect to previous analysis, to reproduce the complex structure of the experimental results. Important new data have been obtained also on the two-pion photoproduction channels ( y p + x+xon and -yp -+ xo.rrop) by the Mainz group20921.

+

+

147

The resonant excitation mechanisms have been understood to be dominated by the &(1520) excitation”, subsequently decaying into Ao7r+ or Ao7ro. The model however could not reproduce the full strength of the 7r+7ro channel. The measurement of the invariant mass spectra of the x7r systemsz1 was the key to reveal for the first time the direct decay D13(1520) -+ pN in the 7r+7ro channel.

5

q photo-production

Most of the CQM models predict more states than those experimentally observed. It is possible that the “missing” states have not been observed because they are weekly coupled to 7rN channels. Evidence of their existence may be observed in other channels, such as q N , p N , Kh and wN. The study of the q meson photeproduction offers the advantage of a reduced complexity for the resonances involved in the reaction. Since 7) carries isospin I = 0, only I = 1/2 N* resonances may be excited and only those having significant qN branching ratio may contribute. Measurements of the C polarization observable add the ability to pin down small contributions from higher multipole resonances through their interference with the main terms. Extraction of the qN partial widths and photocoupling amplitudes of the corresponding resonances are then possible, even if the qN branching ratios are very smallz7. Very precise results for the differential cross section have been obtained by the GRAAL collaboration from the reaction threshold up to E, = 1.1 GeV. They cover the full angular range, for a total of 233 data points.24. The data are in good agreement with existing Maimz6 data and confirm the near isotropic behavior of the angular distribution up to E, = 0.9 GeV, arising from the dominance of the Sll(1535) excitation. A multipole expansion up to second order shows that deviations from isotropy at higher energies are mainly due to quadrupole terms, associated with the 013(1520) resonance. However, the onset of the P-wave is clear at energies above E, = 1.0 GeV, confirming similar results from q electro-prod~ction~~.

Table 3. Values of the Sll(1535) resonance parameters extracted from 9 photwproduction.

0.3 - 0.55

148

0.8

0.6

Ey=0.7458GeV

1

Ey=0.7965GeV

Ey=0.8596GeV

t

0.4

0.2 0 Ey=0~9308GeV

Ey=0.9909GeV

t

0.6

+

-

0

-

0

-

0

0 -

-

'

'

1

'

'

'

'

-

0

0 O & I

0

Q

0

0.4 -

0.2

t

I

I

I

4

-

0 L

Q

I

I

,

,

L

Figure 3. Preliminary results for the beam polarization asymmetry for the reaction: ? + p -+ q + p from the GRAAL collaboration. Open squares are results obtained with the UV Laser line and a maximum y-ray energy of 1487 MeV. They are compared with the previous results obtained with a maximum y-ray energy of 1.1 GeV, shown with open circles. Dashed lines show the latest Partial Wave Analysis of the SAID group[l2], including GRAAL data. Bold and dotted lines show the analysis based on the Li and Saghai quark mode1[25]. Solid lines show a global fit [27] of the GRAAL beam asymmetries (231, the Mainz differential cross sections [26] and the Bonn target asymmetries[28].

Results for the total cross section are available up to E7 = 1.1 GeV. These measures cover the full energy range of the Sll(1535) resonance for the first time. Fig. 3 shows published C beam asymmetry resultsz3 together with a sample of preliminary data up t o E7 = 1.48 GeV. The observable is dominated by the interference of the D13(1520) with the main S-wave.

149

Deviations from the sin% distribution are due to contributions from other multipoles. Data are compared with the multipole analysis performed by the GWU groupl2 including all GRAAL data (B012 solution), plotted as a dashed line. Curves from a new analysis based on a chiral constituent quark modelz5, that includes all known resonances up to 2 GeV and does not incorporate tchannel exchange terms, are also reported. This model requires the inclusion of a third &1(1730) K A quasi-bound state to reproduce the forward peak in the cross section. Bold and dotted curves in Fig. 3 show the results with and without the third 4 1 “missing” resonance. A global fitz7, combining Mainz differential cross section data26, published GRAAL asymmetry dataz3 and Bonn target asymmetry resultsz8, is plotted as a solid line. Results have been also included in the MAID 2000 analysis using an isobar modelz9 and in a coupled-channel analysis using an Effective Lagrangian model and BetheSalpeter equation in K-matrix appro~irnation~~. The values for the SII(1535) resonance parameters, extracted using these different approaches, are summarized in Table 1 and are compared with the values quoted by the Particle Data Group. Clear discrepancies still remain among the values of the resonance width and of the photocoupling amplitude. 6

K+ A and w photo-production

New data are available on the KX channel from the SAPHIR c o l l a b o r a t i ~ n ~ ~ . They show a structure in the differential cross section that has been reproduced33 using an isobar model which includes a missing D13(1960) resonance. The same model predicts for C trends of opposite sign if the missing resonance is included or not. Very preliminary data for the C beam asymmetry in the K + A reaction channel have been produced by the GRAAL collaboration. They have clearly positive values in the energy range from E, = 1050 MeV to E7 = 1400 MeV and confirm the presence of the 013(1960) resonance. More data are expected from the SAPHIR and LEPS collaborations. Very promising results are expected for the y p + w p reaction channel. Total and differential cross sections are dominated by the diffractive terms, described by Pomeron and meson (KO, 77) exchange mechanisms in the t-channel, while resonance contributions have some importance at low energies and backward angles. Polarization observables on the contrary are p r e d i ~ t e d ~ to *’~~ be very sensitive to resonance excitation. Diffractive terms are expected to give very small contribution t o the beam polarization asymmetry C and large asymmetry values are a direct evidence of resonance excitation contributions. First very preliminary measurements on the C asymmetry have been pro-

150

r/

-c.3 -c.4

-0.6 -E.8

F

Figure 4. Very preliminary results from the GRAAL collaboration for the beam asymmetry C integrated over the w decay solid angle, for the reaction G p + wp. Results are compared with prediction from [35]. Dashed curve is the contribution from Pomeron and meson exchange terms alone. Solid curve is the full calculation, including all resonances with masses up t o 2 GeV.

duced by the GRAAL collaboration in the energy region from threshold to 1500 MeV. A sample of these data is reported in Figure 4, together with predictions from Q. Z h a ~ Dashed ~ ~ . curve is the calculation including t-exchange terms only, solid curve is the full calculation including all N* resonances contributions with masses up to 2 GeV. General agreement between data and theoretical predictions is observed and the sizable strength of the C observable is expected to be very sensitive to the inclusion of specific resonances, such as the PI3(1720).

Acknowledgments We are grateful to C. Bennhold, A. Waluyo, Wen-Tai Chiang, B. Saghai and I. Strakovsky for useful discussions and communication of their work prior to publication. We would like to thank J. Ahrens for very useful information and we are very obliged to A. Sandorfi, A. Lehmann and all the Legs-Spin Collaboration for communication of their results prior to publication.

151

References

1. Rev. of Part. Phys. 2000, Eur. Phys. J. C 15, 1-878 (2000). 2. R. Beck et al, Phys. Rev. Lett. 78, 606 (1997). 3. R. Blampied et al, Phys. Rev. Lett. 79, 4337 (1997) 4. R. Beck et al, Phys. Rev. C 61, 035204 (2000). 5. G. Blampied et al, Phys. Rev. C 64, 025203 (2001). 6. R. M. Davidson, NSTAR 2001, Proceedings of the Workshop on the Physics of Excited Nucleons Mainz, Germany 7 -10 March 2001, Ed. D. Drechsel and L. Tiator, World Scientific, 203-206, (2001). 7. R.A. Arndt et al., nucl-th/0106059, 2001. 8. J. Ahrens et al., Phys. Rev. Lett. 84, 5950 (2000). 9. J. Ahrens et al., Phys. Rev. Lett. 87, 022003 (2001). 10. A. Braghieri these proccedings. 11. 0. Hanstein et al. Nucl. Phys. A 632, 561, (1998). 12. Partial Wave Analysis by SAID at GWU. R.A. Arndt, 1.1. Strakovsky and R.L. Workman, Phys. Rev C 53 430, (1996). Said solutions and data base are available at [email protected]. 13. D. Drechsel, 0. Hanstein, S. Kamalov and L. Tiator, Nucl. Phys. A 645, 145 (1999). Predictions are available at URL http://www.kph.unimainz.de/MAID2000. 14. S.B. Gerasimov, Siv. J. Nucl. Phys. 2, 430 (1966); S.D. Drell and A.C. Hearn, Phys. Rev. Lett. 16, 430 (1966). 15. Michael these proceedings. 16. A. Lehman these proceedings. 17. F. Renard Thesis, Univ. J. Fourier, Grenoble, (1999). 18. J. Ajaka et al., Phys. Lett. B 475, 372, (2000). 19. 0. Bartalini et al. accepted for pubblication by Phys. Lett. 20. M. Wolf et al. Eur. Phys. J. A 9, 5 (2000). 21. W. Langgaerten et al., Phys. Rev. Lett. 87, 052001 (2001). 22. J.A. Gomez Tejdor and E. Oset, Nucl. Phys. A 600, 413, (1996). 23. J. Ajaka et al, Phys. Rev. Lett. 81, 1797 (1998). 24. F. Renard et al., Phys. Lett. B 528, 215 (2002). 25. B. Saghai and Z. Li, Eur. Phys. J. A 11, 217 (2001). 26. B. Krusche et al, Phys. Rev. Lett. 74, 3736 (1995). 27. L. Tiator, D. Drechsel and G . Knochlein Phys. Rev. C 60,035210 (1999). 28. A. Bock et al, Phys. Rev. Lett. 81, 534 (1995). 29. Wen-Tai Chiang et al. Proceedings of the Workshop on the Physics of Excited Nucleons Mainz, Germany 7 -10 March 2001, Ed. D. Drechsel and L. Tiator, World Scientific, 171 (2001).

152

30. C. Bennhold et a1 nucl-th/9901066, nucl-th/0008024; T. Feuster and U. Mosel, Phys. Rev. C 59, 460 (1999). 31. R. Thompson et al, Phys. Rev. Lett. 86, 1702 (2001); C. S. Armstrong et al, Phys. Rev. D 60,052004 (1999). 32. M.Q. "ran et all Phys. Lett. B 445, 20 (1998). 33. C. Bennhold et al. nucl-th/0008024. 34. Y . Oh et al. Phys. Rev. C 63,025201 (2001). 35. Q. Zhao, Phys. Rev. C 63, 025203 (2001). Curves are from private communication.

INSTANTONS AND BARYON DYNAMICS DMITRI DIAKONOV NORDITA, Blegdamsuej 17,DK-2100 Copenhagen, Denmark E-mail: diakonovOnordita.dk PNPI, Gatchina, St. Petersburg 188 300, Russia I explain how instantons break chiral symmetry and how do they bind quarks in baryons. The confining potential is possibly irrelevant for that task.

1

Introduction

According to common wisdom, moving a quark away from a diquark system in a baryon generates a string, also called a flux tube, whose energy rises linearly with the separation. The string energy, however, exceeds the pion mass m, = 140MeV at a modest separation of about 0.26fm, see Fig. 1. At larger separations the would-be linear potential is screened since it is energetically favorable to tear the string and produce a pion. Virtually, the linear potential can stretch to as much as 0.4fm where its energy exceeds 2m, but that can happen only for a short time of l/m,. Meanwhile, the ground-state baryons are stable, and their sizes are about 1fm. The pion-nucleon coupling is huge, and there seems to be no suppression of the string breaking by pions. The paradox is that the linear potential of the pure glue world, important as it might be to explain why quarks are not observed as a matter of principle, can hardly have a direct impact on the properties of lightest hadrons. What, then, determines their structure? We know that, were the chiral symmetry of QCD unbroken, the lightest hadrons would appear in parity doublets. The large actual splitting 940) implies that chiral symmetry between, say, N ( !j-, 1535) and N ( is spontaneously broken as characterized by the nonzero quark condensate < ijq >= -(250MeV)3. Equivalently, it means that nearly massless (‘current’) quarks obtain a sizable non-slash term in the propagator, called the dynamical or constituent mass MCp), with M ( 0 ) -N 350MeV. The pmeson has roughly twice and nucleon thrice this mass, ie. are relatively loosely bound. The pion is a (pseudo) Goldstone boson and is very light. The sizes of these hadrons are typically l/M(O) whereas the size of constituent quarks is given by the slope of M ( p ) and is much less. It explains, at least on the qualitative level, why constituent quark models are so phenomenologically successful.

if,

-

153

154

r/fm

2.50

-

2.00

-

1.50

-

1.00

-

0.50

-

0.00

1

2

3

4

5

Figure 1. The lattice-simulated potential between static quarks exceeds mrrat the separation of 0.26 fm (left). The screening of the linear potential is clearly seen in simulations at high temperatures but below the phase transition (right). As one lowers the pion mass the string breaking happens at smaller distances; the scale is fi N 425 MeV N (0.47 frn)?'.

We see thus that the spontaneous chiral symmetry breaking (SCSB) rather than the expected linear confining potential of the pure glue world is key to the understanding the origin of the ground-state hadrons. It may be that for highly excited hadrons the importance of confinement forces 'usSCSB is reversed: I discuss it at the end of the paper. In the main part I briefly review the instanton mechanism of the SCSB suggested and worked out by Victor Petrov and myself in the middle of the 80's. Much analytical and numerical work calculating hadron observables has supported this mechanism, for reviews. There is also growing support from direct lattice see Refs. simulations, see below. Instantons induce strong interaction between quarks, leading to bound-state baryons with calculable and reasonable properties. 334

576

2

What are instantons?

Being a quantum field theory, QCD deals with the fluctuating gluon and quark fields. A fundamental fact is that the potential energy of the gluon field is a periodic function in one particular direction in the infinite-dimensions functional space; in all other directions the potential energy is oscillator-like. This is illustrated in Fig. 2. Instanton is a large fluctuation of the gluon field in imaginary (or Euclidean) time corresponding to quantum tunneling from one minimum of the potential energy to the neighbor one. Mathematically, it was discovered by Belavin, Polyakov, Schwarz and Tiupkin; the tunneling interpretation was given by V. Gribov. The name 'instanton' has been introduced by 't Hooft lo

155

Figure 2. Potential energy of the gluon field is periodic in one direction and oscillator-like in all other directions in functional space.

Figure 3. Smoothing out the normal zero-point oscillations reveals large fluctuations of the gluon field, which are nothing but instantons and anti-instantons with random positions and sizes. The left column shows the action density and the right column shows the topological charge density for the same snapshot. l 1

who studied many of the key properties of those fluctuations. Anti-instantons are similar fluctuations but tunneling in the opposite direction in Fig. 2. Instanton fluctuations are characterized by their position in space-time z p, the spatial size p and orientation in color space 0, all in all by 12 collective coordinates. The probability for the instanton fluctuation is, roughly, given

156

by the WKB tunneling amplitude,

( 4i2F;")

exp(-Action) = exp --

Jd4z

= exp

(-F).

(I)

It is non-analytic in the gauge coupling constant and hence instantons are missed in all orders of the perturbation theory. However, it is not a reason to ignore tunneling. For example, tunneling of electrons from one atom to another in a metal is also a nonperturbative effect but we would get nowhere in understanding metals had we ignored it. Indeed, instantons are clearly seen in nonperturbative lattice simulations of the gluon vacuum. In the upper part of Fig. 3 (taken from the paper by J. Negele et al. 11) a typical snapshot of gluon fluctuations in the vacuum is shown. Naturally, it is heavily dominated by normal perturbative UV-divergent zero-point oscillations of the field. However, after smearing out these oscillations (there are now several techniques developed how to do it) one reveals a smooth background field which has proven to be nothing but an ensemble of instantons and anti-instantons with random positions and sizes. The lower part of Fig. 3 is what is left of the upper part after smoothing. The average size of instantons found in ref. l1 is p w 0.36fm and their average separation is R = ( N / V ) - a w 0.89fm. Similar results have been obtained by other lattice groups using various techniques. A decade earlier the basic characteristics of the instanton ensemble were obtained analytically from the Feynman variational principle 12J3 and expressed through the only dimensional parameter A one has in QCD: p w 0.48/Am N 0.35fm, R w 1.35/Am N 0.95 fm, if one uses A m = 280 MeV as it follows from the DIS data. The theory of the instanton vacuum is based on the assumption that the QCD 'partition function' is saturated by large nonperturbative fluctuations of the gluon field (instantons), plus perturbative oscillations about them. It takes the form of a partition function of a liquid (like H2O) of N+ instantons and N - anti-instantons:

where Uint is the interaction depending on relative positions, sizes and orientations of instantons. Actually, it is a grand canonical ensemble of interacting 'particles' since their numbers N h are not fixed but must be found from the minimum of the free energy and ultimately expressed through A = f exp(- $) appearing through the 'transmutation of dimensions' from

1 57

integrating over perturbative gluons ( a is the UV cutoff, e.g. the lattice spacing). The numbers for p and R quoted above come from the study of this ensemble. a l27I3

3

How do instantons break chiral symmetry?

We now switch in light quarks into the random instanton ensemble. The basic property is that massless quarks are bound by ,instantons with exactly zero ‘energy’. These localized states are called quark zero modes, discovered by ’t Hooft lo. They have definite helicity or chirality: left-handed quarks are localized on instantons ( I ) and right-handed are on anti-instantons ( I ) . However, this is correct only for a single (anti)instanton. If there is a If pair, no matter how far apart, the degeneracy of the two would-be exactly zero modes is lifted owing to the overlap of their wave functions. If there are infinitely many 1 ’ s and ps, each of them brings in a would-be zero mode but, because of the quantum-mechanical overlap, the degenerate levels split and form a continuous spectrum, meaning the delocalization of the would-be zero modes. The effect is similar to the so-called Anderson conductivity: the appearance of the conductivity of electrons bound by random impurities. It can be shown mathematically that a finite density of quark states at zero ‘energy’ means spontaneous chiral symmetry breaking, and one can calculate the chiral condensate from the average overlap of the zero-mode wave functions and express it through the basic quantities characterizing the instanton ensemble, i.e. the average size of instantons and their density 3 . However, there is a simpler physical argument. Each time a quark ‘hops’ from one random instanton to another it has to change its helicity. Delocalization implies quarks make an infinite number of such jumps. An infinite number of helicityflip transitions generates a non-slash term in the quark propagator, i.e. the dynamically-generated mass M ( p ) , see Fig. 4. It implies the spontaneous chiral symmetry breaking. Two different formalisms have been developed in the 80’s to calculate hadron observables: (i) first computing an observable and then averaging it over the instanton ensemble and (iz) first averaging over the ensemble which leads to an effective low-energy theory, and then computing observables in the effective theory. Despite very different appearance the two formalisms give “The first study of the instanton ensemble on a qualitative level was performed by Callan, Dashen and Gross l4 and later on by Shuryak 15. Ilgenfritz and Mueller-Preussker l 6 were the first to study the instanton ensemble quantitatively by modelling the interactions by a hard-core repulsion.

158

Figure 4. Quarks hopping from instantons to anti-instantons and vice versa flip helicity (left). An infinite number of such jumps generates a dynamical mass M ( p ) , in MeV (right).

identical final results. Let me list a few of them:

< qq >= --const. R2p

N

-(255MeV)3,

N

-

M ( 0 ) = const. 7rP 345MeV, (3) R2 -

100 MeV vs. 94 MeV (exper),

const. m,, = -- 980 MeV vs. 958 MeV (exper) . .

ii

N

(4) (5)

where “const.” are computable numerical constants of the order of unity. Recently, the instanton mechanism of the SCSB has been scrutinized by direct lattice methods. At present there is one group l 9 challenging the instanton mechanism. However, the density of alternative ‘local structures’ found there explodes as the lattice spacing decreases, and this must be sorted out first. Studies by other groups 1 7 7 1 8 support or strongly support the mechanism described above. In particular, in a recent paper Gattringer l8 convincingly demonstrates that quarks in near-zero modes concentrate in the regions where the gluon field is either self-dual (1’s) or anti-self-dual (ps). Since near-zero modes are responsible for the SCSB it is a direct confirmation of the instanton mechanism. 17118~19

4

Baryons

There is a remarkable evidence of the importance of instantons for the baryon structure. In Ref. l1 the so-called density-density correlation function inside the nucleon has been measured both in the full vacuum and in the instanton vacuum resulting from the full one by means of smoothing. The correlation

159

(N)

0.01 0

0.5

1.5

1

x (fm)

Figure 5. Density-density correlation function in the nucleon. l 1 Filled circles are measurements in the full gluon vacuum (corresponding to Fig. 3a,b) while open circles are measured in the vacuum with instantons only (Fig. 3c,d). Despite that linear confining potential is absent in the instanton vacuum the nucleon structure seems to be very well reproduced.

in question is between the densities of u and d quarks separated by a distance x inside the nucleon which is created at some time and annihilated at a later time. The two correlators (‘full’ and ‘instanton’) are depicted in Fig. 5: one observes a remarkable agreement between the two, up to x = 1.7fm. It must be stressed that neither the one-gluon exchange nor the linear confining potential present in the full gluon vacuum survive the smoothing of the gluon field shown in Fig. 3. Nevertheless, quark correlations in the nucleon remain basically unaltered! It means that neither the one-gluon exchange nor the linear confining potential are important for the quark binding inside the nucleon. As a matter of fact, the same remark can be addressed to the lightest mesons r and p since the density-density correlators for these hadrons also remain basically unchanged as one goes from the full glue to the reduced instanton vacuum. l 1 Therefore, one must be able to explain at least the lightest T ,p, N on the basis of instantons only. The dynamics remaining in the instanton vacuum is the SCSB, the apearance of the dynamical quark mass M ( p ) , and quark interactions induced by the possibility that they scatter off the same instanton. Actualy these interactions named after ’t Hooft, are quite strong. They are in fact so strong that for quark and antiquark in the pion channel they eat up the 700 MeV of twice the constituent quark mass to nil, as required by the Goldstone theorem. In the vector meson channel ’t Hooft interactions are suppressed, and that is why the p mass is roughly twice the constituent quark mass. In the nucleon they are fully at work but in a rather peculiar way: instanton-induced interactions can be iterated as many times as one wishes in the exchanges between quarks, see Fig. 6 , left. It can be easily verified that the diagram in Fig. 6 , left, can be drawn as three continuous quark lines going from the 1.h.s of the diagram to its r.h.s., without adding closed loops. Therefore, that kind of interaction arises already in the so-called quenched approximation. At the same time, it 495

160

Figure 6. ’t Hooft interactions in the nucleon (left) essentially come to quarks interacting via pion fields (right).

yields plenty of Z-graphs absent in “valence QCD” but which are necessary to reproduce hadron properties. 2o Summing up all interactions of the kind shown in Fig. 6, left, seems to be a hopeless task. Nevertheless, the nucleon binding problem can be solved ezcactly when two simplifications are used. The first exploits the fact that in the instanton vacuum there are two lightest degrees of freedom: pions (since they are the Goldstone bosons) and quarks with the dynamical mass M . All the rest collective excitations of the instanton vacuum are much heavier, and one may wish to neglect them. Pions arise from summing up the qq bubbles schematically shown in Fig. 6, left. The resulting effective low-energy theory takes the form of the non-linear a-model: 4,21 ~ ~ = f [ig f - M e x p ( i ~ ~ ~q. ~ ~ ~ / ~ ~ ( )6 ) ] The absence of the explicit kinetic energy term for pions (which would lead to the double counting) distinguishes it from the Manohar-Georgi model. 22 Expanding the exponent to the first power in nA we find that the dimensionless pion-constituent quark coupling, M Qnqq = - M 4, (7)

Fn

is quite strong. The domain of applicability of the low-energy effective theory (6) is restricted by momenta p < 1/p = 600MeV, which is the inverse size of constituent quarks. At higher momenta one starts to feel the internal structure of constituent quarks, and the two lightest degrees of freedom of Eq. (6) become insufficient. However, the expected typical momenta of quarks in the nucleon are of the order of M M 345 MeV, which is inside the domain of applicability of the low-momentum effective theory. The chiral interactions of constituent quarks in the nucleon, following from the effective theory (6), are schematically shown in Fig. 6, right, where quarks are denoted lines with arrows. Notice that, since there is no explicit

161

kinetic energy for pions in Eq. ( 6 ) , the pion propagates only through quark loops. Quark loops induce also many-quark interactions indicated in Fig. 6 as well. We see that the emerging picture is rather far from a simple one-pion exchange between the constituent quarks: the non-linear effects in the pion field are essential. The second simplification is achieved in the limit of large N,. For N , colors the number of constituent quarks in a baryon is N , and ,all quark loop contributions are also proportional to N,. Therefore, at large N , one can speak about a classical self-consistent pion field inside the nucleon: quantum fluctuations about the classical field are suppressed as l / N c . The problem of summing up all diagrams of the type shown in Fig. 6 is thus reduced to finding a classical pion field pulling N, massive quarks together to form a bound state. 5

Chiral Quark-Soliton Model

Let us imagine a classical time-independent pion field which is strong and spatially wide enough to form a bound-state level in the Dirac equation following from Eq. ( 6 ) . The background chiral field is color-neutral, so one can put N , quarks on the same level in an antisymmetric state in color, i.e. in a color-singlet state. Thus we obtain a baryon state, as compared to the vacuum. One has to pay for the creation of this trial pion field, however. Since there are no terms depending directly on the pion field in the low-momentum theory (6) the energy of the pion field is actually encoded in the shift of the lower negative-energy Dirac sea of quarks, as compared to the free case with zero pion field. The baryon mass is the sum of the bound-state energy and of the aggregate energy of the lower Dirac sea. It is a functional of the trial pion field; one has to minimize it with respect to that field to find the self-consistent pion field that binds quarks inside a baryon. It is a clean-cut problem, and can be solved numerically or, approximately, analylically. The description of baryons based on this construction has been named the Chiral Quark-Soliton Model (CQSM). The model reminds the large-2 Thomas-Fermi atom where N , plays the role of 2. Fortunately, corrections to the model go as l/Nc or even as 1/N: and have been computed for many observables. In the Thomas-Fermi model of atoms corrections to the self-consistent (electric) field are of the order of l/aand for that reason are large unless atoms are very heavy. In the end of the 80’s and the beginning of the 90’s dozens of baryon characteristics have been computed in the CQSM, including masses, mag23724325

162

netic moments, axial constants, formfactors, splittings inside the mutliplets and between multiplets, polarizability, fraction of nucleon spin carried by quarks, etc. - see for a review and references therein. Starting from ’96 a new class of problems have been addressed, namely parton distributions in the nucleon at low virtuality. 27 Parton distributions are a snapshot of the nucleon in the infinite momentum frame. One needs an inherently relativistic model in order to describe them consistently. For example, a bag model or any other nonrelativistic model with three quarks in a bound state, being naively boosted to the infinite-momentum frame gives a negative distribution of antiquarks, which is nonsense. On the contrary, being a relativistic fieldtheoretic model CQSM predicts parton distributions that satisfy all general requirements known in full QCD, like positivity and sum rules constraints. Numerous parton distributions have been computed in the CQSM, mainly by the Bochum group. There have been a number of mysteries from naive quark models’ point of view: the large number of antiquarks already at a low virtuality, the ‘spin crisis’, the large flavor asymmetry of antiquarks, etc. The CQSM explains all those ‘mysteries’ in a natural way as it incorporates, together with valence quarks bound by the isospin-1 pion field, the negative-energy Dirac sea. Furthermore, the CQSM predicts nontrivial phenomena that have not been observed so far: large flavor asymmetry of the polarized antiquarks 29, transversity dictributions 30, peculiar shapes of the so-called skewed parton distributions 31 and other phenomena in hard exclusive reactions. 32 Baryon dynamics is rich and far from naive “three quarks” expectations. 26i6

27328929

6 Conclusions 1. The would-be linear confining potential of the pure glue world is necessarily screened by pion production at very moderate separations between quarks. Therefore, light hadrons should not be sensitive to confinement forces but rather to the dynamics of the spontaneous chiral symmetry breaking (SCSB). 2. Most likely, the SCSB is driven by instantons - large nonperturbative fluctuations of the gluon field having the meaning of tunneling. The SCSB is due to ‘hopping’ of quarks from one randomly situated instanton to another, each time flipping the helicity. The instanton theory of the SCSB is in agreement with the low-energy phenomenology (cf. the chiral condensate < qq >, the dynamical quark mass M ( p ) , F,, m,r ...) and seems to be confirmed by direct lattice methods. Furthermore, lattice simulations indicate that instantons alone are responsible for the properties of lightest hadrons r,P,N , ...

163

3. Summing up instanton-induced quark interactions in baryons leads t o the Chiral Quark-Soliton Model where baryons appear t o be bound states of constituent quarks pulled together by the chiral field. The model enables one t o compute numerous parton distributions, as well as ‘static’ characteristics of baryons - with no fitting parameters. 4. For highly excited baryons ( m = 1.5 - 3 GeV) the relative importance of confining forces us. those of the SCSB may be reversed. One can view a large-spin J resonance as due to a short-time stretch of an unstable string or, alternatively, as a rotating elongated pion cloud. 33 What picture is more adequate is a question to experiment. In the first case the dominant decay is on the average of the type Bar J + Bar, J / z Mes, J/2; in the second case T + Bar~-2 TT + ... Studying it is mainly a cascade BZJ + Barj-1 resonances can elucidate the relation between chiral and confining forces.

+

+

+

References

1. G. Bali, K. Schilling and A. Wachter, in Confinement 95, eds. H. Toki et al. (World Scientific, Singapore, 1995) p.82, hep-lat/9506017. 2. F. Karsch, E. Laermann and A. Peikert, Nucl. Phys. B605,579 (2001), hep-lat/0012023. 3. D. Diakonov and V. Petrov, Phys. Lett. B 147,351 (1984); Sou. Phys. JETP 62,204 (1985); ibid. 62,431 (1985); Nucl. Phys. B272,457 (1986). 4. D. Diakonov and V. Petrov, Spontaneous Breaking of Chiral Symmetry in the Instanton Vacuum, preprint LNPI-1153 (1986), in: Hadron Matter under Extreme Conditions, eds. G. Zinoviev and V. Shelest (Naukova dumka, Kiev, 1986) p.192. 5. D. Diakonov, in: Proc. of Enrico Fermi School, Course 130, eds. A. Di Giacomo and D. Diakonov (10s Press, 1996), hep-ph/9602375; T. Schafer and E. Shuryak, Rev. Mod. Phys. 70,323 (1998). 6. D. Diakonov and V. Petrov, in: At the Frontier of Particle Physics, ed. M. Shifman (World Scientific, Singapore, 2001) p.359, hep-ph/0009006. 7. L.D. Faddeev, Looking for multi-dimensional solitons, in: Non-local Field Theories (Dubna, 1976) p.207; R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37,172 (1976). 8. A. Belavin, A. Polyakov, A. Schwartz and Yu. Tyupkin, Phys. Lett. 59, 85 (1975). 9. A. Polyakov, Nucl. Phys. B120,429 (1977). 10. G. ’t Hooft, Phys. Rev. D14, 3432 (1976).

164

11. M.C. Chu, J.M. Grandy, S. Huang and J.W. Negele, Phys. Rev. D 49, 6039 (1994), hep-lat/9312071. 12. D. Diakonov and V. Petrov, Nucl. Phys. B245, 259 (1984). 13. D. Diakonov, M. Polyakov and C. Weiss, Nucl. Phys. B461,539 (1996), hep-ph/9510232. 14. C. Callan, R. Dashen and D. Gross, Phys. Rev. D17, 2717 (1978). 15. E. Shuryak, Nucl. Phys. B203, 93 (1982). 16. E.M. Ilgenfritz and M. Muller-Preussker, NucZ. Phys. B184, 443 (1981). 17. J. Negele, Nucl. Phys. Proc. Suppl. 73, 92 (1999), hep-lat/9810053. 18. T. DeGrand and A. Hasenfratz, Phys. Rev. D64, 034512 (2001), hep-lat/0012021; C. Gattringer et al., Nucl. Phys. B617, 101 (2001), hep-lat/0107016; T. Blum et aZ., Phys. Rev. D65 014504 (2002); hep-lat/O105006; R. G. Edwards and U. M. Heller, Phys. Rev. D65, 014505 (2002); hep-lat/0105004; I. Hip et al., Phys. Rev. D65, 014506 (2002), hep-lat/0105001; C. Gattringer, hep-lat/0202002. 19. I. Horvfith et al., hep-lat/0201008. 20. K.F. Liu et al., Phys. Rev. D59, 112001 (1999), hep-ph/9806491. 21. D. Diakonov, in: Advanced school on non-perturbative quantum field physics, (World Scientific, Singapore, 1998) p.1, hep-ph/9802298. 22. A. Manohar and H. Georgi, Nucl. Phys. B234, 189 (1984). 23. S. Kahana, G. Ripka and V. Soni, Nucl. Phys. A 415, 351 (1984); S. Kahana and G. Ripka, Nucl. Phys. A 429, 462 (1984). 24. M.S. Birse and M.K. Banerjee, Phys. Lett. B 136, 284 (1984). 25. D. Diakonov and V. Petrov, Sou. Phys. JETP Lett. 43, 57 (1986); D. Diakonov, V. Petrov and P. Pobylitsa, in: Proc. 21st PNPI Winter School (Leningrad, 1986) p.158; Nucl. Phys. B 306, 809 (1988). 26. C. Christov et al., Prog.Part.Nucl.Phys. 37, 91 (1996), hep-ph/9604441. 27. D. Diakonov et al., Nucl. Phys. B 480, 341 (1996), hep-ph/9606314; Phys. Rev. D 56, 4069 (1997), hep-ph/9703420. 28. P. Pobylitsa et al., Phys. Rev. D59, 034024 (1999), hep-ph/9804436. 29. B. Dressler, K. Goeke, M. Polyakov and C. Weiss, Eur. Phys. J. C14, 147 (ZOOO), hep-ph/9909541. 30. P. Pobylitsa and M. Polyakov, Phys. Lett. B 389, 350 (1996), hep-ph/9608434. 31. V. Petrov et al., Phys. Rev. D 57, 4325 (1998), hep-ph/9710270. 32. K. Goeke, M. Polyakov and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 47, 401 (2001), hep-ph/0106012. 33. D. Diakonov and V. Petrov, Rotating chiral solitons lie on linear Regge trajectories, preprint LNPI-1394 (1988); see also D. Diakonov, Acta Phys. Polon. B25, 17 (1994).

THE STRANGENESS CONTRIBUTION TO THE FORM FACTORS OF THE NUCLEON F. E. MAAS FOR. T H E A4-COLLABORATION Johannes Gutenberg ClniversitZt Mainz, Institut f i r Kernphysik, J.J. Becherweg 45, 55299 Mainz, E-mail: [email protected] We report here on a new measurement of the parity violating (PV) Asymmetry in the scattering of polarized electrons on unpolarized protons performed at the MAMI accelerator facility in Mainz. This experiment is the first to use counting techniques in a parity violation experiment. The kinematics of the experiment is complementary to the earlier measurements of the SAMPLE collaboration at the MIT Bates accelerator and the HAPPEX collaboration at Jefferson Lab. After discussing the experimental context of the experiments, the setup at MAMI and preliminary results are presented.

1

Strangeness

1.1 Strangeness in the nucleon The structure of the nucleon is often described in terms of three constituent quarks where these are understood as effective particles with a mass that arises dynamically from a sea of virtual gluons and virtual quark antiquark pairs. The contribution of the strange quarks to this sea is of special interest, since the mass value of the strange quarks is approximately equal to the scale of XQCD and lies inbetween the masses of the very light u and d current quarks and the mass of the much heavier quarks like c,b and t. There is a detailed discussion of the present understanding of the role of strangeness within the nucleon in the literature Unfortunately, the scalar strangeness density Fs does not couple directly to the electr+magnetic probe, therefore the answer on the question of how much strangeness is in the nucleon is not directly available. The analysis of the scattering amplitude in wN-scattering and the connection to the C, term and the scalar density matrix element < NI F s IN > gives a contribution of the strange quark antiquark pairs to the mass of the nucleon on the order of 130 MeV 3 . New data from wN-scattering suggest even a larger value up to 50 % of the proton mass. The observed charm production rate from deepinelastic neutrino nucleon scattering can only be explained if there is a 2% contribution of the strange quarks to the momentum of the nucleon. In polarized deep inelastic muon and electron scattering the axial matrix element

165

166

< NISypy5sIN > is measured. It is equal to the contribution of the strange quarks to the spin of the Proton C,. A value for C, of 0.12 f 0.1 has been extracted4. Our experiment aims at a measurement of the contribution of strange quark antiquark pairs to the elastic vector form factors of the nucleon. 1.2 Extracting the strangeness form factor contribution

The dynamic response of the nucleon structure to electron scattering via the exchange of virtual photons is described in terms of the four elastic form factors: the Dirac form factor F];'"(Q2) of proton and neutron and the Pauli form factor Fg'"(Q2) (another combination are the Sachs form factors, Gg"= FYI" - Fgl" and Gp,n Fg'"). It has been first noted by Caplan M = FP?" and Manohar 5 , that a flavor decomposition of the form factors into the three lightest quark flavors u,d and s can be obtained. This is obtained by combining the form factors of proton and neutron using isospin symmetry and electromagnetic and weak neutral current form factors. If one writes the electromagnetic (FT;;) and the weak form factors (PY;;)decomposed into the three lightest quark flavors:

+

Fp?"

~

Qu 1,z 1,2 = Qu

PP?"

"Fr," + Qd dFrF + Qs "F::," Qd 'F;,'; Qs "FC;

"Fc;+

+

(1) (2)

The left side of Eq. (1) and Eq. (2) represents the eight experimentally accessible electro-magnetic and weak form factors of the nucleon and on the right side are the 12 the unknown flavor contributions. The Q-factors are the electremagnetic and weak charges of the appropriate quark flavor, i.e the electric and the weak charge of quark flavor u,d and s. Isospin symmetry allows to eliminate one half of the unknown quark flavor contributions by replacing the u-quark contributions in the proton by the d-quark contribu-S Fll -+' F I , ~and , tion in the neutron ("F:,2 =d Fc2 -+u F I , ~SFP ) vice versa and to use one strangeness contribution for both proton and neutron. In addition the quark distributions are an intrinsic property of the nucleon and do not depend on the probe. This allows to use the same flavor form factor contributions in Eq. 1 and Eq. 2 (u1d9sF1,2=u9dis F I , ~ Therefore ). the number of unknown flavor contributions on the right side of Eq. 1 and Eq. 2 is now reduced down to 6 unknown flavor contributions u9d3sF1,2,which can be determined, provided the electremagnetic and weak neutral form factors are measured by experiment. The weak neutral form factors enter into the amplitude A4 for elastic scattering of electrons off protons which is described at lowest order (one boson exchange) by the sum of the Feynman diagrams given in Eq. 3: my and

167

mzo. The cross section is given by the square of the amplitude M M * and consists of three terms: the pure y-exchange (m,m;), the 7-Zo interference term (m,m>,) and the pure &exchange (mz,m>o).At the proton vertex the elastic electremagnetic and weak form factors enter and can therefore be measured in electron scattering.

e

e’

e

e’

P’

In elastic electron proton scattering at four momentum transfer in range of 0.1 Gev2 < Q2 < 1 GeV2 the cy-Zo interference term is about 5 orders of magnitude smaller than the pure y exchange. The direct measurement of the weak contribution to the cross section is therefore at present beyond experimental reach. But the parity violating coupling of the ZO gives a unique possibility to separate the pure cy exchange from the interference term. In a measurement of the parity violating asymmetry in elastic scattering of longitudinally polarized electrons on unpolarized protons the pure y exchange (m,ml;) vanishes and one measures directly the interference term. Therefore one has direct access to the weak form factors of the nucleon, since the electremagnetic form factors are known from other experiments. As we have seen above, the determination of the weak form factors is equivalent to a determination of the strangeness contribution to the vector form factors of the nucleon. The experimental quantity which is measured is the difference in the cross section in the scattering of left handed or right handed electrons on unpolarized protons divided by the sum of the two cross sections. This is a parity violating

168

symmetry which can be calculated in the framework of the standard model:

(1 - 4sirl28w) +

+ +

E G ~ G E r G p G" M 2 M 4 cGg2 r G L

€G',G& t rGLGft, cG; 2 + r G L 2

ere r = 4Mp2 Q2 and

E =

+

(1 2(1 + ~ ) t a n ~ ( ; ) and ) - ~t'

=

d ~ ( lr )+ ( l - c2)

sing the flavor decomposition of Eq. 1, the asymmetry in Eq. 5 can be ritten like Eq. 6 as the sum of three terms (7), (8) and (9). (7) contains .ndamental constants and the electremagnetic form factors only. (7) is 'ten referred to as 4. (8) contains the unknown strangeness contribution (9) contains the weak axial form 1 the vector form factors of the nucleon. ctor G A which is known only at Q2 = OGeV2 from neutron beta decay. In rward scattering (9) is strongly suppressed due to the kinematical factors. he sensitivity on the axial term is on the order of 1-2% for HAPPEX and A4 nematics. In the case of backward scattering the sensitivity to the axial form ctor is of the same order as the sensitivity to the magnetic form factor, the :termination of term (9) requires an additional measurement of the parity olating asymmetry Apv on deuterium. Any significant difference between e measured parity violating asymmetry A and Ao is in forward scattering direct measure of the strangeness contribution to the vector form factors of e nucleon. Experiments 1

Approaches

parity violation electron scattering one finds two experiment a1 difficulties d the existing experiments use different techniques to overcome these as

169 Table 1. The different experimental approaches t o separate inelastic from elastic scattering processes at the very high scattered particle flux have been optimized to meet the specific kinematical requirements of each of the experiments. Elastic++Inelastic Experiment S A M P L E 6 ~ 7 ~ 8 ~ 9 low energy, no .Ir-production HAPPEX11~'2~13~ l4ll5 magnetic spectrometer A416 crystal calorimeter (E) GOI8 time of flight (T)

Measurement of High Rate integrating, air Cerenkov integrating in focal plane counting, histogramming E counting, histogramming T

summarized in table 1. First difficulty is the size of the asymmetry without strangeness contribution A0 in Eq. 3 which is used as an estimate of the expected measured asymmetry. For the existing and planned experiments it is on the order of A0 M lop6. A significant determination of the strangeness contribution requires a measurement at a very high rate of elastic scattered electrons in order to determine the asymmetry in reasonable experimental time with an accuracy of a few percent. Second, in the applied Q2 range of the existing and planned experiments, one has inelastic channels like nonresonant .rr-electroproduction or excitations of nucleon resonances like the A . These inelastic channels have to be separated very well from the elastic scattering, since they have their own parity violating asymmetries which are a priori unknown.

2.2

The SAMPLE collaboration at the MIT-Bates accelerator

The SAMPLE collaboration has m e a s ~ r e dat~the ~ ~MIT-Bates ~~ accelerator under backward scattering angles between 130" and 170' using a large solid angle air Cerenkov detector. The beam energy of 200 MeV ensures, that inelastic scattering from .rr-electroproduction is negligible. The Cerenkov light produced by elastic scattered electrons is focused into a photomultiplier tube and the current of the photomultiplier tube is integrated and digitized. The systematic change of beam parameters with helicity are naturally more difficult t o control at the pulsed machine, but on the other hand the lack of any spectrometry or calorimetry makes the experimental setup simpler. The published experimental result for the a s ~ r n m e t r yon ~'~ the proton is:

AFp = -4.92 f0.61 f0.73ppm

( 10)

170

The reported value for the quasielastic deuterium asymmetry' is:

A Y p = -6.79 f0.64 f0.55ppm

(11) The combination of the SAMPLE results from hydrogen and deuterium yield a value for the strangeness magnetic form factor contribution: (12) G&(Q2 0.1GeV2) = 0.14 & 0.29 -f 0.31 From the measurements on proton and deuterium it is possible to extract also a value for the isovector axial form factor:

G>(T = 1)

=

+0.22 f0.45 f 0.39

(13) which is in contrast to the calculated value of Zhu et.al.1° of G>(T = 1) = -0.83 f 0.26. In order to investigate this difference and the Q2-dependence of G2 the SAMPLE collaboration has proposed an additional measurement at even lower Q2 of 0.04 GeV2'. The measurement has been finished end of January 2002 and the analysis is in progress.

2.3 The H A P P E X collaboration at TJNAF The Hall A Proton Parity Experiment (HAPPEX) collaboration has measured parity violation in electron scattering at Jefferson Laboratory using the two spectrometers in Hall A. Both identical spectrometers have been used symmetrically and have been set to very forward scattering angles (6 = 12.3'). The scattered elastic electrons have been selected using a lucite-lead detector sitting in the focal plane of the spectrometer. The shape of the calorimeter has been adjusted to detect elastic scattered electrons only which are in the focal plane very well separated from the inelastic channels. The measured asymmetry isl1>l2

A,(Q2 = 0.477GeV2,6 = 12.3')

=

(-14.60 f 0.94 f 0.54) ppm

(14)

The experiment is sensitive to the combination GLt0.392GL t0.018G2. The contribution from the axial form factor had been estimated from calculation'' to ( - 0 . 5 6 f 0 . 2 3 ) p . The value of the strangeness contribution to the asymmetry has been normalized to the proton magnetic form factor and is: G& 0.392GL = 0.091 f 0.054 f 0.039 GLhP The HAPPEX collaboration is planning on two further measurements: A measurement at a lower Q2 of 0.1GeV213which then gives a different combination of G& and G&. The second proposal14 is a measurement with elastic scattering from 4He where all magnetic and axial contributions cancel giving a very clean measurement of G&.

+

171

pol. electron source P=80%, 1=20pA transmission

1022 PbF2-crystsls

Figure 1. A schematic overview on the principle of the A4 experiment is shown.

2.4

The A4 collaboration at the MAMI facility an Main2

The A4 collaboration16 has performed a measurement of the parity violating asymmetry in the scattering of longitudinally polarized 854.3 MeV electrons on unpolarized protons using counting techniques. This is the first time, that a parity violating asymmetry in electron scattering has been measured by counting individual, scattered particles. Particles scattered from the hydrogen target are detected between 30" < 8 < 40" (0.7 srad), resulting in a Q2 at 35" of 0.23 GeV2. The particle rate of elastic scattered electrons in the solid angle of the detector is about 10 MHz where the energy of the elastically scattered electrons is 734 MeV at 35" scattering angle. In addition there is an almost ten times higher background of about 90 MHz coming from other processes. Scattered electrons from pion production are closest in energy to elastic scattered electrons (610 MeV at 35"). Since the pion production has an unknown parity violating asymmetry by itself, the energy resolution of the PbFz-detector has to be good enough to separates these two processes at level better than 1%.Some of the photons from TO-decay can carry almost the energy of an elastic electron due to the three body m-production and additional

172

Figure 2. The left side shows a schematic of the mechanical setup of the lead fluoride calorimeter. The electron beam coming from the left is at about 2.2 m height. The right side is a schematic of the mechanical setup of the associated readout electronics which is in total about 3 m high.

boost17. Figure 1 shows the principle of the experimental setup. It can be divided in three different parts: 1. The electron source with the subsequent MAMI accelerator is the first and important part of the experiment. Helicity correlated changes of beam parameters cause trivial asymmetries in the PbF2detector and therefore need to be suppressed with substantial effort already at the electron source and within the electron accelerator. 2. The fast fully absorbing PbFz-Cerenkov calorimeter with the high power hydrogen target and the luminosity monitor detect the flux of particles and measure the particle energy. 3. In the associated experiment readout electronics the particles are registered and histogrammed with a dead time of 20 ns according to their deposited energy in order to separate elastic scattered electrons from other inelastic channels like n-production. Electrons from a high polarization strained layer GaAs crystal at a current of 20 p A and with a longitudinal polarization of about 80 % are accelerated within the three stages of the MAMI racetrack microtron up to an energy

173

22000L 20000

18000 16000 14000b

4000k

"0

&f 50

100

150

200

250

Figure 3. The datashow an energy spectrum of scattered particles from the hydrogen target as read directly from the hardware memory. The Number of counts per channel is displayed versus the ADC channel. The only correction comes from the differential nonlinearity of the ADC.

of 854.3 MeV. A fast reversal at about 25 Hz of the electron polarization is achieved by a Pockels-cell, which reverses the circular polarization of the laser light hitting the GaAs-crystal. An additional slow reversal of the electron polarization is done by putting in or out an additional X/Zplate in the optical system (GVZ). The electron current at the source is stabilized in a closed feedback loop by measuring the electron current in front of the high power hydrogen target and modulating the power of the laser light hitting the GaAs-crystal. Independently any difference in the electron current for the two different helicity states is controlled to a level of several ppm by adjusting the angle of an additional permanently installed X/2-plate. The energy of the electron beam is stabilized and controlled to a level of A E / E = by measuring the phase advance of the electrons in the last turn of the t h r d stage of MAMI by heterodyne methods and modulating the phase of the accelerating microwaves in the third stage linacs. In order to stabilize and control the position and the angle of the electron beam, the horizontal and vertical position of the electron beam is measured at two locations separated by 10 m in front of the hydrogen target by using position sensitive microwave cavities.

174 n

g20,

W

out

-20

in out out in out in 1

2

4

6

8

10

1

1

1

1

in out in out ,

12

1

1

1

1

1

1

1

14 16 Sample P

Figure 4. The measured decorrelated polarization corrected asymmetries are shown with X/2-plate in or out respectively as a function of the data sample.

The position signal is feedback to fast modulating coils, which then stabilize position and angle of the beam. The stabilization systems within the accelerator and the beam line have made it possible to efficiently suppress false asymmetries in the PbFz-detector. The mean of the helicity correlated variation of individual beam parameters over a data sample correspond to false asymmetries in the PbFz-detector which are less than 0.05 ppm or less than 1 % of the expected asymmetry in the PbFz-detector. The target system is a special new design, whch enforces turbulent flow in the target cell, so that the effective heat conductance is enhanced by transverse flow. The target can stand without boiling the full 20 p A of electron beam current also without any rastering of the electron beam. The left part of Fig. 2 shows a design drawing of the 1022 channel PbFz-Cerenkov calorimeter. For the measurements presented here, only half of the 1022 detector and electronics channels had been installed. The completion of the solid angle is in progress and almost completed. Scattered electrons coming from the left (electron beam height: 2.2 m) pass through the high power liquid hydrogen target. The scattered particles produce an electromagnetic shower in a cluster

175

of lead fluoride crystals. The crystals have a length of between 16-20 radiation lengths and a width of about $ of a Moliere radius so that the full electre magnetic shower of an elastic scattered electron is contained in a 3 x 3 crystal cluster. The Cerenkov light is read out by photomultiplier tubes. 8 waterCerenkov luminosity monitors are located &symmetrically under a scattering angle of 4-10" where the asymmetry from elastic scattering is negligible. The right part of Fig. 2 shows the mechanical setup of the associated 3 m high readout electronics, which consists of 1022 identical readout channels and which has been developed in the Institut fiir Kernphysik in Mainz. The photomultiplier signals of every 3 x 3 cluster are summed in a summation amplifier, integrated over 20 ns, digitized with a fast digitizer and stored in a fast first in - first out pipeline chip. A local maximum signal is derived by comparing the signal of the center crystal with the 4 direct neighbors. The additional requirement of an energy deposit above a threshold triggers the fast digitization. Any second particle hitting the same cluster or any direct neighboring cluster within the integration time of 20 ns would hinder the determination of the energy of the scattered particle and is therefore vetoed by the veto circuit. In this circuit the local maximum signals from the 5 x 5 cluster around the central 3 x 3 cluster need to be controlled. The distribution of the analogue and digital signals is done by a special bus structure where every detector module is connected to the 8 neighboring modules for the analogue signals and where every veto circuit is connected to the 24 neighboring modules for the digital signals. This requires also that the topology of the electronics is the same as the detector, i.e. neighboring detector modules go into neighboring electronics channels. The registered events in the pipeline are histogrammed in hardware memory in VMEbus based modules. The upper part of Fig. 2 right contains the analogue sum, the trigger and veto circuit and the digitization, the lower part contains the galvanically separated VME-bus based histogramming circuits. The whole lead fluoride detector is a completely new development and is used here for the first time. The whole system of electronics and detector achieves an energy resolution of 3.5 % at 1 GeV and a total dead time of 20 ns. The average rate per channel is about

500 k H z Fig. 3 shows a histogram of the scattered particle energies as read out from the histogramming memory of the data acquisition electronics. One can see the peak of elastic scattered electrons in the right part of the spectrum. There is a distinct valley between the elastic scattering and the A-excitation. At lower energies Moeller and Moeller-Mott scattering and excitation of higher resonances mixes together. The leftmost part of the spectrum is defined by the discriminator threshold.

176

There are at present 1022 histograms (511 for each polarization direction) per 5 minutes run which give at present a total of about 10,000,ooO histograms. These histograms together with the recorded beam parameters represent the data set for the analysis. The number of scattered elastic electrons is determined by integrating the histogram between the lower and the upper elastic cut. The number of elastic scattered events is then normalized to the luminosity signal. In a final step the correlation of the cross section with the change of electron beam parameters is analyzed by a standard multidimensional regression analysis in order to determine the measured asymmetry in elastic scattering. The polarization of the electron beam has been measured with a Moeller polarimeter in the hall of the 3-spectrometer setup, where the electron beam is antiparallel with respect to the A4 beam line. The Moeller polarimeter itself has a high accuracy of about 2 % per measurement. The fact that one has to interpolate between two measurements leads to a reduction in the knowledge of the polarization, which is reflected in an enlarged error on the polarization. Fig. 4 shows the final decorrelated, polarization corrected asymmetry as a function of the data sample. The data samples have been taken in a period from November 2000 until June 2001 and April 2002. The dependence of the combined decorrelated asymmetry value on different parameters which are used to select PbF2-spectra or to reject runs because of instable beam conditions etc. has been checked. It has been found that there is no significant variation of the asymmetry value on the different cut parameters. The combined preliminary result on the asymmetry from all data sets is:

Aemp= (-7.3 f0.5 f 0.8) x

lop6

(16)

The first error is the pure statistical error coming form the counting statistics of the scattered particles. The second error is the combined systematical uncertainty from the regression analysis and the uncertainty in the polarisation etc. The isolation of the individual electric or magnetic contribution is not possible with one measurement at this Q2 value only. The further program of the ACcollaboration involves the installation and commissioning of a laser backscatter Compton polarimeter and a transmission Compton polarimeter, which will reduce the uncertainty in the polarization down to possibly 2-3% from now 7 %. The completion of the missing 511 detector and electronics channels is also in progress and very important for the further measurement program. Due to the fact that we use crystals in the calorimeter the Q2 can be changed by changing the beam energy or by reverting the whole detector. This will make it possible to measure at a Q2 of 0.1 GeV2 in forward scat-

177

tering (8 = (35 f 5)") by lowering the beam energy to 570 MeV. In addition the statistical and systematical error at the Q2 value of 0.23 GeV2 will be further reduced. The present planning foresees, that the whole detector will be reverted, so that the scattering angle will be changed to backward scattering between 140" and 150'. We plan measurements at Q2 = 0.23 GeV2 and Q2 = 0.47GeV2 at this backward angle. In combination with the SAMPLE and HAPPEX measurements it will then be possible to make a full flavor separation at the three Q2 values in order to reveal the contribution of the strangeness to the vector form factors of the proton. Acknowledgments

Ths work has been supported by the Deutsche Forschungsgemeinschaft in the framework of the SFB 201, SPP 1034. We are indebted to K.H. Kaiser and the whole MAMI crew for their tireless effort to provide us with good electron beam. We are also indebted to the Al-Collaboration for the use of the Moeller polarimeter. References 1. Musolf et all Phys. Rep. 239,1 (1994).

2. D.H.Beck and B.McKeown, Phys. Rev. D 36,2109 (1987). 3. B.Borasoy and U.-G.Meissner, Ann.Phys. 254,192 (1997). 4. H.Lipkin and M.Karliner, Phys. Lett. B 461,280 (1999). 5. D.Kaplan and A.Manohar, NucI. Phys. B 310,527 (1988) 6. Mueller B.A., et al. Phys. Rev. Lett. 78, 3824 (1997) 7. Spayde D.T., et al. Phys. Rev. Lett. 84,1106 (2000) 8. Hasty R., et al. Science 290,2117 (2000) 9. Ito T., spokesperson. MIT-Bates Lab experiments 00-04 (2000) 10. Zhu S.L., et al. Phys. Rev. D 62,033008 (2000) 11. Aniol K.A., et al. (HAPPEX coll.) Phys. Rev. Lett. 82,1096 (1999) 12. Aniol K.A., et al. (HAPPEX coll.) 13. Kumar K., Lhuillier D., spokespersons. Jefferson-Lab experiment 99-115 14. Armstrong D., spokesperson. Jefferson-Lab experiment 00-114 (1999) 15. Beise E., spokesperson. Jefferson-Lab experiment 91-004 (1991) 16. von Harrach D., spokesp., Maas F.E. contact. MAMI exp. A4-01-93 17. S. Ong, M.P.Rekalo and J. Van de Wiele, Eur.Phys.J. A6, 215 (1999) 18. Beck D., spokesperson. Jefferson-Lab experiment 00-006 (2000)

E L E C T R O M A G N E T I C P R O D U C T I O N OF P I O N S I N THE R E S O N A N C E R E G I O N - T H E O R E T I C A L ASPECTS T. SAT0 Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043 Japan E-mail: [email protected] Theoretical approaches to investigate the structure of nucleon resonances from the pion electroproduction are briefly reviewed. Application of the dynamical approach on the &3(1232) region and the consequences on the y N + A transition form factors are discussed in comparison with the recent data.

+

1

Introduction

A challenging problem in nuclear physics is to understand the hadron structure and reactions in terms of QCD and investigate the role of confinement and chiral symmetry. One way to proceed is to test the predictions of QCD inspired models or lattice simulations using the data of resonance excitations by GeV electron. The baryon resonances in the meson-baryon continuum are excited from the resonant and non-resonant mechanisms. From the unitarity condition, resonance amplitude inherently contains both resonant and non-resonant mechanisms. Since most of the resonant parameters in hadron models are obtained by perturbative calculations of resonance decay, it is necessary to develop an appropriate reaction theory to separate the reaction dynamics to examine the predictions of the hadron models. The main objective of the dynamical approach developed by Refs.[l,2](SL model) is to extract electromganetic couplings of resonances and investigate the role of meson degrees of freedom from the pion photo and electroproduction with the meson-exchange model. The first place to carry out the program is the electromagnetic excitation of the A:p,(1232), which is isolated and almost elastic resonance. Here the interest is the Q2 development of the y N -+ A form factors. The electric and Coulomb quadrupole form factors are particularly interesting in connection with the deformation of the baryons and the helicity conservation law on the exclusive reaction at large Q2. Photon asymmetry data of pion phctoproduction at LEGS3 and Mainz4 have revealed a few % negative E2/M1. New precious and systematic data of pion electroproduction at JLAB5-', MIT-Bates'o>'', M a i n ~ ~ ~ and y'~ NIKHEF14 allow us to investigate the Q2 dependence of y N -+ A form factors and detailed test of the reaction dy-

+

+

178

179

namics, which will help to understand the mechanism of the quadrupole form factors. In this contribution, we briefly describe the existing theoretical a p proaches to extract resonance information form the data in section 2. A p plication of the dynamical approach for the pion electroproduction in the A33(1232) region and the consequence of the model in comparison with the recent data are discussed in section 3. 2

Theoretical Approaches

Essentially three theoretical approaches have been used to extract resonance parameters from the data in A region. One approach is based on the dispersion theory, which is applied for the A resonance region by Mainz group15. The other is effective Lagrangian appr~ach'"'~ based on the K-matrix unitarization with the tree approximation on the K-matrix. The last one is the dynamical approach of meson-exchange model, which has been investigated by several g r o ~ p s ~ - ~ Here , ~ ~we - ~briefly ~ . discuss the later two approaches. 2.1

Effective Lagrangian Approaches

Pion electromagnetic production can be described using Lippmann-Schwinger equation or Bethe-Salpeter equation with Green's function Go and driving term V as

T = V + VGoT, K

=V

+ Re(G0)K.

(1)

The on-shell T-matrix is expressed by only on-shell information of the Kmatrix. T-matrix is then given in the following matrix form for all possible open channels

In the effective Lagrangian approach, one approximates K-matrix by a driving term V evaluated by the Lagrangian model. Taking the first order perturbation of the electromagnetic interaction, T-matrix is approximated as

The first interaction Vp7 is meson production with electromagnetic current and the rest describes the meson-baryon scattering. One can reduce the number of unknown coupling constants of the model by evaluating the strong and

180

electromagnetic interactions V simultaneously with the Lagrangian model. In the Gies~en-GW”.’~works, the open channels are explicitly taken into account, where two pions channel is approximated by effective meson and resonances in the same partial wave can interfere with each other. If we restrict the intermediate state n in Eq. (3) by nN channel, one can obtain the formula of MAID18

2 GeV is referred to as the deep inelastic region. This distinction is rather artificial, and one key point of quark-hadron duality is that these two regions are actually connected. It is clear that duality in inclusive electron scattering must hold in the scaling region, for Q2 -+ m, as perturbative QCD is valid there, and therefore will describe the hadronic reaction. In deep inelastic scattering, the kinematics are such that the struck quark receives so much energy over such a small space-time region that it behaves like a free particle during the essential part of its interaction. This leads to the compellingly simple picture that the electromagnetic cross section in this kinematic region is determined by free electron-quark scattering, i.e. duality is exact for this process in the scaling region. The really interesting question is if duality will be valid approximately at lower Q 2 ,in a region where the cross section is dominated by resonances, which are strongly interacting

225 0.45 0.4 0.35

03

0 Q’= 1.7 (GeVlc)’

0.25

e:

0.2 0.15

0.1 0.05

“0.1

0.2

0.3

0.4

0.5

5

0.6

0.7

0.8

0.9

1

(e) loam Nicutsrcu OZ/OZ/W

Figure 1. Experimental data for F2(lOMeV1

l

1500

1400

1300

lux) N1/2+

N3I2’

N7/2+

NlR

N3n

NSlf

Figure 5. Model (conventional and hybrid) and experimental N baryons. For each set of quantum numbers, the mass spectrum is indicated (in MeV). The thin bars indicate quark model predictions for conventional baryon masses. The four fully filled thin bars around 1870 MeV are the flux-tube model hybrids. l9 The large rectangular blocks are the mass ranges of known experimental states.

(6) Electroproduction. In the flux-tube model, which is an adiabatic picture of a hybrid baryon, there is the qualitative conclusion that “ep + e X should produce ordinary N*’s and hybrid baryons with comparable crosssections”. 28 However, the conclusions obtained from the three quark - gluon picture of a hybrid baryon is different. For large Q2 electroproduction, the Q2 dependence of the amplitudes is summarized in Table 3. Since the photon has both a transverse and longitudinal component, the amplitude for a conventional baryon is expected to dominate that of the hybrid baryon as Q2 becomes large. For small Q2 the conclusion agrees with the large Q2 result for transverse photons, but is more dramatic for longitudinal photons: the

’

252 Table 3. Q2 dependence of amplitudes for the electroproduction of conventional or hybrid baryons with transverse or longitudinal photons, valid at large Q2.

II Conventional I Hybrid I Transverse Longitudinal

l/Q3 l/Q4

l/Q5 l/Q4

amplitude vanishes. It has accordingly been concluded that the (radially excited) conventional baryon is dominantly electroproduced (depending on the details of the calculation), with the hybrid baryon subdominant relative to the resonances S11(1535),013(1520) and A as Q2 increases. 29 The Q 2 dependence of the electroproduction of a resonance can be measured at Jefferson Lab Halls B and C and an energy upgraded Jefferson Lab. A hybrid baryon is expected to behave different from nearby conventional baryons as a function of Q2. One needs to perform partial wave analysis at different Q2. For large Q 2 cross-sections are small, which would make this way of distinguishing conventional from hybrid baryons challenging. 29730

Various characteristics of the N(1440) (Roper) have been argued to be consistent with its being dominantly a hybrid baryon: Its mass is consistent with bag model lo and QCD sum rule 2o estimates, it is suppressed in large Q2 electroproduction 29 and the width ratio ra/I'totis consistent with QCD sum rule decay calculations 27. The A( 1405) (J = and A(1520) (J = have recently been proposed to be hybrid baryons based on the idea that this hypothesis solves a J ordering problem in this system: for hybrid baryons the ordering in a constituent gluon model is as observed, while it is opposite in (most) quark models. 31 We highlight current experimental searches for hybrid baryons. Photoand electroproduction efforts at Halls B and C at Jefferson Lab (Newport News) can isolate hybrid baryons in y N -+ hybrid -+ ( p , w , q)N at masses less than 2.2 GeV. As previously remarked, the higher mass decay channels are of most interest. Similar searches at the Crystal Barrel and SAPHIR detectors at ELSA (Bonn) is under way. Particularly, at Crystal Barrel hybrid baryons is planned to be isolated in y N -+ hybrid -+ (7, no) Sll(l535) + (7, r o )q N . Hybrid mesons in flux-tube model decay strongly to P S-wave mesons and not to S+S-wave mesons. If this is also true for hybrid baryons, decay to a Pwave baryon ( 4 1(1535)) and an S-wave meson ( q or r o )should be prominent. In Q production hybrid baryons are searched for at BES at BEPC. Searches for hybrid baryons in ! I ! + hybrid i j -+ pfj (q,rO) have been undertaken.

3)

z)

+

253

Acknowledgments

This research is supported by the Department of Energy under contract W7405-ENG-36. References

1. T. Barnes, contribution at the COSY Workshop on Baryon Excitations (May 2000, Julich, Germany), nucl-th/0009011. 2. E.I. Ivanov et al., Phys. Rev. Lett. 86, 3977 (2001). 3. T.T. Takahashi, H. Matsufuru, Y. Nemoto and H. Suganuma, Phys. Rev. Lett. 86, 18 (2001); ibid., Proc. of “Int. Symp. on Hadron and Nuclei” (February 2001, Seoul, Korea), published by Institute of Physics and Applied Phyics (2001), ed. Dr. T.K. Choi, p. 341; ibid., T. Umeda, Nucl. Phys. Proc. S. 94, 554 (2001). 4. Yu. A. Simonov, these proceedings; D.S. Kuzmenko and Yu. A. Simonov, hep-ph f 0202277. 5. S. Capstick and N. Isgur, Phys. Rev. D 34, 2809 (1986). 6. C. Alexandrou, Ph. de Forcrand and A. Tsapalis, Phys. Rev. D 65, 054503 (2002). 7. C.E. Carlson and N.C. Mukhopadhyay, Phys. Rev. Lett. 67,3745 (1991). 8. C.-K. Chow, D. Pirjol and T.-M. Yan, Phys. Rev. D 59, 056002 (1999). 9. T . Barnes, Ph. D. thesis, California Institute of Technology, 1977; T. Barnes and F.E. Close, Phys. Lett. B 123, 89 (1983). 10. E. Golowich, E. Haqq and G. Karl, Phys. Rev. D 28, 160 (1983). 11. C.E. Carlson, Proc. of the 7th Int. Conf. on the Structure of Baryons (October 1995, Santa Fe, NM), p. 461, eds. B. F. Gibson et al. (World Scientific, Singapore, 1996). 12. C.E. Carlson and T.H. Hansson, Phys. Lett. B 128, 95 (1983). 13. I. Duck and E. Umland, Phys. Lett. B 128, 221 (1983). 14. P.R. Page, Proc. of “The Physics of Excited Nucleonsn (NSTAR2000) (February 2000, Newport News, VA). 15. J. Merlin and J. Paton, J. Phys. G 11,439 (1985). 16. K.J. Juge, J. Kuti and C.J. Morningstar, Nucl. Phys. Proc. S. 63, 543 (1998). 17. E.S. Swanson and A.P. Szczepaniak, Phys. Rev. D 59, 014035 (1999). 18. T.J. Allen, M.G. Olsson and S. Veseli, Phys. Lett. B 434, 110 (1998). 19. S. Capstick and P.R. Page, Phys. Rev. D 60, 111501 (1999). 20. L.S. Kisslinger et al., Phys. Rev. D 51,5986 (1995); Nucl. Phys. A 629, 30c (1998); A.P. Martynenko, Sou. J. Nucl. Phys. 54, 488 (1991).

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21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

S.M. Gerasyuta and V.I. Kochkin, hep-ph/0203104. T.D. Cohen and L.Ya. Glozman, Phys. Rev. D 65, 016006 (2002). E. Klempt, these proceedings. A.M. Zaitsev (VES Collab.), Proc. of ICHEP’96 (Warsaw, 1996). D.E. Groom et al. (Particle Data Group), Eur. Phys. J. C 15,1 (2000). H. Li (BES Collab.), Nucl. Phys. A 675,189c (2000); B.-S. Zou et al., hep-ph/9909204. L.S. Kisslinger and Z.-P. Li, Phys. Lett. B 445, 271 (1999). N. Isgur, Phys. Rev. D 60, 114016 (1999). Z.-P. Li et al., Phys. Rev. D 44, 2841 (1991); 46, 70 (1992). T. Barnes and F.E. Close, Phys. Lett. B 128,277 (1983). 0. Kittel and G.F. Farrar, hep-ph/0010186. P.R. Page, Proc. of <STdInt. Conf. on Quark Confinement and Hadron Spectrum” (Confinement 111), (June 1998, Newport News, VA). K.J. Juge, J. Kuti and C.J. Morningstar, Nucl. Phys. Proc. S. 63,326 (1998).

255

Gerry Miller, David Emst, Hall Crannell, and Mike Finn

Ed Brash and Garth Huber

Nucleon Electromagnetic Form Factors

E.J. Brash Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, SK SdS OA2, Canada E-mail: brash @uregina.ca

The electromagnetic form factors of the proton and neutron contain all the information about the charge and current distribution of these baryons, and thus provide strong constraints on the fundamental theory of strong interactions. Indeed, over the last several years, there have been a number of high profile experiments which aim to measure the nucleon form factors at increasingly large momentum transfers, which corresponds t o probing the nucleon at very small distance scales. At the same time, there has been a monumental effort on the theoretical front t o develop a coherent picture which would account for the observed behaviours. In this paper, I will present the current state of experimental knowledge of the nucleon form factors, as well as discuss the theoretical and phenomenological efforts in this area. .

1

Introduction

It has long been known that the proton and neutron are not point-like particles. The fact that the static magnetic moments of the nucleons differ significantly from the predictions of Dirac for spin-; fermions was the first and perhaps the strongest evidence which pointed t o a finite spatial size of the nucleon; this result was discovered almost 70 years ago. Moreover, finite spatial size is strongly coupled to substructure, which, for the nucleons, is embodied in the QCD description of the quark and gluon degrees of freedom within the nucleon. Within such a description, the moving charged quarks give rise to charge and magnetization current densities, which are characterized by the electromagnetic form factors of the nucleon. Thus, the elastic electromagnetic form factors are crucial to our understanding of the nucleon’s internal structure. From an experimental standpoint, the differential cross section for elastic eN + eN scattering is described completely in terms of the Dirac and Pauli form factors, Fl and F2, respectively, based solely on fundamental symmetry arguments. Further, the Sachs form factors, G E and ~ G M ~which , are simply derived from FI and Fz, reflect the distributions of charge and magnetization current within the nucleon.

256

257

2

2. I

Electromagnetic Form Factors of the Proton Rosenbluth Separation Experiments

Until recently, the form factors of the proton have been determined experimentally using the Rosenbluth separation method 3 , in which one measures elastic ep cross sections at constant Q2, and varies both the beam energy and scattering angle to separate the electric and magnetic contributions. In terms of the Sachs form factors, the differential cross section for elastic e p scattering has traditionally been written as

where r = Q2/4M; and 8, is the in-plane electron scattering angle. For elastic e p scattering, the so-called nonstructure cross section, uns is given by

where aemis the electromagnetic coupling constant, and E’(E) is the energy of the scattered (incident) electron. From the measured differential cross section, one typically derives a ‘keduced cross section”, defined according to

+

where t: = (1 2(1 + r )tan2(6,/2>}-’ is a measure of the virtual photon polarization. Equation 3 is known as the Rosenbluth formula, and shows that fits to reduced cross section measurements made at constant Q2 but varying E values may be used to extract both form factors independently. With increasing Q” the reduced cross sections are increasingly dominated by the magnetic term Gil.lp;at Q2 = 3 GeV’, the electric term contributes only a few percent of the cross section. Experimentally, this makes the extraction of the electric form factor exceedingly difficult at large momentum transfers. for the electric and magnetic In Fig. 1, we show the world data form factors of the proton extracted from e p elastic scattering cross section measurements, prior to 1998. Several features are noteworthy. In general, over the momentum transfers probed in these experiments, it was found empirically that the form factors followed an approximate dipole form, consistent with an exponential charge distribution, viz. 4~5767778~9710

258

For the magnetic form factor, the agreement with the dipole form is apparent up to Q2 x 5 GeV2. Above Q2 x 15 GeV2, the deviations from the dipole form are much larger. In the case of the electric form factor, the difficulty of the experiments at large momentum transfers is evident. For Q2 > 1 GeV’, not only are the error bars large, but the data from different experiments are not consistent with one another. It is clear that a tremendous effort has gone into the analysis of these difficult experiments, however, one is forced to speculate that some of the experiments have underestimated the systematic errors. For example, the Rosenbluth experiments apply radiative corrections to their data at leading order, i.e. one hard photon emitted, which can vary significantly with 6 depending on the specific experiment. However, higher order radiative corrections, i.e. involving more than one photon, could in fact change the slope of the reduced cross section versus 6 plot, and thus have an impact on the extracted form factors. 1.4

1.4

1.o

1.o

l2, in which one measures, using a focal plane polarimeter, the transverse (P t ) and longitudinal (Pe)components of the recoil proton polarization in 'H(e', e'fi scattering, using a longitudinally polarized electron beam. The proton form factor ratio is given simply by

Here, E, (Eet)is the incident (scattered) electron energy. The polarization transfer method offersa number of advantages over the traditional Rosenbluth separation technique. Using the ratio of the two simultaneously measured polarization components greatly reduces systematic uncertainties. For example, a detailed knowledge of the spectrometer acceptances, something which plagues the cross section measurements, is in general not needed. Moreover, it is not necessary to know either the beam polarization or the polarimeter analyzing power, since both of these quantities cancel in measuring the ratio of the form factors. The dominant systematic uncertainty is the knowledge of spin transport, although in comparison to the size of the systematic uncertainties in cross section measurements, this too is small. Finally, the most recent theoretical calculations verify the assertion that the form factor ratio is unaffected by radiative processes at the momentum transfers involved here.

2.3 Eaperimental Measurements The first experimental measurement of the proton electromagnetic form factor ratio, r , using the recoil polarization technique, was carried out by Milbrath et al. at MIT-Bates 13; they measured the ratio at Q2 = 0.38and0.5 GeV2. Subsequently, at Mainz, Dieterich et al. l4 carried out a similar lower momentum transfer measurement, at Q2 = 0.4 GeV2. The results of these experiments were consistent with the results of previous Rosenbluth separation experiments, and in particular the MIT-Bates experiment gave the community confidence in the recoil polarization technique. Through the use of a focal plane polarimeter (FPP) installed in one of the two high resolution spectrometers (HRS) in Hall A at Jefferson Lab, the JLab FPP collaboration has carried out a series of measurements since 1998, which span the momentum transfer range 0.5 < Q2 < 5.6 GeV2'y2>l5. This collective set of measurements represent the results of two dedicated experiments, E93027 and E99007, as well as results from other experiments, most notably a series of photoproduction experiments, which use the e p elastic scattering reaction as a background subtraction technique.

260

To extract the proton form factor ratio from the ratio of transferred polarization components in ep elastic scattering, one begins by measuring the ratio of normal to transverse polarization components at the focal plane of the proton HRS. The polarization components are related to the azimuthal (4) distribution of the scattered events according to f*=l++:sincp+c;coscp,

(6)

where the f refers to the two helicity states of the longitudinally polarized electron beam and

Thus by taking the difference between the two helicity states, the difference spectrum becomes fdiff = diff - , / i f f coscp. +z (8) The tremendous advantage of working with the difference spectrum is that instrumental asymmetries in the polarimeter, which are dominantly uncorrelated with electron beam helicity, will cancel in taking the difference between helicity states. Moreover, in evaluating the ratio of polarization components, one sees that it is not necessary to have any knowledge of the precise values of the electron beam polarization, P,, and the analyzing power of the second scatterer, Ay(6). Following the extraction of the polarization components at the focal plane, one determines the corresponding components at the target scattering vertex using the well-determined spin precession matrix of the electromagnetic elements of the HRS (quadrupole and dipole magnets). The form factor ratio is then determined directly from Eq. 5 above. In Fig. 2a, we show as filled symbols the data from the polarization transfer measurements for the ratio, r = p p G ~ , / G ~together ,, with data from Rosenbluth separation measurements. The polarization transfer measurements have revealed the somewhat surprising result that the form factor ratio decreases with increasing Q2.As well, the JLab results are in considerable disagreement with the Rosenbluth separation results at large momentum transfers. 2.4

Discussion of Proton Form Factor Results

The first issue that will be addressed is the notable discrepancy between the JLab data and the Rosenbluth separation results, in particular the data of Andivahis et al., who measured the form factor ratio at large momentum transfers at SLAC. According to Eq. 1, the electric part of the e p cross section decreases

26 1 1.5

__

.. ,

.

,

..

1 .o

I" a

B 2

0.5

0.0

3)

1 0' (GeV')

10

1 0' (&$)

10

Figure 2: (a) Published world d a t a for r = p p G ~ p / G ~ open p ; symbols indicate Rosenbluth separations while filled symbols indicate polarization transfer measurements In the case of the Rosenbluth data, the error bars shown are the result of combining systematic and statistical errors in quadrature. For the polarization transfer measurements, the error bars shown are statistical only; the systematic uncertainties are in general a small fraction of the statistical error in these experiments. The dot dash line is the parameterization from ref. l 6 t o the cross section data, which indicates r M 1. (b) Fit to polarization transfer measurements from Jefferson Lab 18. Included are the most recent data a t large QZ from E99007'. Also shown are calculated ratios from recent published fits to the electromagnetic form factors by Lomon l7 within the Gari-Kriimpelmann framework. 495,6,7,8,9

1,2,13714715.

with increasing Q 2 . Based on the new JLab data, which are of high quality both from a statistical and a systematic viewpoint, we have calculated the contribution of the electric part to the total ep cross section, and show the results in Fig. 3. One sees that in fact the electric part accounts for only about 5% of the total ep cross section at Q2 = 3 GeV2, and is a mere 1%at Q2 = 5 GeV2. Given the difficulty in controlling systematic uncertainties in the Rosenbluth separation experiments, where absolute cross sections must be measured to better than 5%, it is not surprising that the ratio results from the Rosenbluth separation experiments begin to diverge, both from one another and from the JLab data, a t about Q2 = 3 GeV2, precisely where the electric contribution to the total cross section becomes comparable in size to the systematic uncertainties of the experiment. The JLab results for the form factor ratio have motivated a tremendous number of theoretical calculations. In Fig. 4a, we show a sample of such

262

0

2

4

6

8

Q‘ [GeVi

Figure 3: Contribution of the electric term to the total e - p elastic scattering cross section.

c a l c ~ l a t i o n s ” compared ~ ~ ~ ~ ~ to ~ ~the ~ ~JLab ~ ~ data. ~ ~ ~ The ~ , feature of the new breed of calculations that appears most important at this point is the inclusion of relativistic effects. In addition, although the various theoretical treatments, e.g. the solition model, di-quark model, constituent quark model, etc., view the problem of nucleon stucture from apparently different viewpoints, an important commonality is that the dominant interaction is non-perturbative, or “soft”, at these momentum transfers. All indications are that at the momentum transfers involved in the JLab experiments, we are, perhaps not suprisingly, still far away from the perturbative region. This is most notably demonstrated in Figure 4b, where we show the ratio F2,/FlP, which can be extracted directly from the experimentally determined ratio G E ~ / G M ,scaled , by a factor of Q2. Theoretical analyses of the hard-scattering process, which must dominate at very large Q2, show that this scaled ratio should reach a constant value. The new JLab data clearly demonstrate that this is not yet the case. In Figure 4c, we again show F2,/FlP, now scaled by a single factor of Q. It is an experimental fact that this ratio reaches an approximately constant value at Q2 2 GeV2,and remains constant up to the maximum momentum transfer that has been measured. Ralston et al? have argued that this behaviour corresponds to the pQCD expectation if one takes into account contributions to the proton quark wavefunction from states with non-zero orbital angular momentum. In a different approach which again points to the importance of N

263 2.0

1.5

1.5

9

p 1.0

& 5?

5

1.0

0-

9 0.5

0.5 0

J h b 99-027

s slab

*-am

JLab 03-02?

a llrb

89-007

0.0

0.0 0.0

20

4.0

6.0

8.0

Q2 in GeV2

10.0

Q2 in GeV2

Q2 in GeV2

Figure 4: (a)Jefferson Lab data for r = ~ A ~ G E ~ / Gcompared , U ~ , to various theoretical models. (b) Jefferson Lab data for Q 2 F z p / F ~ p(c) . Jefferson Lab data for Q F z p / F l p

relativistic spin-dependent effects, Miller and Fra@ have calculated Fzp/F1, within the context of a relativistic constituent quark model. They show that the requirement of Poincark invariance of the proton wave function leads to a violation of the helicity conservation rule, because the non-perturbative wavefunction is a mixture of different helicity states. Their treatment results in a scaling of QFzp/Flp,in good agreement with the new JLab data.

3

Electromagnetic Form Factors of the Neutron

A detailed understanding of the electromagnetic structure of the neutron is equally important as for the proton. Indeed, most modern theoretical efforts seek a consistent description of all four of the elastic nucleon form factors simultaneously. As well, the neutron form factors represent essential ingredients for both measurements and calculations of a host of other fundamental physical observables. Perhaps most notable among these are the nuclear electromagnetic form factors. Interestingly, at a momentum transfer of 5 GeV', GE,, and G E should ~ be approximately equal to one another, based on currently available data and predictions, and thus in principle, one would desire to know the neutron electric form factor to a comparable level of accuracy to that of the proton in order to have an accurate description of deuteron form factors at these momentum transfers. In addition, knowledge of the neutron electromagnetic form factors is currently the largest and limiting systematic uncertainty for experiments which seek to extract the strange electric and magnetic form factors of the nucleon in parity-violating electron scattering.

264

Unfortunately, our knowledge of the electromagnetic form factors of the neutron is much poorer than for the proton. This is, of course, a direct result of two undeniable facts - the charge of the neutron is zero, and there are no free neutron targets. From an experimental standpoint then, neutron form factor measurements are fundamentally extremely challenging. However, one can also take the viewpoint that since the electric form factor of the neutron is approximately zero at all momentum transfers, deviations from zero represent a sensitive measure of more complicated dynamical effects. At very low Q2, the slope of G E ~ ( Qis~well ) known from the scattering of thermal neutrons from atomic electrons. At higher momentum transfers, measurements had proceeded always in the past from inclusive unpolarized e -2 H scattering. Of course, performing the Rosenbluth separation for these experiments is difficult, just as in the case of the proton form factor measurements, due to the now familiar magnetic/electric imbalance. In addition, the proton subtraction which is necessary when one uses a deuteron target adds another level of difficulty, due to both experimental systematic uncertainties which arise, as well as the required detailed theoretical knowledge of the target wavefunction. Over the last several years, a host of experiments have been carried out at Bates, NIKHEF, Mainz, and JLab which have measured the neutron electric and magnetic form factors at ever increasing momentum transfers. In an attempt to address some of the systematic problems that plagued the previous Rosenbluth separation measurements, in many cases these experiments have carried out double-polarization measurements, where one makes use of a polarized electron beam, together with either the use of a polarized target or the measurement of the scattered neutron polarization. With the technology available today, these two methods have comparable figures of merit. Moreover, the systematic uncertainties involved are different, and thus a crosscomparison of the results is very informative. In Fig. 5, we show a compilation of the most recently available world data for the neutron electric form factor It is important to note that at this time, the final results for the two JLab experiments are not available, and thus the central values of the data points have been placed on the Galster parametrization 27 curve. In both cases, the error bars shown are those obtained from the experiment spokespersons. In addition, both of these groups have reported at this conference that their prelimary analyses indeed fall within one standard deviation of the Galster curve. 28729*30~31932~33734735.

265 0.12

0.1

0.08

5 CY

0.06

0.04

0.02

0

I 0.5

0'

(dd)

1.5

2

Figure 5: World data for the neutron electric form factor, GE,,.The dashed curve is the Galster parametrization 2 7 . The solid curve is the most recent phenomenological GariKrumpelmann type fit by Lomon 17.

4

Summary

The last several years have seen remarkable progress in our experimental knowledge of the electromagnetic form factors of the nucleon. At the same time, major advances have been made on the theoretical front, and now it appears that we have a much better understanding of the relevant degrees of freedom at the momentum transfers currently attainable. Recent calculations have shown that the inclusion of relativistic effects are crucial in understanding the proton form factor ratio data, but still suggest that the constituent quarks, as opposed to the current quarks of perturbative QCD, are the relevant objects in this energy regime. In Fig. 6 , we show the currently available world data for all four elastic nucleon form factors. In particular, we draw attention to the blue and red curves in each panel. These curves are the Gari-Krumpelmann model fits of Lomonl7, prior to and after inclusion of the JLab proton form factor ratio and neutron electric form factor data, respectively. Clearly, while such phenomenological model fits are useful, especially when trying to develop a self-consistent understanding of all four form factors, their predictive power is somewhat limited, as the model parameters depend strongly on the data sample used. The tremendous flurry of recent theoretical activity in this area, together with the limited predictive ability of phenomenogical models noted above, strongly underscores the need for the next generation of experiments which

266

Q2 [ GeV2 1

Q2 [

GeV2 I

Figure 6: World data for the elastic nucleon electromagnetic form factors. In all panels, the blue and red curves are recent phenomenological Gari-Kriimpelmann type fits by Lomon,'l as discussed in the text. The green curves in the proton form factor plots are the recent empirical parametrizations of Brash et al. l a . The dashed magenta curve shown in the proton magnetic form factor plot is the parametrization of Bosted 16, and the dashed curve shown in the neutron electric form factor panel is the Galster parametrizationz7.

seek to extend the current measurements to higher momentum transfers. Indeed, the next five years will see new experiments carried out at JLab which will measure the proton form factor ratio to a Q2 of 9 GeV2,and the neutron form factor to a momentum transfer of 3.2 GeV2,nearly doubling the current range in both cases. In addition, the planned energy upgrade of the CEBAF accelerator to 12 GeV will allow to measure these fundamental quantities to even higher momentum transfers, thus providing crucial constraints on the most advanced theoretical efforts. Acknowledgments

I wish to thank C.F. Perdrisat, V. Punjabi, M.K. Jones, and 0. Gayou for their assistance in the preparation of the transparencies used in the presentation and material used in this manuscript. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). References

1. M.K. Jones et al., Phys. Rev. Lett. 84, 1398 (2000)

267

2. 0 Gayou et al., Phys. Rev. Lett. 88, 092301 (2002). 3. M.N. Rosenbluth, Phys. Rev. 79, 615 (1950). 4. L. Andivahis e t al., Phys. Rev. D 50, 5491 (1994). 5. W. Bartel et al., Nucl. Phys. B 58, 429 (1973). 6. Ch. Berger et al., Phys. Lett. B 35, 87 (1971). 7. J . Litt et al., Phys. Lett. B 31, 40 (1970). 8. L.E. Price et al., Phys. Rev. D 4, 45 (1971). 9. R.C. Walker et al., Phys. Rev. D 49, 5671 (1994). 10. T. Jannsens et al., Phys. Rev. 142, 922 (1966). 11. A.I. Akhiezer and M.P. Rekalo, Sov. J. Part. Nucl. 3, 277 (1974). 12. R.G. Arnold, C.E. Carlson, and F. Gross, Phys. Rev. C 23, 363 (1981). 13. B. Milbrath et al., Phys. Rev. Lett. 80, 452 (1998), Phys. Rev. Lett. 82, 2221(E) (1999). 14. S. Dieterich et al., Phys. Lett. B 500, 102 (2001). 15. 0. Gayou et al., Phys. Rev. C 64, 038202 (2001). 16. P.E. Bosted, Phys. Rev. C 51, 409 (1995). 17. Earle L. Lomon, Phys. Rev. C 64, 035204 (2001). 18. E.J. Brash et al., Phys. Rev. C 65, 051001R (2002). 19. A.F. Sill et al., Phys. Rev. D 48, 29 (1993). 20. M. De Sanctis et al. Phys. Rev. C 62, 025208 (2000). 21. D.H. Lu et al., Phys. Rev. C 57, 2628 (1998). 22. R.F. Wagenbrunn e t al., Phys. Lett. B 511, 33 (2001). 23. G. Holzwarth, 2. Phys. A 356, 339 (1996). 24. F. Cardarelli, S. Simula, Phys. Rev. C 62, 065201 (2000). 25. J . Ralston et al., in Intersections between Particle and Nuclear Physics, AIP C o d . Proc. No. 549 (AIP, Melville, NY, 2000), p. 302; (private communication). 26. G. Miller and M. Frank, Los Alamos Preprint, nucl-th/0201021. 27. S. Galster et al. Nucl. Phys. B 32, 221 (1971). 28. T. Eden et al. Phys. Rev. C 50, R1749 (1994). 29. M. Ostrick et al., Phys. Rev. Lett. 83, 276 (2001); C. Herberg et al., Eur. Phys. J . A 5, 131 (1999). 30. J . Becker et al., submitted to European Physics Journal. 31. D. Rohe et al., Phys. Rev. Lett. 83, 4257 (1999). 32. I. Passchier et al., Phys. Rev. Lett. 82, 4988 (1999). 33. D. Day and I. Sick, spokespersons, JLab Experiment E93-026. 34. R. Madey and S. Kowalski, spokespersons, JLab Experiment E93-038. 35. R. Schiavilla and I. Sick, Phys. Rev. C 64, 041002 (2001).

VIRTUAL COMPTON SCATTERING H. FONVIEILLE for the Jefferson Lab Hall A and VCS Collaborations Labomtoire de Physique Corpusculaire IN2P3-CNRS Universite' Blaise Pascal Clermont-II, F63177 Aubibre Cedex, Fmnce E-mail: [email protected] Virtual Compton Scattering off the proton: y * p 4 'yp is a new field of investigation of nucleon structure. Several dedicated experiments have becn performed at low c.m. energy and various momentum transfers: yielding specific information on the proton. This talk reviews the concept of nucleon Generalized Polarizabilities and the present experimental status.

Virt,ual Compbon Scat,t,ering (VCS) off t.he prot,on: y * p ~p has emerged within t.he last. t.en years as a powerful tool t.0 sbudy the int,ernal structure of the nucleon, bringing forward exciting new concepts and observables. The field can be subdivided according to different c.m. energy domains. At. high energy (s >> At&) and large momenbum t.ransfer (Q2 >> A{&), QCD factorizat,ion allows t.he use of t,he VCS process t.0 access: i) t.he nucleon Generalized Part,on Distributions (GPDs) via Deep VCS at, small t ; ii) the nucleon Distribution Amplitudes via hard Compton scatt,ering at large t '. At. low energy, t,he VCS process gives access t,o the nucleon Generalized Polarizabilities or GPs, which are t.he main focus of this t,alk. The basic concepts are introduced and an experimental review is given of the experimenbs performed in t,he t,hreshold regime (& 5 ( M N AtT)) and resonance region. --f

+

1

Concept of Generalized Polarizabilities

These are t,he generalizat,ion to a non-zero Q2 of the polarizabilities int,roduced in Real Compton Scatt,ering (RCS). Let, us recall t.hat.polarizabilit,ies measure how much t.he internal st,ructure of a composit,e particle is deformed when an external EM field is applied. The description of the RCS process at low energy involves six polarizabilities ( a ,p, and ~ i , i= 1 , 2 , 3 , 4 ) which parametrize the unknown part of nucleon structure, due t.0 its internal EM deformation (see ref.3 and references therein). Performed since the sixties, RCS experiments have measured the prot,on electric and magnetic polarizabilities ( Y E and 3, the results of which can be summarized as: i) t.he proton is a rather rigid object (polarizabilities are

268

269

ep-, amplitude

-

+ P _ _ _ _ _ _ _ __.__ _. _ .I L .________________.,_..___.__________ I -l“-Il

..,’

Compton Born

~

Compton Non-Born

Berhe-Heirler

Figure 1. Decomposition of the photon electroproduction amplitude into: Born (s and u channels), Non-Born, and BH contributions.

y p center-of-mass

:

Figure 2. VCS kinematic variables.

small), ii) p~ is smaller than a ~due , to a cancellation between its paramagnetic and diamagnetic contributions. These observables can be generalized t.0 any Q 2 ,such t,hat in VCS a t low energy one probes the nucleon polarizability locally inside the particle, with a distance scale given by Q 2 . Equivalently, VCS can be seen as elast.icscattering on a nucleon placed in an applied EM field, and hence the GPs can be seen as a measurement of “distorted” form factors. In all cases these observables are intrinsic characteristics of the particle, and provide a valuable and original test of models describing nucleon structure. 1.1

Photon electroproduction amplitude

VCS is accessed by photon electroproduction ep 4 em , which is the coherent sum of the Compton process and the BetheHeitler (BH) process, or electron bremsstrahlung; see Fig. 1. The main kinematic variables are defined in Fig. 2: the initial and final photon threemomenta q and q’ and the final photon angles , 8 and #, in the (yp) center of mass. The (ep + em)kinemat,ics is fully defined by these four variables plus the virt,ual photon polarisation c. The low-energy behavior of the amplitude Tee?has first been worked out

270 Tablc 1. The six lowest order Generalized Polarizabilities (also called dipole GPs. due to 1‘ = 1). find y

initial y*

h.I 1

hiI 1 M2

M1

S proton spin-flip 0 1 0 1 1 1

by P. Guichon et a1 ‘. Only a brief summary is given here, and more det.ails can be found in ref.5. The Compton amplitude decomposes int,o a Born t,erm, characterized by a prot,on in the intermediate st,at.e, and a Non-Born term cont,aining all ot,her int,ermediat,est,at,es. The BH and Born amplitudes are ent,irely calculable, wit,h prot,on EM form factors as input,s. The Non-Born amplitude T N Bcont,ains t,he unknown part of bhe nucleon st,ructure. Below pion threshold a Low Energy Theorem (LET) allows to expand TNBin powers of q’ ; t,he first, t,erm of t.he expansion is a known analytical funct,ion of six independent GPs, which are the goal of t.he measurements. These GPs are derived from a multipole expansion of T N B .One defines mut,ipole amplitudes HFi”’)’ according to t,he t,wo involved EM transit,ions: p ( p ’ ) st,ands for inibial (final) photon polarization st.ates (0,1,2 = longitudinal, magnetic, electric), 1 (1’) is t.he t,ot’alangular momentum of the init,ial (final) transibion, and S = (0), 1 stands for proton (non)spin-flip. The H N B mukipoles depend on photon momenta q and q’ . The GPs are defined (up t,o dimensional factors) as t,he limit of H N B when q’ + 0 , i.e. in the limit of a st,at,icEM field; they are denoted P(P’”P’)’ and depend only on q. Table 1 summarizes the notations for the two scalar ( S = 0) and the four spin GPs ( S = l),and also shows their continuity to the real photon point, (Q2= 0). Below pion threshold, the VCS amplit,ude is purely real; above pion threshold it becomes complex, and resonances can be produced on-shell. One may say that the GPs are conceptually linked t,o the contribution of virtual resonant int,ermediat,est,at,es,ext’rapolat,eddown to q’ = 0 . 1.2 Photon electroproduction cross section The photon electroproduction cross section is evaluated from the relat.ion: ITeey12= I T B H + B , ,-t ~ ~ ~R~~ ( T B H x+ TBN~B~) ~ I T N B.~Below ~ pion

+

27 1

threshold, I T N B (can ~ be neglected and thus the GPs are extracted via the interference term (BH+Born)(NB).The LET leads to the following expression for the unpolarized cross section: a d U ( e m ) = duBH+Born

(P.S.) x

[

+

211( P L L ( q )

-

where (P.S.) is a phase space factor and t1,t2, are known kinematic coefficients ’. The t,wo st,ruct,ure functions (PLL- ~ P T T and ) PLT are linear combinations of t,he GPs, given e.g. by t,he following choice: PLL(q) = - 2 d

hfjV

G E ( & ~P(O1’O1)O ) (4)

$

PTT(q) = -3 G M ( Q ~ ) X PLT(q) =

fi

Q

[

P(ll”l)l(q) -

G E ( Q 2 )P ( l l > l l ) O ( q+ )

Jz&

32

P(01”2)1(q)]

& GM(Q2)P ( o l , o l ) l(4) . 40

’.

no.

where Q2, 0 are specific kinematic variables So in an unpolarized experiment performed at fixed q and E , one measures two structure functions: (PLL- ~ P T , ) sensitive to the electric GP a ( Q 2 ) P(O1,ol)O , and PLT sensitive to the magnetic GP p(Q2) P(llill)O . N

N

1.3 Methods to extract GPs Two methods are presently used to extract GPs from absolute (em)cross sections. Method 1 is based on the LET, and only works below pion threshold. In bins of photon angles (Ocm,q5), one forms the quantity (dneZpduBH+BoTn)/(P.S.) measured at finite q f , and extrapolates it to q‘ = 0 to obtain the term in brackets in eq. 1. Present experimental data suggest that, at least in most of the phase space, the extrapolation can be done assuming that the 0 ( q f 2 ) contribution in eq. 1 is negligible. The bracketed term is then easily fitted as a linear combination of the two structure functions (PLL- ~ P T T and ) PLT a t fixed q and E. Method 2 is based on the formalism of Dispersion Relations (DR) and works below pion threshold as well as in the first resonance region. In this model the imaginary part of the VCS amplitude is given by the sum of T N intermediate states, computed from y * N ---t T N data (MAID model), plus adcr is a short notation for the fivefold differential cross section d 5 0 / d a y dk’lab dQcm P’ ’ bThe important notion is that Q2is equivalent to q.

272 Table 2 . VCS experiments.

I

II

experiment

JLab E93-050 Batcs E97-03 Batcs E97-05

Q2

(GeV2) 0.33 1.0:1.9 0.05 0.12

cncrgy fi < ( A ~ N All,) < 1.9 GeV

p cone

taking 1995+97

+

6'. ' 3 2000

status (a end 2001) published final stage analysis analysis

higher order cont,ribut,ionswhich are not const,rained by the model. The lat,t,er have t,o be fit.t,edt.o t.he VCS dat,a, under t.he form of t,wo free paramet,ers A, and Ap describing t,he Q2-dependence of t.he scalar GPs a and ,b. The knowledge of t,he paramet,ers at. a given value of Q2 t,hen yields t,he model predict,ion for t.he st,ruct,urefunctions PLL , PTT and PLT at. t.his moment,um t.ransfer.

1.4

GP effect on cross sections

Figure 3-left. shows the various component,s of t.he phot,on electroproduction cross sect,ion, in and out, of t,he leptonic plane, for select,ed kinemat.ics. The Bet.heHeit,ler peak is dominant. around t,he incident, and scat.tered electron direcCions; as one goes out-of-plane it fades away, giving a smoot,her cross sect.ion behavior. Figure %right shows t,he expected effect,of GPs on the cross section, as given by t.wo different calculat,ions: the lowest. order (or bracket,ed) t,erm of eq. 1, and t,he full DR prediction. Out-of-plane, the GP effect is roughly const,ant,,of t,he order of -10 %. In-plane the GP effect has a more complicat.ed pat,t,ern, due to the BH interference.

2

Experiments

Table 2 summarizes t.he VCS experiments performed so far. All of them have detected the scattered electron and out,going proton in high-resolution magnetic spectromet,ers, selecting the exclusive phot,on channel by the missingmass bechnique. Also, being unpolarized experiments, they all measure t,he same two struct.ure functions, at different,values of q. An accurate determination of the absolute fivefold cross secbions is necessary, due to t.he relat,ively small polarizability effect.

273 ....................................................... .. ~ 8 0 ; p . C 4 ~ .....~ ................. d ........... ~

~

0 .c

eg.

0.5 0.4

-1

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............

0.3

........... ~ . . ............,. ...........................

0.2

......

...............

. . . . . . . . . . . . :. . . . . . .

0.1 0 -0.1

1 0-

-0.2 -0.3 in-plane angle (deg)

in-plane angle (deg)

-

.- 0.5 0

2 0.4 0.3 0.2

-1

0.1 0 -0.1

-2

1 0-

-0.2 -100

0

100


-0.3

-100

0

100


Figure 3. (ep + epy) cross section components for: q = 1.08 GeV/c, q’ = 105 MeV/c, and E = 0.95 . The abscissa is the azimuthal angle of the outgoing photon when the polar axis is chosen perpendicular to the leptonic plane. “OOP” is the polar angle using this convention. Left plots: BH+Born (solid), BH (dashed), and Born (dotted) contributions. Right plots: the ratio ( d a c p - d a g H + g o r n ) j d a g H + g o r n for two calculations of d a c p : i) a first order GP effect, taking PLL - $PTT = 2.3 GeV-’ and PLT = -0.5 GeV-* (solid), ii) a DR calculation for parameter values A, = 0.92 GeV, A0 = 0.66 GeV (dash-dotted).

2.1

The MAMI experiment

’

The Mainz experiment measured photon electroproduction cross sections in the leptonic plane, at Q2 = 0.33 GeV2. The two structure funct,ions PLL- PTT/E and PLT were determined using the LET method as described in section 1.3, at q = 0.6 GeV/c and 6 = 0.62. Results are plotted in Fig. 4; they show good agreement with the calculation of Heavy Baryon Chiral Perturbation Theory ’. Several models predict an extremum of PLT at low Q 2 ,a feature which will be interesting to confirm experimentally. This turnover can be related to the behavior of the para- and diamagnetic contri-

274

100

PLL--PV/t(GeV')

0

90

c

80

-2

70

v

hP T

-1

60

50

-6

40 30 20

a

h PT i$.r10

10 0 0

0.4

0.2

Q' (GeV')

0

0.2

0.4 Q' (GeV')

Figure 4. VCS unpolarized structure functions measured at M i n z and their value a t the real photon point '. The curves represent two model predictions (CHPT and ELM lo), including (in dark grey) or not including (in light gray) the spin GI's (effect indicated by a n arrow).

but.ions to t.he p polarizability. In CHPT it originabes from the pion cloud, which yields a diamagnetic contribut,ion of posit,ive sign, visible at low Q2. For a review of model predictions see ref.9.

2.2

The BATES experiments

The Bates experiment 97-03 l1 has been performed at Q2 = 0.05 GeV2, i.e. in the region of the expected t,urnover of PLT. Measuremenk have been done in-plane and at 90" out-of-plane, using the OOPS spectrometers. The experiment covers a limited range in polar angle 6,, around 90°1 so t,he st,ruct.ure functions will be extract,ed mostly from the &dependence of t,he cross section. Dat,a analysis is in progress, presently concentrating on Montecarlo studies and absolute normalization. This experiment represents a Lab achievement, having made the first use of the high duty factor beam in the South Hall Ring and of the full OOPS system. The Bates experiment 97-05 l2 has been performed at Q2 = 0.12 GeV2 to study t,he N -+ A transit.ion, and data analysis is also in progress.

2.3 The JLab experiment Experiment E93-050 l3 was performed in Hall A of the Thomas Jefferson National Accelerator Facility (JLab) at Q2 = 1.0 and 1.9 GeV2. Data covers the region below pion threshold, and the resonance region up t.0 fi = 2 GeV at. Q2 = 1.0 GeV2.

275

The sbrong L0rent.z boost, from ~p cent,er-of-masst,o lab focuses the out,going prot,on in a narrow cone (see Table 2) allowing the hadron arm accept'ance t.0 cover t,he full phase space of t,he out,going phot,on in c.m. The key poi& t,o obtain accurat,e cross sections are a det,ailed Mont,e-carlo simulat,ion (including radiative correct,ions) and a det,ailed st,udy of cut,s in order to eliminat,e background, mainly due t.0 puncht,hrough prot,ons. Absolut,e nornializat,ion is checked in t,woways: i) by comput,ing t.he ( e p e p ) cross secbion from elast,ic dat,a t,aken during t.he experiment; ii) using t,he VCS dat,a, namely bhe import,ant' property that, bhe (epy) cross sect.ion should t,end t,o t,he known (BH Born) cross sect,ion when t,he final photon moment,um q' bends t,ozero ',Both t,est.sshow t,hat.the absolut,e normalization is correct, wit,hin 1-2 percent,, when using t.he most recent determinat,ion of proton form fact'ors: the JLab measurement, of t,he rat.io p G ~ / G n i and t,he Gbf fit. of ref.15. 0 Analysis below pion threshold: photon elect,roproduction cross sect,ions have been obt,ained at, fixed q = 1.08(1.60) GeV/c and fixed E = 0.95(0.88), corresponding t.0 the dat,a set, a t Q2 = 1.0 (1.9) GeV2. As an example, Fig. 5 shows some of t.he out,-of-plane cross sections measured for bot,h data set,s. These data illust,rat.ehow t,he (small) G P effect, increases with q' and how ibs shape agrees wit.h t,he LET prediction. More debails can be found in ref.17. of eq. 1 does not show any The quant,ity (doezp- duBH+BoVn)/(P.S.) not,iceable 9'-dependence, so it is averaged over q' and then fitted according lo the first method of section 1.3. The fit is performed on (in-plane out,-ofplane) cross sections and gives a reasonably good x2,confirming the validity of the low-energy expansion at these rat,her high Q2. Numerical results are report,ed in Table 3. A second analysis of t,his dat,a below pion threshold is presently underway, based on t.he DR model. A preliminary result at Q2 = 1.9 GeV2 is included in Table 3. 0 Analysis in the resonance region: these are the first VCS measurements ever performed in this kinematic domain. The initial goal was bo st,udy how resonances couple t,o the doubly EM channel, and search for possible missing resonances. Doing an excitation scan in W = 4 from M N to 1.9 GeV, cross sect,ions have been det,ermined at a fixed Q2 = 1.0 GeV2, backward angle Ocm = 167.2' and beam energy 4.032 GeV 16. They are presented in Fig. 6 as a funct,ion of W for various azimut.ha1angles 4. The DR model reproduces well t,he Delta region. Using these data, bhe second method of section 1.3 --f

+

''

+

=indeed, in eq. 1 the bracketed term is of order ( q ' ) O and the phase space factor (P.S.) is of order ( q' ) l .

276 Q2=

1.0GeV2

Q 2 = 1.9 GeV2

q=1080 MeWc &=0.95 €Y=(4@,14@)

q= 1600MeV/c, & = 0.88

t

I

., .

lo

. . . . . . . ........................................................................................................

l

~

-50

i

~

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,

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.

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.

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.

.

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.

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50

100

Figure 5. ( e p --t e m ) cross sections measured at JLab versus in-plane angle, for OOP= 50' (left) and 25' (right). Error bars are statistical only. The angle in abscissa is the same as in Fig. 3. The curves correspond to: BH+Born calculation (solid) and a first order G P effect (dotted).

has been applied for the first time. The free parameters of the DR model are adjusted by a x2 minimization, yielding the values of the two structure functions a t Q2= 1.0 GeV2 and E =0.95. Results are reported in Table 3. 2.4

Results summa?

Table 3 summarizes our present knowledge of the two structure functions measured in unpolarized VCS: the MAMI result, and the preliminary JLab results obtained so far, both below and above pion threshold. One first notices the fast decrease of the observables with Q 2 ,similarly to form factors. Second,

277 n

g

L

u!

-7

0

10

Lo

7

II

i lo-’

-s

0

$10-9 0

Lo

d-

-8

II

‘c10

%

2 S

0

Lo

Y

< b

b

II

lo-8

%

% 1o

0

-~

Lo 0 7

102

II 8

10-’

0

1o - ~

Lo

m 7

1o-8

II

%

1 0-’

0

-

Lo

lo-’

(D

o-8

II

1

8 I

I

I

I

I

W (GeV)

Figure 6. Photon electroproduction cross sections in the resonance region. The curve spanning the whole range in W is the BH+Born calculation. The curve limited to W < 1.25 GeV is the DR prediction for parameter values Aa = 1.0 and Ap = 0.45 GeV.

for the JLab data there is a nice agreement between the results obtained by the two methods, LET and DR. These new measurements should stimulate theoretical calculations of GPs at high Q2. Indeed most model predictions are presently limited to Q2 = 0.22 f 0.45 =t0.39 G& 0.392GL = 0.025 f 0.020 f0.014 GS, 3.8G: Gg O.1GL GS G k 0.2GL GS O.lGS,

+

+ + + +

G L , G&, G;

Table 1. Scope of the experiments measuring the strange form-factors.

different targets (like SAMPLE or HAPPEX 11), then they utilize kinematic suppression of one of the observables (resp. G& or G2). The Go program5 is the only one planned which will completely separate Gg, G& and G:. Asymmetries are measured with hydrogen target at forward (7”) and lydrogen and deuterium targets at backward (110”) electron angles. Moreover, the complete Go experiment will measure the evolution of those observables for three different momentum transfers Q 2 . Figure 1 shows the expected total errors of the Go measurements compared to the predictions of two different models : Chiral Perturbation Theory6 and Lattice QCD’. Note that though both models computations actually agreea with the zero-compatible results of the published SAMPLE and HAPPEX experiments, they predict non-zero individual values for G& and GL. Also, note that given the precision of the experiment, the Go data points will be sensitive to the Q 2 evolution such as the ones predicted by those models. The projected errors presented here include the statistical accuracy of the measurements (? = 5%), the systematic precision, as well as the knowledge of the electro-magnetic form-factors of the proton and the neutron. Though the Go collaboration has designed a specific apparatus of large solid angle (0.5-0.9 str), able to handle a large luminosity ( 2 ~ 1 cm-’ 0 ~ ~s-l), the Go overall errors are dominated by statistics .

aNote that the Chiral model actually uses the SAMPLE and the HAPPEX results t o fix two of its perturbative constants.

357 1.0

1.0

0.5

0.5

0.0

0.0

-0.5

-0.5

-1.0

-1.0

0.0 0.2

2

Figure 1. The projected errors of the Go measurements compared to two different models.

0.4

0.6

0 '

(GaV?

oa

1.0

1.2

0.0

0.2

0.4

0.6

0.0

1.0

1.2

9' (GoV')

The Go experimental technique

The Go experiment will use a 40pA beam with 70% polarization hitting a long cryogenic target (0.2 cm). A special purpose, super-conducting toroidal spectrometer, with azimuthally symmetric angular acceptance has been constructed. In the forward angle mode (see sketch in figure 2), individual particles will be counted in a set of 16 pairs of scintillators per octant placed in the focal plane. Each scintillator pair provides one bin in Q2. The bending angle is 35" and collimators protect the detectors from direct view of the beam. In the first part of the experiment, the protons recoiling from ep scattering at a fixed incident electron beam of 3 GeV will be detected at 0, = 70" f 10" for Q2 ranging from 0.1 to 1.0 GeV2. Time of flight measurement over a 32 ns window will be used to supplement momentum selection by the spectrometer and separate elastic from inelastic contributions. For this purpose, the beam will be pulsed at 31.25 MHz, although usually CEBAF operates at 499 MHz. Custom timeencoding electronics allow readout of high rates of the order of 2 MHz per scintillator pair. In a second part of experiment, the full detector will be rotated back-to-front in order to detect electrons at backward angles (0, = 111" f lo"), giving a comfortable lever arm for a Rosenbluth separation. In this configuration, each incident beam energy (0.4, 0.6 and 0.8 GeV) will correspond to a given Q2 (resp. 0.3, 0.5 and 0.8 GeV2). An additional scintillator hodoscope will allow kinematic separation of elastic and inelastic electrons. Inelastic asymmetries will measure the weak neutral transition current in the region of the A-resonance'. In order to separate the axial form-factor G,: data will be taken with proton and deuterium targets. For the deuterium measurements, aerogel Cerenkov counters will provide r / e separation.

358 Figure 2. Sketch of the Go apparatus in the forward configuration. The recoil particles are deflected by the magnet toward 8 focal plane detectors called octants. E k l m n Be

3

Conclusion

The Go experiment is currently undergoing installation in Hall C at JLab. All components (magnet, target, detectors and electronics) of the apparatus have been completed by an international (North American and French) collaboration of 80 physicists and are mounted on the beamline. Commissioning of the apparatus will take place between October and December 2002. The schedule for the different phases of the Go experiment, will be interleaved with other experiments using the standard Hall C apparatus. By performing a complete separation of Gg, GG and G;, the Go experiment will enlarge the extent of existing data on the strange quark content of the nucleon. Moreover, the complete Go experiment will measure the evolution of these form-factors for Q2 ranging from 0.3 to 0.8 GeV’.

References 1. F. Mass, Strunge form-factors of the ~iucleon,these proceedings. 2. S. Covrig, Status o,f the SAMPLE Deu.te.r.l:rint, experiment at 125 MeV, these proceedings. 3. R. Hasty et al., Science 290, 2117(2000). 4. K.A. Aniol et al., Phys. Lett. B 509, 211(2001). 5. JLab proposals E00-006 and E01-116, D. Beck spokesperson,

http://www.npl.uiuc.edu/exp/GO/GOMain.html 6. T. Hemmert, B. Kubis and U. Meissner, Phys. Rev. C60:045501, 1999. 7. S.J. Dong, K.F. Liu and A.G. Williams, Phys. Rev. D58:074504, 1998. 8. JLab proposal E01-115, S.P. Wells and N. Simicevic spokespersons.

THE NUCLEON FORM FACTORS IN THE CANONICALLY QUANTIZED SKYRME MODEL E. NORVAISAS, A. ACUS Institute of Theor. Phys. and Astronomy, Goitauto 12, Vilnius 2600, Lithuania E-mail: [email protected]; [email protected] D.O. RISKA Helsinki Institute of Physics; Dept. of Phys., University of Helsinki, 0 0 0 1 ~Finland E-mail: [email protected] The canonical quantization procedure in SU(2) Skyrme model ensures the existence of stable soliton solution with nucleons quancum numbers. An interesting consequence of the canonical ab initio quantization of the model is the natural appearance of a finite effective pion mass even for the chirally symmetric Lagrangian. The explicit expression for electric and magnetic form factors of nucleon have been derived. The calculated form factors are close to empirical ones.

1

Introduction

The chiral topological soliton model with topologically stable solutions, which represent baryons is that of T.H.R. Skyrme. The first comprehensive phenomenological application of the model to nucleon structure was the semiclassical calculation of the static properties of the nucleon in ref.2. That approach to the model did however have the more principal imperfection in that its lack of stable semiclassical solutions with good quantum numbers. In ref.3 was shown the existence of stable canonically quantized skyrmion solutions. In addition the Skyrme model was generalized to representations of arbitrary dimension of the SU(2) group. An interesting consequence of the canonical ab initio quantization of the Skyrme model is the natural appearance of a finite effective pion mass even for the chirally symmetric Lagrangian. This realizes Skyrme’s original conjecture that ”This (chiral) symmetry is, however, destroyed by the boundary condition (V(o0)= l), and we believe that the mass (of pion) may arise as a self consistent quanta1 effect ” To derive the explicit expressions for electric and magnetic form factors of the nucleon we employ the expressions €or the Noether currents derived in ref.3. Numerical results are plotted for the representations with j = 1/2; 1; 3/2 and also for the reducible representation j = 1@ 1/2 CB 1/2 @ 0. The different representations of the quantized Skyrme model may be interpreted as different phenomenological models.

’.

359

360

2

Quantum skyrmion

The chirally symmetric Lagrangian density that defines the Skyrme model may be written in the form 2: f: 1 L[u(r,t)]= - - ~ { R , R P } -%{ [R,, R ” ] ~ } , (1) 4 32e2 where RP is the ”right handed” chiral current R, = (8,U)Ut. The unitary field U(r, t ) in a general reducible representation of the SU(2) group, may be expressed as a direct sum of Wigner’s D matrices in terms of Euler angles. Quantization of the skyrmion field U is brought about by means of rotation by collective coordinates that separate the variables, which depend on time and spatial coordinates U(r, q(t)) = A (q(t))&(.)At (q(t)).Here the matrix Uo is the generalization of the classical hedgehog ansatz to a general reducible representation3. The collective coordinates q(t) are dynamical variables that satisfy the commutation relations [qa, qb] # 0. The energy of the canonically quantized skyrmion, which represents a baryon with spin-isospin e in an arbitrary reducible representation has the form:

+

Here M ( F ) is the classical skyrmion mass, a ( F ) is the moment of inertia of the skyrmion and A M j ( F ) is a (negative) mass term, which appears in the canonically quantized version of the model:

AMj(F)=

15e37::2(F) /dii2

sin2 F 15 + 4d2 sin2 F ( l - 2)I.

+ 2d39 + 2dl FI2

(3)

where di are constants and depends only on representation j (see ref.3). Dimensionless variable p is defined as f = ef,r. In the semiclassical case, the quantum mass correction A M j ( F ) drops out, and variation of the expression (2) yields no stable solution. The canonical quantization procedure leads to the expanded energy expression (2), variation of which yields a (selfconsistent) integro-differential equation with boundary conditions F ( 0 ) = T and F ( m ) = 0. In contrast to the semiclassical case, the asymptotic behaviour of F ( f ) at large f falls off exponentially as:

F(F) = k

(7+ r--) -T

exp(-rTz,F).

(4)

The stable quantum skyrmion exist if rTz: > 0. The positive quantity rn, = ef,rTz, admits an obvious interpretation as an effective pion mass.

361

I 0.5

1 Q ' (GeV I c)'

1.5

2

Figure 1. Proton electric form factor G c ( Q 2 )with relativistic corrections.

t

1 0.5

1 Q1

1.5

2

lGeV I c)

Figure 2. Proton magnetic form factor GP,(Q2) with relativistic corrections.

3

Form factors

The two parameters of the Lagrangian density, fn and e , have been determined here so that the empirical mass of the proton (938 MeV) and its electric mean square radius (0.735 fm') are reproduced for each value of j. The expressions for nucleon form factors we derived in ref.4. Here we present the numerical calculations of electric and magnetic nucleon form factors in the representations of the SU(2) group with j = 1/2,1,3/2 and in the reducible representation 1 @ 1/2 @ 1/2 @ 0. The effect of Lorentz boosts for these form factors is taken into account by means of the rescaling. The best agreement with experimental data on the form factors obtain with the reducible SU(2) representation, which in fact is the SU(3) group octet restricted to the SU(2). The electric and magnetic proton form factors and magnetic neutron form factor are close to experimental data. In Fig.3 we plotted electric form factors of neutron. The experimental data in this case have too wide uncertainty

362

0.5

1

1.5

Q'(GeV/c12

Figure 3. Neutron electric form factor Gg(Q2)with relativistic corrections.

-t

Figure 4. Neutron magnetic form factor G&(Q2) with relativistic corrections.

margins for model discrimination. The new experimental results indicates this form factor to much larger than what earlier data have suggested and thus closer to the present calculated values, even though these are still much larger than the empirical results. References 1. T.H.R. Skyrme, Nucl. Phys. 31, 556 (1962). 2. G.S. Adkins, C.R. Nappi, and E. Witten,NucZ. Phys. B 228, 552 (1983). 3. A. Acus, E. NorvaiBas and D.O. Riska, Phys. Rev. C 57, 2597 (1998). 4. A. ACUS,E. NorvaiBas and D.O. Riska, Physica Scripta 64, 113 (2001). 5. S. Platchkov et al., Nucl. Phys. A 510,740 (1990). 6. C. Herberg et al., Eur. Phys. J. A 5 , 131 (1999). 7. J. Becker et al., Eur. Phys. J. A 6, 329 (1999).

SOFT CONTRIBUTION TO THE NUCLEON ELECTROMAGNETIC FORM FACTORS

R.J. FRIES Physics Department, Duke University, P. O.%ox 90305, Durham, N C 27706 and Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany

V. M. BRAUN, A. LENZ AND N. MAHNKE Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany E. STEIN Physics Department, Maharishi University of Management, NL-6063 NP Vlodrop, Netherlands and Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany We present a calculation of the nucleon form factors in the light cone sum rule approach' employing higher twist distribution amplitudes that were recently obtained using conformal symmetry of QCD.2 Comparing our predictions with the most recent measurements at Jefferson Lab we find that the experimental data are well described by soft contributions that include nonleading helicity structures in the nucleon distribution amplitudes.

The coupling of the nucleon to the electromagnetic field can be described by the Dirac and Pauli form factors F1(Q2)and F2(Q2),

or equivalently by the the electric and magnetic Sachs form factors G E ( Q ~ ) and G M ( Q ~defined ) as G M ( Q ~=)F1(Q2)++F2(Q2) and G E ( Q ~=)P I ( & ' ) + Q2/(4M2)F2(Q2).Here P is the nucleon momentum, M its mass and q the momentum of the photon that couples to the nucleon. At Q2 = 0 the Pauli and Dirac form factors are normalized to the electric charges FP(0) = 1, F;"(O) = 0 and magnetic moments E;(O) = 1.79, F,"(O) = -1.91 of the nucleon, respectively. In the range of intermediate momentum transfer, i.e. a few GeV2, we expect that the hard contribution corresponding to a minimal number of gluon

363

364

Figure 1. Tree level diagram for the parton side of the sum rule.

exchanges between the quarks has to be supplemented by soft, or end-point contributions that are due to the so-called Feynman mechanism to transfer the large momentum and can be thought of as originating &om the overlap of soft wave functions. In several model calculations it was shown that soft contributions alone are capable of producing the form factors comparable with the data. The motivation for this work is first, to demonstrate that wave function components with a different helicity structure compared to the leading twist are important for the soft contribution, and, second develop a quantitative and less model-dependent approach for their evaluation. We suggest to use light cone sum rules (LCSRS) for this purpose, develop the necessary formalism and report the results of the first, leading order calculation of the nucleon form factors in this approach. The calculation uses in an essential way the results of ref.2 where a complete description of the lowest Fock state of the nucleon in terms of distribution amplitudes with different helicity has been worked out in detail. The three-quark nonleading helicity structures correspond to contributions with orbital angular momentum and have higher twist; they give rise to helicity-violating contributions to exclusive amplitudes and proved to be crucial for the description of the form factors. The LCSR calculation starts with the evaluation of the correlator

z”T,(P, q) = i

1

d4x eiq.z@IT { m $ m ( ~IP) )l

(2)

where jEmis the electromagnetic current, z a light cone vector and ~ c z ( 0 )= eiik [u~(O)C#U’(O)] 7 5 $dk(0) is an interpolating field for the proton. Using Eq. (1) one can find the nucleon contribution as:

(3)

365

2

I

6

' Qz

1

2

'

Qz

Figure 2. LCSR prediction for the soft contribution to the magnetic form factor of the proton (left) and the neutron (right) vs SLAC data. G D = dipole fit. ASY = asymptotic distribution amplitudes, SR = P-waves included, dashed = asymptotic with smaller ratio -A1

/fN-

Figure 3. The same as above for the ratio of electric over magnetic and electric over dipole form factors, respectively. SLAC and Jefferson Lab data are shown.

Here P' = P - q . On the other hand we can calculate this correlator in perturbative QCD. The lowest order contribution is given by the diagram in Fig. 1. Here the nucleon distribution amplitudes enter the game. From symmetry we see that only the vector structures can contribute. To the leading conformal spin accuracy the calculation involves two nonperturbative parameters fN and XI corresponding to the normalization of twist-3 and twist-4 amplitudes that are chirality-conserving and chirality-violating, respectively. In the final results only the ratio XI/ fN enters. We also include an additional off-light cone correction which brings in no new parameters. A matching of structures between the partonic calculation for z"T, and the corresponding hadronic calculation in Eq. (4)finally gives expressions for F1(Q2)and F2(Q2).In Fig. 2 we show results for the magnetic form factors of the proton and the neutron in comparison with SLAC data.3*4In Fig. 3 we show the same for the electric form factors in comparison with SLAC4 and recent Jefferson Lab data.5*6We give the results for the asymptotic distri-

366 I

1

2

3

4

5

6

Q’ 1

Figure 4. The ratio QFz/Fl for the proton vs. recent Jefferson Lab data.

bution amplitudes as well as including P-waves in the conformal expansion.2 The asymptotic distribution amplitudes generally give much better results. We also show curves where we decreased the relative normalization of twist-4 to twist-3, -A1 f f N ,to about 30% below the standard value of 5.1. With this value, which is still consistent with the theoretical error bars, the magnetic form factors can be described quite nicely. In particular we can reproduce the correct Q2 dependence in this region. For the electric form factor the results, now including spin flip amplitudes, also look reasonable. We would like to stress that these first results have to be considered as a demonstration of viability of the approach. A quantitative description requires the calculation of a, corrections to the parton side of the sum rule. Recently new Jefferson Lab data7 for the ratio F 2 fF1 has been discussed intensively. The data indicates that this ratio behaves like 1f Q rather than the expected 1/Q2 for intermediate Q2. In Fig. 4 we show the LCSR result for QF2 f F l for the proton versus data from Jefferson We note that the LCSR prediction for the ratio QFAIF1 is indeed flat in a broad region. References 1. V. M. Braun, A. Lenz, N. Mahnke and E. Stein, Phys. Rev. D 65,074011

(2002). 2. V. Braun, R. J . Fries, N. Mahnke and E. Stein, N d . Phys. B 589, 382 (2000). 3. L. Andivahis et al., Phys. Rev. D 50, 5491 (1994). 4. A. Lung et al., Phys. Rev. Lett. 70, 718 (1993). 5. M. K. Jones et al., Phys. Rev. Lett. 84, 1398 (2000). 6. 0. Gayou et al., Phys. Rev. C 64, 038202 (2001). 7. 0. Gayou et al. Phys. Rev. Lett. 88, 092301 (2002).

ELECTROWEAK PROPERTIES OF THE NUCLEON IN A CHIRAL CONSTITUENT QUARK MODEL S. BOFFI AND M. RADICI Dipartimento di Fisica Nucleare e Teorica, Universitd d i Pavia, and INFN, Sezione d i Pavia, I-27100 Pavia, Italy L. GLOZMAN, W. PLESSAS AND R.F. WAGENBRUNN Institut fur Theoretische Physik, Universitat Graz, A-SO10 Graz, Austria W. KLINK Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA Results for all elastic electroweak nucleon form factors are presented for the chiral constituent quark model based on Goldstone-boson-exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The direct predictions of the model yield a remarkably consistent picture of the electroweak nucleon structure.

We present results for the elastic electroweak nucleon observables as a progress report of a more comprehensive programme aiming at a consistent description of the electroweak properties of baryons at low energy. The theoretical context is represented by the chiral Constituent Quark Model (CQM) based on the Goldstone-boson exchange (GBE) quark-quark interaction, that is induced by the spontaneous chiral symmetry breaking in QCD and that accurately reproduces the baryon spectrum of light and strange flavors The dynamics of quarks inside the nucleon is essentially relativistic. Therefore, we have adopted the point-form realization of relativistic quantum mechanics, where the boost generators are interaction-free and make the theory manifestly covariant 2 . The electromagnetic photon-quark interaction is assumed point-like, but in point-form the momentum delivered to the nucleon is different from the one delivered to the struck quark; hence, we will name this approach the Point-form Spectator Approximation (PFSA) 3 . The quark wave functions deduced from fitting the baryon spectrum are used as input and no further parameter is introduced, since quarks are considered point-like and the point-form allows for an exact calculation of all boosts required by a covariant description. Results have recently been published for electromagnetic *, axial and pseudoscalar nucleon form factors. They are summarized here in Figs. 1-2, and in Tab. 1. The agreement with experimental data is remarkable and it indicates that by a proper choice of low-energy degrees of freedom a quark model is capable

'.

367

368 1.5

.,

/

1.25

1 0.75

0.5 ,

1.2

-I

1

Y

0.8 0.6 1.2 1

0.8 0.6 10 -2

10

-'

1 O'(GeV/c)'

Figure 1. Proton electric and magnetic form factors. Top and middle panels: ratios of electric ( G C ) and magnetic proton form factors to the standard dipole parametrization G D . Bottom panel: ratio of GC to G L . PFSA predictions of the GBE CQM (solid lines) are compared with nonrelativistic results (dashed lines) and experiment. In the top and middle panels the experimental data are from Ref. In the bottom panel recent data from TJNAF (filled triangles) are shown together with various older data points (see Ref. and references therein). All the ratios are normalized to 1 at Q2 = 0.

(GL)

'.

Table 1. Proton and neutron charge radii and magnetic moments as well as nucleon axial radius and axial charge. Predictions of the GBE CQM in PFSA (third column), in nonrelativistic approximation (NFUA, fourth column), and with the confinement interaction only (last column). Exp. 0.780(25) -0.113(7) 2.792847337(29) lo -1.91304270(5) lo 0.635(23) l 1 1.255f'O.006 lo

PFSA 0.81 -0.13

I NFUA I I

0.10 -0.01

I

Conf. 0.37 -0.01

;;lfig

369

0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04

2 1.75 1.5 1.25 1 0.75 0.5 0.25 0 0

1.2 1.1 1 0.9 0.8 0.7 0.6 -2 10

1

2

0

3 4 QZ( GeV/c)'

1

QZ( GeV/c)*

4 Q2(GeV/c)'

10 10 -l

2

""""

'

"-

'

10-1

""""

'

"

1

Q'(GeV/c)'

Figure 2. Left panel: neutron electric and magnetic form factors; in the top panel, G;; in the bottom panel, ratio of G& to the standard dipole parametrization G o , normalized to 1 at Q2 = 0; solid and dashed lines as in Fig. 1; the dot-dashed line represents the PFSA results for the case with confinement only; experimental data are from Ref. l 2 (top) and Ref. l3 (bottom). Right panel: nucleon axial and induced pseudoscalar form factors G A and G p , respectively; the PFSA predictions of the GBE CQM are always represented by solid lines; in the top panel, a comparison is given to the nonrelativistic results (dashed) and to the case with a relativistic current operator but no boosts included (dot-dashed); experimental data are shown assuming a dipole parameterization with the axial mass value M A deduced from pion electroproduction (world average: squares, Mainz experiment l 1: circles) and from neutrino scattering l4 (triangles); in the bottom panel, the dashed line refers to the calculation of G p without any pion-pole contribution; the experimental data are from Ref. 15.

of describing the spectroscopy and the low-energy dynamics of baryons at the same time. However, a more detailed comparison with data shows that there

370

is still room for quantitative improvements, e.g. by considering two-body electromagnetic current operators and constituent quark sizes. References

L.Ya. Glozman et al., Phys. Rev. D 58,094030 (1998). W.H. Klink, Pbys. Rev. C 58,3587 (1998). S. Boffi et al., hep-ph/0108271,Eur. Phys. J A, in press. R.F. Wagenbrunn et al., Phys. Lett. B 511,33 (2001). L.Ya. Glozman et a]., Phys. Lett. B 516,183 (2001). L. Andivahis et d.,Phys. Rev. D 50,5491 (1994); R.C. Walker et al., Phys. Rev. D 49, 5671 (1994); A.F. Sill et d.,Phys. Rev. D 48, 29 (1993); G. Hohler et al., Nucl. Phys. B 114,505 (1976); W. Bartel et al., Nucl. Phys. B 58,429 (1973). 7. M.K. Jones et al., Phys. Rev. Lett. 84,1398 (2000). 8. K. Melnikov and T. van Ritbergen, Phys. Rev. Lett. 84,1673 (2000). 9. S. Kopecky et al., Phys. Rev. Lett. 74,2427 (1995). 10. D.E. Groom et al., Eur. Phys. J. C15, 1 (2000). 11. A. Liesenfeld et al., Phys. Lett. B 468,20 (1999). 12. T. Eden et al., Pbys. Rev. C 50, R1749 (1994); M. Meyerhoff et al., Phys. Lett. B 327,201 (1994); A. Lung et al., Phys. Rev. Lett. 70,718 (1993); C. Herberg et al., Eur. Phys. J. A 5, 131 (1999); I. Passchier et al., Phys. Rev. Lett. 82,4988 (1999); D. Rohe et al., Phys. Rev. Lett. 83,4257 (1999); M. Ostrick et al., Phys. Rev. Lett. 83,276 (1999); J. Becker et d.,Eur. Phys. J. A 6,329 (1999). 13. P. Markowitz et al., Phys. Rev. C 48,R5 (1993); S. Rock et al., Phys. Rev. Lett. 49,1139 (1982); E.E.W. Bruins et al., Phys. Rev. Lett. 75, 21 (1995); H.G m et al., Pbys. Rev. C 50,R546 (1994); A. Lung et al., Phys. Rev. Lett. 70,718 (1993); H. Anklin et al., Phys. Lett. B 336, 313 (1994); H.Anklin et al., Phys. Lett. B 428,248 (1998). 14. T. Kitagaki et al., Phys. Rev. D 28,436 (1983). 15. G. Bardin et al., Phys. Lett. B 104,320 (1981); Seonho Choi et al., Phys. Rev. Lett. 71,3927 (1993). 1. 2. 3. 4. 5. 6.

NUCLEON HOLOGRAM WITH EXCLUSIVE LEPTOPRODUCTION

A.V. BELITSKY Department of Physics, University of Maryland, College Park, MD 20742-4111,

USA

D. MULLER Fachbereich Physik, Universitat Wuppertal, 0-42097 Wuppertal, Germany

Hard exclusive leptoproductions of real photons, lepton pairs and mesons are the most promising tools to unravel the three-dimensional picture of the nucleon, which cannot be deduced from conventional inclusive processes like deeply inelastic scattering.

1. From macro to micro Why do we see the world around us the way it is? Human eyes can detect electromagnetic waves in a very narrow range of wavelength, A, w 0.4 - 0.7pm, which we call visible light. The light from a source, say the sun, is reflected from the surface of macro-objects and is absorbed by the eye’s retina which transforms it into a neural signal going t o the brain which forms the picture. The same principle is used in radars which detect reflected electromagnetic waves of a meter wavelength. The only requirement t o “see” an object is that the length of resolving waves must be comparable t o or smaller than its size. The same conditions have to be obeyed in case one wants t o study the microworld, e.g., the structure of macromolecules (DNA, RNA) or assemblies (viruses, ribosomes). Obviously, when one puts a chunk of material in front of a source of visible light, see Fig. 1, the object merely leaves a shadow on a screen behind it and one does not see its elementary building blocks, i.e., atoms. Obviously, visible light is not capable t o resolve the internal lattice structure of a crystal since the size of an individual atom, say hydrogen, is of order ratom, ( a e m m e ) - ’ (10 KeV)-l and the light does not diffract from it. Therefore, to “see” atoms in crystals one has to have photons with the wavelength A, 5 ratom,or equivalently, of

-

371

372

Figure 1. Left: A beam of visible light does not resolve the crystal’s structure. Right: A n X-ray beam does and creates a diffraction pattern o n the photo-plate.

the energy E7 2 r,:,. To do this kind of “nano-photography” one needs a beam of X-rays which after passing through the crystal creates fringes on a photo-plate, see Fig. 1. Does one get a three-dimensional picture from such a measurement? Unfortunately, no. In order to reconstruct atomic positions in the crystal’s lattice one has to perform an inverse Fourier transform. This requires knowledge of both the magnitude and the phase of diffracted waves. However, what is measured experimentally is essentially a count of number of X-ray photons in each spot of the photo-plate. The number of photons gives the intensity, which is the square of the amplitude of diffracted waves. There is no practical way of measuring the relative phase angles for different diffracted spots experimentally. Therefore, one cannot unambiguously reconstruct the crystal’s lattice. This is termed as “The Phase Problem”. None of techniques called to tackle the problem provides a parameter-free answer. When we study hadronic matter at the fundamental level we attempt to perform the “femto-photography” of the interior constituents (quarks and gluons) of strongly interacting “elementary” particles such as the nucleon. Quantum ~ p w p adynamics, the theory of strong interaction, is not handy at present to solve the quark bound state problem. Therefore, phenomenological approaches, based on accurate analyses of high-energy scattering experimental data and making use of rigorous perturbative QCD predictions, are indispensable for a meticulous understanding of the nucleon’s structure. As we discuss below most of high-energy processes resolving the nucleon content, such as described in terms of form factors and inclusive parton densities, suffer from the same “Phase Problem” and therefore they lack the opportunity to visualize its three-dimensional structure. A panacea is found in newborn generalized parton distributions ’, which are measurable in exclusive leptoproduction experiments.

373

2. Form factors Nucleon form factors are measured in the elastic process CN 4 C’N’. Its amplitude is given by the lepton current L,(A) = Gt(k - A)y,ue(k) interacting via photon exchange with the nucleon matrix element of the quark electromagnetic current j,,(z) = C , e,q(z)y,q(z):

Here the matrix element of the quark current is decomposed in terms of Dirac and Pauli form factors (A = p2 - P I ) , accompanied by the Dirac bilinears h, = 21N(P2)ypUN(Pl)and el, = 2 1 ~ ( ~ 2 ) i a , ~ A ~ u ~ ( ~ 1In ) the Breit frame pi = -pi = A/2 there is no energy exchange El = E2 = E and thus relativistic effects are absent. The momentum transfer is threedimensional A2 = -A2, so that -#

(P2ljO(O)lPl) =

(PZ(I(O)IPI)

I

i = ---$;[A 2MN

x Z]@IGM(--A~) ,

(2)

+

are expressed in terms of Sachs electric G E ( A ~ ) = F1(A2) A2/(4M;)Fz(A2) and magnetic G M ( A ~ = ) F1(A2) F2(A2) form factors. Introducing the charge q = J d 3 Z j o ( Z ) and magnetic moment ii = 1d 3 Z [ Zx ;](z) operators, one finds the normalization

6

6

+

The interpretation of Sachs form factors as Fourier transforms of charge and magnetization densities in the nucleon requires to introduce localized nucleon states in the position space 1Z) as opposed to the plane-wave states used above Ip),

Here a very broad wave packet Q(p3 = const is assumed in the momentum space. Then the charge density p(Z) of the nucleon, localized at Z = 0, is

(2 = OIjo(Z)~Z= 0)

cT73

= @;@,lp(.’) = p;+1 J -e-ib’?GE( -&2)

1

(5)

and similar for the magnetic form factor. The famous Hofstadter’s experiments established that the proton is not a point-like particle ppoint(Z) =

374 * Generalized panan dishibution at 11-0

* Parton density

Formfdctor

Figure 2. Probabilistic interpretation of form factors, parton densities and generalized parton distributions at 1) = 0 in the infinite momentum frame p , + 00.

S3(?) which would have GFint = const, but rather G E ( - ~ ’ ) z (1 +

L . ” T & / with ~ ) -the ~ mean square radius T N x 0.7fm.

The Breit frame is not particularly instructive for an interpretation of high-energy scattering. Here an infinite momentum frame (IMF) is more useful, see discussion below. In this frame, obtained by a z-boost, the nucleon momentum is p , = (p1 p z ) , 00. In the IMF one builds a nucleon state localized in the transverse plane at b l = (2,y)

+

--f

Then one finds that the transverse charge distribution of the nucleon wave packet, see Fig. 2, is given by the two-dimensional Fourier transform of form factors ( P a b l = Olj,

Fi (-A:)+

(bl) I P Z , bl = 0) = h+

... .(7)

As previously one assumes a rather delocalized transverse momentum wave function CpL!D*(p, + A1/2)!D(pL- A l / 2 ) M 1. Thus, we can interpret form factors as describing the transverse localization of partons in a fast moving nucleon, irrespective of their longitudinal momenta and independent on the resolution scale. 3. Parton densities The deeply inelastic lepton-nucleon scattering LN amplitude 1 A N X = @Lp(q)(PXIjp(O)lP) 7

+

L’X probes, via the (8)

375

the nucleon with the resolution h/Q M (0.2fm)/(Q inGeV), set by the photon virtuality q2 = -Q2. Recalling that the nucleon’s size is r N 1fm, one concludes that for Q2 of order of a few GeV, the photon penetrates the nucleon interior and interacts with its constituents. The cross section of the deeply inelastic scattering is related, by the optical theorem, to the imaginary part of the forward Compton scattering amplitude N

The very intuitive parton interpretation has its clear-cut meaning in the IMF. A typical interaction time of partons is inversely proportional to the energy deficit of a given fluctuation of a particle with the energy EO and three-momentum po = ( p L o , z o p Z ) into two partons with energies E1,2 and three-momenta p 1 , 2= ( P ~ z1,2pZ). ~ , ~ It , scales, for p , -+00, as

A t - - =1 AE

1

P.2 4 0O. (10) P ~ o / x o- P ~ , / X I- ~ : 2 / ~ 2 Therefore, one can treat partons as almost free in the IMF due to the time dilation. The virtual photon “sees” nucleon’s constituents in a frozen state during the time of transiting the target which is, thus, describable by an instantaneous distribution of partons. Here again the analogy with X-ray crystallography is quite instructive: Recall that an X-ray, scattered off atoms, reveals crystal’s structure since rapid oscillations of atoms in the lattice sites can be neglected. Atoms can be considered being at rest during the time X-rays cross the crystal. The transverse distance probed by the virtual photon in a Lorentz contracted hadron, is of order h z l 1/Q, see Fig. 2. One can conclude therefore that simultaneous scattering off an nparton cascade is suppressed by an extra power of (l/Qz))”-’. The leading contribution to daDIs is thus given by a handbag diagram, i.e., the photonsingle-quark Compton amplitude. The character of relevant distances in the Compton amplitude (9) is a consequence of the Bjorken limit which implies large Q2 (small distances) and energies v = p . q (small times) at fixed ZB = Q2/(2v). By going to the target rest frame one immediately finds that at large Q2 the dominant contribution comes from the light-cone distances z 2 M 0 (l/Q2) between the points of absorption and emission of the virtual photon in (9) because zl/(Mzg), Z+ M ~ B / Q ~ . Since the hard quark-photon subprocess occupies a very small spacetime volume but the scales involved in the formation of the nucleon are

EO- El

N

- E2

N

N

-

376

much larger, hence, they are uncorrelated and will not interfere. The quantum mechanical incoherence of physics at different scales results into the factorization property of the cross section (9),

where fg is a parton distribution, - the density of probability to find partons of a given longitudinal momentum fraction x of the parent nucleon with transverse resolution 1/&,

1

1

(PlQ(Oh+q(z-n)lP) = 2P+

dx { f9(x)e--ixz-p+ - fQ(x)eixz-P+} . (12)

No information on the transverse position of partons is accessible here, Fig. 2.

4. Generalized parton distributions Both observables addressed in the previous two sections give only onedimensional slices of the nucleon since only the magnitude of scattering amplitudes is accessed in the processes but its phase is lost. These orthogonal spaces are probed simultaneously in generalized parton distributions (GPDs), which arise in the description of deeply virtual Compton scattering (DVCS) l N Py*N --+ PN’y in the Bjorken limit. In the same spirit as in deeply inelastic scattering, the latter consists of sending q2 = (q1 q2)’/4 4 --oo to the deep Euclidean domain while keeping A2 E ( p 2 - p 1 )2

and a handbag coefficient function, so that one gets

377

P.

Figure 3.

+

Geometric picture of deeply virtual Compton scattering.

where Fq = Hq, Eq and the contribution from a crossed diagram is omitted. GPDs depend on the s-channel momentum fraction x, measured with respect to the momentum p , and t-channel fraction q z q . A / q . p , which is the longitudinal component of the momentum transfer A M q p + A l , as well as its square A2 N” - (A: 4M$q2) / (1 - q 2 ) . Due to the reality of the final state photon q M -vcs) ABH

and measures the real part of the DVCS amplitude modulated by the harmonics of the azimuthal angle between the lepton and photon scattering planes 4; If on top of the charge asymmetry one further forms either beam or target polarization differences, this procedure would allow to cleanly extract the imaginary part of the DVCS amplitude where GPDs enter in diverse combinations. These rather involved measurements have not yet been done. Luckily, since the ratio of BH to DVCS amplitude scales like [ A 2 / q f ( l- ~ ) ] l / ~ / for y , large y or small -A2, it is safe to neglect ( A D V C S ~ ~ as compared t o other terms. Thus, in such kinematical settings one has access to the interference in single spin asymmetries, ‘1’.

d ~ e r J - . e ~ w y ( + A e) daeru+eilvjy(-Ae)

M

(ADVCS- A;>vcs) ABH

which measure GPDs directly on the line x = E a s shown in Fig. 5. Experimental measurements of these asymmetries were done by HERMES l1>l3 and CLAS l 2 collabarations. The comparison to current GPD models is demonstrated in Fig. 6. In order to go off the diagonal x = J one has to relax the reality constraint on the outgoing y-quantum, i.e., it has to be virtual and fragment into a lepton pair L L with invariant mass qg > 0. Thus, one has to study the process.lN -+ PLLN’. In these circumstances, the skewedness parameter r] independently varies for fixed Bjorken variable since J x -v(/q:l - yZ)/(/y?/ y;), and one is able to scan the three-

+

38 1 0.6r

. 58

= 0.11 0.4

(b)

5B = 0.12

-Az =

0 . 2 7 GeV'

'

-0.2.

-0.4 -0.6'

HERMES '

-3

-2

-0.4.

PRELIMINARY HERMES

--/

l1

l3

I

-1

0

1

2

3

4;

4;

Figure 6. Beam spin asymmetry (a) in e + p + e+mand unpolarized charge asymmetry (b) from HERMES with E = 27.6 GeV are predicted making use of the complete twistthree analysis for input GPDs from Ref. ': model A without the D-term (solid) and C with the D-term (dashed) in the Wandzura-Wilczek approximation lo as well as the model B with the D-term (dash-dotted) and included quark-gluon correlations. The dotted lines on the left and right panels show 0.23 sin 4; and -0.05+0.11 cos 4!, HERMES fits, respectively. Note that a toy model for quark-gluon correlations while only slightly changing the beam asymmetry, however, strongly alter the charge asymmetry.

dimensional shape of GPDs, see Fig. 5. Unfortunately, the cross section for DVCS lepton pair production is suppressed by azm as compared to DVCS and also suffers from resonance backgrounds, see, e.g., 14. Finally, perturbative next-to-leading (NLO) and higher-twist effects are shortly discussed. Estimates of the former are, in general, model dependent. NLO contributions to the hard-scattering amplitude l5 of a given quark species are rather moderate, i.e., of the relative size of 20%, however, the net result in the DVCS amplitude can be accidentally large ',l6. This can be caused by a partial cancellation that occurs in tree amplitudes. Evolution effects l7 in the flavor non-singlet sector are rather small. In the case of gluonic GPD models we observed rather large NLO corrections to the DVCS amplitude for the naive scale setting = -qq '. For such models one also has rather strong evolution effects, which severely affect LO analysis. However, one can tune the factorization scale p~ so that to get rid of these effects. The renormalon-motivated twist-four and target mass corrections l9 await their quantitative exploration.

''

References 1. D. Muller et al., Fortschr. Phys. 42 (1994) 101; X. Ji, Phys. Rev. D 55 (1997) 7114; A.V. Radyushkin, Phys. Rev. D 56 (1997) 5524. 2. M. Diehl, hep-ph/0205208; 3. M. Diehl et al., Nucl. Phys. B 596 (2001) 33; S.J. Brodsky, M. Diehl, D.S. Hwang, Nucl. Phys. B 596 (2001) 99. 4. X. Ji, Phys. Rev. Lett. 78 (1997) 610.

382

A.V. Belitsky, X. Ji, Phys. Lett. B 538 (2002) 289. M. Burkardt, Phys. Rev. D 62 (2000) 071503. J.P. Ralston, B. Pire, hep-ph/0110075. A.V. Belitsky, D. Muller, A. Kirchner, Nucl. Phys. B 629 (2002) 323. M. Diehl et al., Phys. Lett. B 411 (1997) 193; A.V. Belitsky et al., Nucl. Phys. B 593 (2001) 289. 10. A.V. Belitsky, D. Muller, Nucl. Phys. B 589 (2000) 611; N. Kivel et al., Phys. Lett. B 497 (2001) 73; A.V. Radyushkin, C. Weiss, Phys. Rev. D 63 (2001) 5. 6. 7. 8. 9.

114012. 11. 12. 13. 14. 15.

A. Airapetian et al. (HERMES Coll.), Phys. Rev. Lett. 87 (2001) 182001. S. Stepanyan et al. (CLAS Coll.), Phys. Rev. Lett. 87 (2001) 182002. F. Ellinghaus, these proceedings. E.R. Berger, M. Diehl, B. Pire, Eur. Phys. J. C 23 (2002) 675. A.V. Belitsky, D. Muller, Phys. Lett. B 417 (1997) 129; L. Mankiewicz et al., Phys. Lett. B 425 (1998) 186; X. Ji, J. Osborne, Phys. Rev. D 58 (1998)

094018. 16. A. Freund, M. McDermott, Phys. Rev. D 65 (2002) 074008. 17. D. Muller, Phys. Rev. D 49 (1994) 2525; A.V. Belitsky, D. Muller, Nucl. Phys. B 537 (1999) 397; A.V. Belitsky, A. Freund, D. Muller, Nucl. Phys. B 574 (2000) 347. 18. A.V. Belitsky, A. Schafer, Nucl. Phys. B 527 (1998) 235. 19. A.V. Belitsky, D. Muller, Phys. Lett. B 507 (2001) 173.

383

-

Anatoly Radyushkin, Andrei Belitsky,Christian Weiss, and Latifa Elouadrhiri

Riad Suleiman and Steve Wood

DEEPLY VIRTUAL COMPTON SCATTERING AT JEFFERSON LAB, RESULTS AND PROSPECTS LATIFA ELOUADRHIRI Physics Division, Jefferson Lab, Newport News, Virginia, USA E-mail: [email protected] Recent results from the Deeply Virtual Compton Scattering (DVCS) program at Jefferson Lab will be presented. Approved dedicated DVCS experiments at 6 GeV will be discussed.

1

INTRODUCTION

The recently developed formalism of “Generalized Parton Distributions” (GPDs) showed that information on quark-quark correlations, the transverse quark momentum distribution, and contributions of correlated quarkantiquark pairs (mesons) to the nucleon wave function can be obtained in hard exclusive leptoproduction experiments. GPDs provide a unifying framework for the interpretation of an entire set of fundamental quantities of hadronic structure, such as,the vector and axial vector nucleon form factors, the pcr larized and unpolarized parton distributions, and the spin components of the nucleon due t o orbital excitations. Deeply Virtual Compton Scattering (DVCS) is one of the key reactions to determine the GPDs experimentally, and it is the simplest process that can be described in terms of GPDs. One of the first experimental observation of DVCS was obtained from the recent analysis of CLAS data with a 4.2 GeV polarized electron beam in a kinematical regime near Q2= 1.5 GeV2 and ZB = 0.22 New measurements at higher energies are currently being analyzed, and dedicated experiments are planned. The high luminosity available for these measurements will make it possible to determine details of the Q2,ZB, and t dependences of GPDs. ‘j2v3

‘.

2

FIRST OBSERVATION OF EXCLUSIVE DVCS WITH THECLASDETECTOR

The DVCS/Bethe-Heitler (BH) interference has recently been measured using the CEBAF Large Acceptance Spectrometer in Hall B at Jefferson Lab *. The data were collected as a by-product of the 1999 run with a 4.25 GeV polarized electron beam. At energies above 4 GeV, the CLAS acceptance covers a wide

384

385

VCS

BH

Figure 1. Feynman diagrams for VCS and BetheHeitler processes contributing to the amplitude of ep -t epy scattering.

range of kinematics in the deep inelastic scattering domain (W 2 2 GeV and Q2 2 1 GeV2). The open acceptance of CLAS and the use of a single electron trigger ensures event recording for all possible final states. This experiment measures DVCS via the interference with the Bethe-Heitler (figure 1. At beam energies accessible at Jefferson Lab, the BH contribution in the cross section is predicted to be several times larger than the DVCS contribution in most regions of the phase space. The dominant BH process can be turned into an advantage by using a longitudinally polarized electron beam: one can measure the helicity-dependent interference term that is proportional to the imaginary part of the DVCS amplitude. In this case the pure real BH contribution is subtracted out in the cross section difference. For the present DVCS analysis, electron and proton were both detected in the CLAS detector, the reaction Zp -+ epX was studied and the number of single photon final states was extracted by fitting the missing mass ( M i ) distributions. The beam spin asymmetry was then calculated as:

Here P, is the beam polarization and, N T ( - ) is the extracted number of Z' -+ e p y events at positive (negative) beam helicity. The resulting qk dependence is shown in figure 2. A fit to the function

+

F ( 4 ) = Asin4 Bsin24 (2) yields A = 0.217 f 0.031 and B = 0.027 f 0.022. If the handbag diagram dominates, as expected in the Bjorken regime, B should vanish and only the contribution from transverse photons should remain, described by the parameter A. The GPD analysis including twist-3 contribution shows sensitivity of these data to ijGq correlations 5.

386 ,..........__ ...,_

0.41

..............

-0.4 l

0

50

u

l

100

,

l

150 0 9

,

l

200

,

l

250

,

l

300

,

L

350

deg

Fiwre 2. q5 dependence of the Zp --t em beam spin asymmetry at 4.25 GeV. Data are integrated over the range of Q2 from 1 to 2 GeV2, Z B fIom 0.13 to 0.35 (with the condition W > 2 GeV) and -t from 0.1 to 0.3 GeV2. The shaded region is the range of the fit function A(+) defined by statistical and systematical uncertanties. The curves are model calculations according to Ref.

’.

3

DEDICATED DVCS EXPERIMENTS AT JEFFERSON LAB

There are two dedicated DVCS experiments planned to run using the 6 GeV polarized electron beam. Both experiments plan to detect all three particles in the final state, the scattered electron, the recoil proton, and the photon. The first experiment E00-110 is a Hall A experiment which is expected to run in 2003. The DVCS beam spin asymmetries and cross section differences will be measured at three Q2 intervals, for a fixed interval of XB. The experiment will provide a precise check of the Q2dependence of the ep + epy cross section differences (for different beam helicities). The second experiment E01-113 is a dedicated CLAS DVCS experiment. The main goal of this experiment is to measure the t , 4, and X B dependence of the beam spin asymmetry for several fixed Q2 bins. This quantity is sen-

387

sitive to the model description of the GPDs. This will be the first time this dependence will be studied with high sensitivity using the DVCS process. A second goal will be to extract the helicity-dependent cross section difference, which directly determines the imaginary part of the DVCS amplitude. The results of these two experiments, Hall A and CLAS, on the Zp -i em cross section will allow tests of the &'-dependence to check the scaling behavior. As CLAS covers a broad kinematic range, we will be able to test the Q' dependence for different XB. This will verify that we are in a regime where a direct interpretation of the results in terms of GPDs is possible. Observation of significant scaling violations would provide important input for the analysis in terms of higher twist effects. 4

SUMMARY

A first measurement of the beam spin asymmetry in the exclusive electroproduction of real photons in the deep inelastic regime was presented. We see a clear asymmetry, as expected from the interference of the DVCS and BH processes. It has been shown that our results can be accomodated within a GPD analysis '. This supports the expectations that DVCS will allow access to GPDs at relatively low energies and momentum transfers. This opens up a new avenue for the study of nucleon structure which is inaccessible in inclusive scattering experiments. Dedicated DVCS experiments at 6 GeV electron beam energy are planned, which will allow significant expansion of the Q2 and ZJJ range covered in these studies. The high luminosity available for these measurements will make it possible to map out details of the Q', ZB, and t dependences of GPDs. References 1. D. Muller et al., Fortschr. Phys. 42 (1994) 2,101. 2. X. Ji, Phys. Rev. Lett. 78, 610 (1997); Phys. Rev. D 55, 7114 (1997). 3. A.V. Radyushkin, Phys. Lett. B 380, 417 (1996); Phys. RRv. D 56, 5524 (1997). 4. S. Stepanyan et al., Phys.Rev.Lett., 87 182002 (2001). 5. A. Belitsky, D. Muller, and A. Kirchner, Nucl.Phys., B629,323 (2002). 6. P. Bertin, C. HydeWright, F. Sabati6 et aZ., CEBAF experiment EOO110. 7. V. Burkert, L. Elouadrhiri, M. Garson, S. Stepanyan et al., CEBAF experiment Eo1-113.

TWIST-3 EFFECTS IN DEEPLY VIRTUAL COMPTON SCATTERING MADE SIMPLE C . WEISS Institut fiir Theoretische Physik Universitat Regensburg, 0-93053 Regensburg, Germany E-mail: [email protected] We show that electromagnetic gauge invariance requires a “spin rotation” of the quarks in the usual twist-2 contribution t o the amplitude for Deeply Virtual C o m p ton Scattering. This rotation is equivalent to the inclusion of certain kinematical twist-3 (“Wandzura-Wilczek type”) terms, which have been derived previously using other methods. The new representation of the twist-3 terms is very compact and allows for a simple physical interpretation.

Deeply Virtual Compton Scattering (DVCS), r * ( q ) + N ( p )+ r ( q ’ ) + N ( p ’ ) at large q2 and finite t = (p’--p)’, is the simplest process which could probe the generalized parton distributions (GPD’s) in the nucleon. New experimental results for spin and charge asymmetries of the cross section have been reported at this meeting, allowing for a first comparison of GPD models with data The crucial property of DVCS (and a number of other hard electroproduction processes) is that the amplitude can be factorized in a hard photonquark amplitude, and a soft matrix element containing the relevant information about the structure of the nucleon. Technically, this factorization can be accomplished using QCD expansion techniques familiar from the theory of deep-inelastic scattering. Originally only the contribution from twist2 operators was i n ~ l u d e d .It~ was realized that in this approximation the amplitude is not transverse (electromagnetically gauge invariant); the violation is proportional to the transverse component of the momentum transfer, which is not suppressed at large q 2 . A gauge invariant amplitude up to terms O ( t / q 2 )is obtained by including certain “kinematical” twist-3 contributions. These have been derived in various approaches: Momentum-space collinear e ~ p a n s i o n ,coordinatespace ~ light cone e x p a n s i ~ n , ~ and > ~ a parton-model based a p p r ~ a c hIn . ~the usual formulation the twist-3 terms are parametrized by auxiliary GPD’s given by certain integrals over the basic twist-2 GPD’s, much like the Wandzura-Wilczek part of the spin structure function g 2 ( x ) in inclusive DIS. In addition to restoring gauge invariance of the twist-2 contribution, the twist-3 terms give rise t o new helicity amplitudes and strongly influence the predictions for the spin and charge asymmetries of the DVCS cross section.8

388

389

twist-2

+ crossed

+ crossed

(4

(b) Figure 1.

In this talk I would like to point out that the kinematical twist-3 terms in the DVCS amplitude have a simple physical interpretation as being due to a “spin rotation” applied to the twist-2 quark density matrix in the n u c l e ~ n . ~ This allows for a very compact representation of the twist-3 effects. Most important, it shows that, in spite of the apparent complexity of the amplitude at twist-3 level, DVCS is still a LLsimple” process. The results reported here have been obtained in collaboration with A. V. Radyushkin (Jefferson Lab and Old Dominion U.) Consider virtual Compton scattering off an electron in QED at tree level, see Fig. la. It is well-known that transversality of the amplitude, q,T’, = 0 and T,,q; = 0, requires not only the Ward identities relating the electromagnetic vertex and the free-field propagator, but also the on-shell conditions for the external particles, i. e., the Dirac equations for the electron spinors. Turning now to DVCS off a hadron, the twist-2 contribution to the amplitude in QCD is given by exactly the same diagrams its Fig. l a , describing virtual Compton scattering off a free quark, only the wave functions of the initial and final particle have been replaced by the transition matrix element of the appropriate non-local quark/antiquark density matrix between the hadronic states, see Fig. lb. The twist-2 part of the latter is defined as

plus a similar contribution with ,y- -+ 75ys^(a and i -+fy5. The density matrix is presented here in perhaps somewhat unusual form, in coordinate space, with the quark/antiquark “ends” located at X f ,212 (X is the center coordinate, z the separation); i and j are the Dirac spinor indices. Here $ and .J, are

390

+ crossed Figure 2.

the quark fields (we omit the flavor labels), and the bilinear operator is really a traceless QCD string operator, see Ref.g for details. What is important is that this-twist-2 density matrix does not satisfy the freefield Dirac equations with respect to the quark/antiquark LLends”; the violation is proportional to the momentum transfer A = p’ - p . The reason is, simply put, that in the twist-2 operator in Eq.(l) the quark spin is projected on a fixed direction, determined by the vector z , while the Dirac equations require that the spin projection changes between the two ends in accordance with the momentum transfer between the quark lines.a As a consequence, the twist-2 part of the DVCS amplitude alone is not electromagnetically gauge invariant; the amplitude violates transversality by terms proportional to A. It is not difficult to see what must be done in order to fix this problem. We must rotate the spin projection of the quarks in the density matrix (1) such as to align it with the momenta of the incoming and outgoing quark ends. This is achieved by a position-dependent rotation with a matrixg

The modified density matrix is

(x

1 - A)

aIn the usual collinear expansion around a fixed light-like direction, the vector operator in Eq.(l) would have a large “plus” component, while the quark/antiquark ends have transverse momenta because of A, # 0.

391

plus the same with T~ -+ ~~7~ and 2 + i y 5 . This “rotated” form satisfies the Dirac equations with respect to the external ends, up to terms proportional to t , see Ref.g for details. As a result, the DVCS amplitude obtained with Eq.(3) is gauge invariant up to terms of order O ( t / q 2 ) . Schematically, our modification of the twist-2 contribution to the DVCS amplitude can be represented as in Fig.2, with the spin rotation as an “intermediate step” between the twist-2 density matrix and the free quark Compton amplitude. In the terminology of the light cone expansion, the spin rotation of Eq.(3) amounts t o the inclusion of certain twist-3 operators, which, however, are completely given in terms of total derivatives of twist-2 operators (“kinematical twist-3”). When substituting parametrizations for the basic twist-2 matrix elements, Eq. (3) reproduces the Wandzura-Wilczek type relations for the twist-3 GPD’s, which were derived previously using other techniques.6 Thus, all the complexity of the kinematical twist-3 effects in DVCS can be reduced t o the simple spin rotation of Eq.(3). The effect of kinematical twist-3 terms on DVCS observables have been discussed in the literature.8 The twist-3 terms affect in particular the spin and charge asymmetries of the cross section. The spin rotation representation could be helpful in developing a more intuitive understanding of the twist-3 effects in DVCS observables. This problem certainly deserves further study. C.W. is supported by a Heisenberg Fellowship from Deutsche Forschungsgemeinschaft (DFG). References

1. A. Airapetian et al. [HERMES Collaboration], Phys. Rev. Lett. 87, 182001 (2001); G. van der Steenhoven, this meeting. 2. L. Elouadrhiri [CLAS Collaboration], this meeting. 3. X. Ji, Phys. Rev. D55 (1997) 7114; J. C. Collins, L. Frankfurt and M. Strikman, Phys. Rev. D56 (1997) 2982; A. V. Radyushkin, Phys. Rev. D56 (1997) 5524. 4. I. V. Anikin, B. Pire and 0. V. Teryaev, Phys. Rev. D62,071501 (2000). 5. A. V. Belitsky and D. Muller, Nucl. Phys. B589 (2000) 611. 6. A. V. Radyushkin and C. Weiss, Phys. Lett. B 4 9 3 (2000) 332; Phys. Rev. D 63 (2001) 114012. 7. M. Penttinen et al., Phys. Lett. B 4 9 1 (2000) 96. 8. N. Kivel, M. V. Polyakov and M. Vanderhaeghen, Phys. Rev. D 63, 114014 (2001). A. V. Belitsky, A. Kirchner, D. Muller and A. Schafer, Phys. Rev. D 64, 116002 (2001); Phys. Lett. B 510, 117 (2001). 9. A. V. Radyushkin and C. Weiss, Phys. Rev. D 63 (2001) 114012.

MEASUREMENT OF HARD EXCLUSIVE REACTIONS WITH A RECOIL DETECTOR AT HERMES R.. KAISER. (ON BEHALF O F T H E HER.MES COLLABOR.ATION) Department of Physics and Astronomy, University of Glasgow, Glasgow G i 2 SQQ, United Kingdom E-mail: [email protected]. uk

The HERMES collaboration is planning to use a &coil Detector in combination with a high density unpolarized gas target to measure hard exclusive redions. This paper outlines the design of the detector and gives projedions for measurements of the beam spin and beam charge asymmetries in Deeply Virtual Compton Scattering (DVCS).

1

Exclusive Measurements at HERMES

Historically, the investigation of the spin structure of the nucleon in electron scattering has been synonymous with inclusive measurements, i.e. only the scattered electron was detected. In more recent times, semi-inclusive measurements have substantially extended the understanding of the nucleon spin. Nowadays, exclusive processes, where all reaction products are detected, are becoming a promising and powerful experimental tool. HERMES has already observed and investigated several different exclusive reactions, including the exclusive electroproduction of charged and neutral pions and of pmesons Recently, the beam-spin azimuthal asymmetry associated with Deeply Virtual Compton Scattering (DVCS) and, even more recently, the beamcharge asymmetry in DVCS were measured by HERMES for the first time. Both measurements rely on the interference between the DVCS and the BetheHeitler (BH) processes occurring at HERMES energies. However, the missing mass resolution of the HERMES spectrometer is not sufficient to identify exclusive events individually and to separate them e.g. from those about 10% of the events where an intermediate A-resonance was created '. For this reason, exclusivity can only be established at the level of a data sample and only on the basis of restrictive cuts. The main aim of the Recoil Detector is to substantially improve this situation by establishing exclusivity at the event level, i.e. to reduce the non-exclusive background to levels below 1%. 233.

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The HERMES Recoil Detector

The design requirements on the Recoil Detector are defined by the kinematics and the nature of the particles involved in the exclusive reactions, as well as by those of the expected background reactions. The main background results from events with intermediate A-production; events with higher resonances can be removed by an invariant mass cut. Hence the particle types that are in principle to be detected are protons, pions, neutrons and photons from TO-decay. All exclusive physics processes that will be investigated produce a low momentum recoil proton at large laboratory angles. The left panel of figure 1 shows the kinematic distribution of recoil protons from BH/DVCS events in terms of momentum y and polar laboratory angle 8 , as obtained from Monte Car10 simulations that include the correct relative weights. The equivalent distribution for exclusive pO-productionis shown in the right panel. The Recoil Detector consists of three active detector parts (cf. figure 2): A

Figure 1. LefkKinematic distribution of recoil protons from BH/DVCS in momentum p and polar angle 0. Right: Corresponding distribution for exclusive po production. Boxes indicate the acceptance of silicon and SciFi detector.

silicon detector around the target cell inside the beam vacuum, a scintillating fibre (SciFi) tracker in a longitudinal magnetic field of 1 Tesla and a photon detector consisting of several layers of scintillator strips inside and outside of the magnet. The photon detector uses an extra layer of lead, the cryostat and the return yoke of the magnet as shower material. The thickness of the target cell wall (75 pm, perhaps 50 pm) and of the beam pipe (1.2 mm) is kept to a minimum to achieve the lowest possible momentum thresholds for the silicon and the SciFi detector. The acceptance of silicon and SciFi detector in p and

394

3 is indicated by the boxes in figure 1. By measuring the energy deposition

of ;he emerging recoil particles the silicon detector will provide the momentum nformation for recoil protons with momenta below 450 MeV/c. The fact that t is located inside the beam vacuum makes it possible to detect momenta as ow as 135 MeV/c, corresponding to kinetic energies as low as 9 MeV. The kiFi-detector measures the momentum of recoil protons between about 250 tnd 1400 MeV/c. It also detects pions and provides particle identification PID) for the separation of pions and protons. The photon detector detects ieutral pions through their decay photons and improves the pion/proton s e p tration for momenta above about 400 MeV/c. The exclusivity of a given event s established through the positive identification of the recoil proton, the a b ence of additional pions and cuts utilizing mainly the transverse-momentum )alance that can then be established by comparing the measured recoil proon momentum to the missing momentum calculated from the spectrometer nformation. Monte Car10 studies shown that in this way more than 90% of vents with intermediate A-resonances can be rejected, reducing the overall iackground to below 1%.

395

3

Projections for DVCS Measurements

One of the main measurements at HERMES with the Recoil Detector will be the beam charge and the beam spin asymmetry in DVCS. Projections for these asymmetries based on an integrated luminosity of 2 ft-’ taken with an unpolarized hydrogen target are shown in figure 3 together with the published HERMES data and predictions based on different GPD models.

*

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Figure 3. Left: Projection for a measurement of the beam helicity asymmetry at HERMES BS a function of the azimuthal angle, 4, between the scattering and the production plane, in comparison to the 1996/97 data (open points). Right: Projection of the statistical accuracy of the lepton charge asymmetry as a function of the azimuthal angle, 4. Preliminary results of HERMES 1998/2000 data are shown for comparison (open points). Both projections are based on 2 fb-l and we shown in comparison to different GPD models.

References 1. HERMES Collaboration, hepex/0104005 and DESY-01047. 2. HERMES Collaboration, Eur. Phys. Journ. C17, 389 (2000) 3. HERMES Collaboration, hep-ex/0102037 and DESY-0G189 4. HERMES Collaboration, Phys. Rev. Lett. 87, 182001 (2001) 5. F. Ellinghaus, proceedings at QCD-”02, Ferrara, 2002, to be published in Nucl. Phys. A 6. HERMES Collaboration, Nucl. Instrum. Meth. A 417,230 (1998) 7. HERMES Collaboration, DESY PRC 02-01, HERMES 02-003. 8. V. Korotkov and W.-D. Nowak, Eur. Phys. Journ. C, in press, [arXiv:hepph/O108077)

DISPERSION RELATION FORMALISM FOR VIRTUAL COMPTON SCATTERING OFF THE PROTON B. PASQUINI', D. DRECHSEL', M. GORCHTEIN', A. METZ3, M. VANDERHAEGHEN' ECT*,Villazzano (fiento), and Universitci degli Studi di Tknto, Thnto, Italy Institut fur Kemphysik, J . Gutenberg-Universitat, Mainz, G e m a n y Division of Physics and Astronomy, VU, Amsterdam, The Netherlands We describe a dispersion relation formalism to the virtual Compton scattering reaction off the proton as a new tool to analyze VCS experiments above pion threshold, where one observes increasing effects of the generalized polarizabilities.

In Virtual Compton scattering (VCS) off a proton target, y*+ p --t y + p , a spacelike virtual photon (y*)interacts with a proton and a real photon (y) is produced. At low energies, the real photon plays the role of an applied quasi-static electromagnetic field. On the other hand, the non-zero four momentum transfer squared of the virtual photon, Q 2 , allows one to study the spatial distribution of the polarization effects induced in the target, by means of generalized polarizabilities (GPs) which are functions of Q2. Unpolarized VCS observables have been obtained from experiments at MAMI and at JLab 2,3, and further data are currently under analysis at MIT-Bates '. VCS experiments at low outgoing photon energies can be analyzed in terms of lowenergy expansions (LEXs) '. In the LEX, only the terms to leading order in the energy of the real photon are taken into account. These terms can be parametrized by 6 GPs. However, in order to increase the sensitivity of the VCS cross sections to the GPs, it is advantageous to go to higher photon energies, provided one can keep the theoretical uncertainties under control when approaching the pion threshold. To this aim, we developed a dispersion relation formalism for VCS ', and here we report the essential of this analysis. The VCS process can be achieved through the e p + em reaction. In this process, the final photon can be emitted either by the proton, referred to as fully virtual Compton scattering (FVCS), or by the lepton, corresponding to the Bethe-Heitler (BH) process. The BH contribution is exactly calculable from QED in terms of the the proton electromagnetic form factors, while the FVCS amplitude contains the VCS subprocess y*p -+ yp. Furthermore, the scattering amplitude for VCS can be decomposed into a Born (B) and a nonBorn part (NB) . The Born amplitude, defined as in Ref. ', contains only properties of the proton in its ground state. The residual non-Born contribution contains the information of the excitation spectrum. These nucleon

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structure information can be parametrized in terms of 12 non-Born invariant amplitudes, denoted by q N B ( Q 2 , v , ti) ,= 1, ...,12, which are functions of 3 invariants: Q 2 , v = (s - u)/(4M), and t ( s , t and u are the Mandelstam variables for VCS, and A4 is the proton mass). For the amplitudes one can write down the following unsubtracted dispersion relations (DRs)

FFB

) F?(Q2,v,t) ReFFB(Q2,v,t) = F r L e ( Q 2 , v , tv’ ImsFi(Q2,v’,t ) :P dv’ y” - v’

+

FF

J,trn

FrLe

,

where is the Born contribution, represents the nucleon-pole contribution, and Im,Fi are the discontinuities across the s-channel cuts of the VCS process, starting at the pion production threshold vo. To ensure the convergence of the unsubtracted DRs in Eq. (1), it is necessary that at high energies (v + 00 at fixed t and fixed Q’) the amplitudes ImsF,(&’,v,t) drop fast enough. It has been shown that unsubtracted DRs hold only for ten of the 12 amplitudes. For the remaining two amplitudes, denoted by Fl and F5,we close the contour of the integral in Eq. (1) by a semi-circle of finite radius v, in the complex plane, i.e. we evaluate the unsubtracted dispersion integrals for F1 and F5 along the real v-axis in a finite range (-vmaz5 v 5 +v,,,), and the remaining contribution from the finite semi-circle of radius v, in the complex plane is described by an “asymptotic contribution”. The imaginary parts of the amplitudes F, in Eq. (1) are obtained through unitarity from the dominant contribution of T N intermediate states, using as input the pion photo- and electroproduction multipoles of the phenomenological MAID analysis 7. The asymptotic contribution to the amplitude F5 results from tchannel nO-exchange, while the asymptotic contribution to the amplitude F I originates predominantly from t-channel nn intermediate states. In addition, it turns out that higher-energy dispersive contributions ( m N ,...) mainly affect the Fl and F 2 amplitudes. Since the dispersive terms beyond ?rN are very poorly known, we parametrize these contributions to F1 and FZby energy independent constants, fixed at arbitrary &’, v = 0 and t = -&’. In this way we introduce two free parameters which can be expressed in terms of the electric, a(&’), and magnetic, P(&’), GPs, which have to be fitted to experimental VCS data at each fixed value of Q’. However, in order to provide predictions for VCS observables at different values of Q 2 , we take the following parametrization for the &’ dependence of the scalar GPs

398

where the values at Q2 = 0 are fitted to real Compton scattering (RCS) data s. The present status of the analysis of the VCS experiments at JLab has been reported in this conference In particular, results for the unpolarized structure functions PLL- PTTf~ and PLT have been extracted from the analysis of JLab data below pion threshold, using both the LEX and the DR formalisms. A nice agreement between the results of both methods was found 2 . In Fig. 1, we show the results for PLL and PLT at Q2 = 1 GeV2 and at Q2 = 1.9 GeV2, from the JLab experiment at Q2 = 0.33 GeV2, from the MAMI experiment ’, and at real photon point, from the TAPS results s. To extract PLLfrom the data, we calculate the relatively small (spin-flip) contribution PTT in the DR formalism and subtract it from the measured value of PLL - PTT/E. By dividing out the form factor G E , PLL is proportional to a(&’),whereas PLT is proportional to P(Q2) plus some correction due to the spin flip GPs which are small in the DR formalism. One sees from Fig. 1 that the electric polarizability is dominated by the asymptotic contribution and has a similar Q2 behavior as the dipole form factor. The total result for PLT results from the interplay of a large dispersive B N term, related to the paramagneticxontribution of p(Q2),and a large asymptotic contribution, associated with a diamagnetic mechanism due to pion-cloud effects. These two contributions have a different Q 2 dependence and give rise to an interesting structure in PLT,in particular at low Q 2 . In order to show the potentiality of VCS above pion threshold to extract information on the GPs, in Fig. 2 we display the DR predictions for the cross sections in the A(l232)-resonance region, in MAMI kinematics. It is seen that the e p -+ epy cross section rises strongly when crossing the pion threshold, and the region between pion threshold and the A-resonance peak clearly displays an enhanced sensitivity to the GPs through the interference with the rising Compton amplitude due to A-resonance excitation. Therefore, this energy region is very promising to measure VCS observables with a larger sensitivity to the GPs. Such an experiment is underway at MAMI, and the first results from JLab about VCS in the resonance region at Q2 = 1 Gev2 have been shown in this conference 233. 213.

293,

References

1. J. Roche et al., Phys. Rev. Lett. 85, 708 (2000). 2. H. Fonvieille, these proceedings.

3. L. Van Hoorebeke, these proceedings; L. Todor, these proceedings. 4. R. Miskimen, spokespersons MIT-Bates experiment, 97-03.

5. P.A.M. Guichon, G.Q. Liu, A.W. Thomas, Nucl. Phys. A591,606 (1995). 6. B. Pasquini, D. Drechsel, M. Gorchtein, A. Metz, and M. Vanderhaeghen, Phys. Rev. C 62, 052201 (R) (2000); Eur. Phys. J. A 11, 185 (2001).

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Q2 (GeV') Q2 (QV2) Figure 1. Results for the unpolarized VCS structure functions PLL (left panel) and PLT (right panel) divided by the proton electric form factor. Dashed lines: dispersive nN contributions. Dotted lines: asymptotic contributions calculated from Eq. (2) with A, = 0.92 GeV (left panel) and A0 = 0.66 GeV (right panel). Solid curves: total results, sum of the dispersive and asymptotic contributions. The RCS data are from Ref. 8 , the VCS data are: at Q2 = 0.33 GeV2 from Ref. ', at Q2 = 1 GeVZ and Q2 = 1.9 GeV2 from Refs. 233.

~ = 0 . 6 2 a=0.6GeV

0.1

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0.3

q' (GeV) 4'(QV) Figure 2. Left panel: differential cross section for the reaction e p -+ ep7 as function of the B contrioutgoing-photon energy q' in MAMI kinematics. Dashed-dotted curve: BH bution. The total DR results are calculated with the asymptotic contribution of Eq. (2) corresponding to a fixed value of A, = 1 GeV and three values of A@: h p = 0.7 GeV (dotted curve), Ap = 0.6 GeV (solid curve), and Ap = 0.4 GeV (dashed curve). Right where @ is a phase-space factor. The thick panel: Results for ( d 5 0 - d5~BH+Born)/@q', curves show the DR calculation with the full q' dependence and the thin horizontal curves are the DR results within the LEX formalism. The data are from Ref. l.

+

7. D. Drechsel, et d.,Nucl. Phys. A645, 154 (1999). 8. V. Olmos de Le6n et al., Eur. Phys. J. A 10, 207 (2001). 9. N. d'Hose and H. Merkel, spokespersons MAMI experiment, (2001).


Session on Baryon Structure and Spectroscopy Convenors T. S. H. Lee M. Manley B. Schoch S. Simula


MESON-PHOTOPRODUCTION WITH THE CRYSTAL-BARREL DETECTOR AT ELSA M. OSTRICK Physakalisches Institut der Universztat Bonn, Nussallee 12, 53115 Bonn, Gewnany E-mail: [email protected] The photoinduced production of neutral mesons off protons has been studied with the Crystal-Barrel-detector at the electron stretcher facility ELSA. First data demonstrate that reactions with multi-photon final states can be reconstructed with high efficiency. Preliminary results on ~p -+ pnono and ~p + pnoq show evidence for successive decays of high mass states through different intermediate resonances.

1

Introduction

The excitation spectrum of baryons and even basic ground state properties are still not understood directly in the framework of QCD. Different models using constituent quarks and meson clouds as relevant degrees of freedom are able to reproduce the main features of the baryon mass spectrum at low excitation energies. However, it is still impossible to decide experimentally which of the proposed types of effective quark-quark interaction is realized in strong QCD 1*2,3.At higher energy most of these models predict many more baryonic states than observed so far. This may be due to the lack of experimental data different from KN-scattering, or due to additional symmetry breaking in the three quark system which reduces the relevant number of degrees of freedom. The intimate relationship between excited baryons and the photoproduction of mesons allows to study individual resonances in selective decay channels, different from K N and to search for contributions of "missing" states '. In this context, the production of neutral mesons is of special interest, as many non-resonant production amplitudes are strongly suppressed compared to reactions, where charged mesons are involved. The Crystal-Barrel-Experiment at ELSA focuses on photoinduced production of these neutral mesons and meson pairs, e.g. KO, q, q', w , KO, nono, n'q, vr],which decay into multi-photon final states. The accessible range in the center-of-mass energy reaches from the two pion threshold up to 2.6 GeV. In the following, the experimental setup is described and the status of analysis of the reactions -yp + nOnOpand y p + noqp is discussed.

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Experimental setup

The measurements were performed at the electron stretcher and accelerator ELSA in Bonn which provides an electron beam with a maximum energy of Eo =3.2 GeV. Quasi-monochromatic photons are produced by means of bremsstrahlung tagging. The tagging spectrometer covered a range in the photon energy from E7 = 0.22 - 0.95. Eo at a total flux of N7 = 2 . 106s-' in this energy range. Mesons are produced in a 5cm liquid hydrogen target which is surrounded

scintiIlatorwalls

scintillating fiber detector

/

Crystal-Barrel (1380 Csl, Crystals) Figure 1. detector setup

by three layers of scintillating fibers for the identification and tracking of charged particles. Decay photons can be measured with the Crystal-Barrel electromagnetic calorimeter which consists of 1380 CsI crystals and covers 98% of the full solid angle in the laboratory system (see Fig. 1). The large solid angle coverage together with the energy resolution of 2.5% at a photon energy of 1 GeV and the angular resolution of 1 . 2 O allows to reconstruct multi-photon final states efficiently. This basic detector arrangement can be completed by dedicated fast detectors for charged and neutral particles in forward direction. In 2001 a wall of plastic scintillators was used as time of flight spectrometer for forward going protons.

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First data and status of analysis

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In 2001 data including all reaction channels mentioned above have been taken simultaneously. In 4 weeks of data taking an integrated luminosity of Ltot M 5 . 1O5pbarn-l has been accumulated. The data are presently being analysed L

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and all results presented here are preliminary, without flux normalisation and acceptance correction. Figure 2 shows events, where a proton has been identified together with two, four or six photons in the final state. In the first case (yp + my) the distribution of the yy invariant mass shows clear peaks from T O + yy and q + yy decays. Also signals from w + TOY and q' + yy decays can be observed. The w-meson appears here due to events, where one low energy photon escaped detection. The q-meson can also be clearly identified in its decay into three no mesons (right spectrum in Fig. 2). The spectrum in the center of Figure 2 contains yp + p4y events with one no meson already identified. The invariant mass distribution of the remaining yy-pair shows clear signals from TO- and q-decays, which demonstrates that the reactions yp + p2x0 and, for the first time, yp + pnoq can be clearly identified. The observation of the production of a meson pair allows to study transitions between high mass resonances and other excited (N*,A*) or ground states (e.g. A(1232)). Double TO production has recently been measured at MAMI up to a center of mass energy of & = 1.55 GeV '. The data confirm the sequential decay of the &3(1520) resonance with the A(1232) as intermediate state.

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At ELSA higher excitation energies are accessible. As an example Figure 3 shows a Dalitz-plot for events at center of mass energies between 1.8 < f i < 2.2 GeV. The number of entries is plotted as function of squared invariant masses, calculated from the three particles in the final state. In case of double ro-production an event appears with two entries due to the two indistinguishable pions. Structures in the Dalitz-plot deviating from phase N

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space indicate resonant intermediate states or, at least, correlations between the particles. In the example of Figure 3 not only a peak at the A(1232)mass but also a second peak around Adplr M 1.5 GeV is visible. This can be interpreted as the observation of a sequential decay of states around 2 GeV not only via the A resonance but also through excited states around 1.5 GeV. Similar decay chains are observed in the photoinduced r0v production. In this case, the isoscalar v meson connects states of the same isospin. As an example the Dalitz-plot at center of mass energies between 1.9 < & < 2.3 GeV is shown on the right side of Figure 3. The p r o mass peaks at the mass of the A( 1232), indicative for the observation of sequential decays of excited A*-states around 2 GeV. In addition, the structure at 1.52 GeV2 in the p17 invariant mass hints at the observation of the Sll(1535) as intermediate state. In order to determine the quantum numbers of the excited states involved and to identify contributions different from s-channel resonances a partial wave analysis of the data as well as a comparison to recent model calculations7 and measurements of observables including polarisation degrees of freedom' are in progress.

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Summary and outlook

The photoproduction of neutral mesons off protons has been measured up to center of mass energies of 2.6 GeV using the Crystal-Barrel-Calorimeter at ELSA. Reactions with multi-photon final states can be reconstructed with high efficiency. A first preliminary analysis of the reactions yp + p o 7 r o and yp + p7roq provides evidence for successive decays of high mass resonances via different intermediate states. Flux-normalisation, acceptance corrections and a partial wave analysis of the data are in progress. The measurements of photoinduced reactions off protons and nuclei with the Crystal-Barrel-Detector at ELSA will be continued in 2002/03 using the TAPS' calorimeter as detector for forward going charged and neutral particles. An improved tagging system and a coherent bremsstrahlung facility will provide linearly polarised photons at a total flux of N , = 107s-'.

References 1. S. Capstick, contribution to Baryon2002, Newport-News/USA 2. S. Capstick and N. Isgur, Phys.Rev.DS4, 2809 (1986) 3. U. Loring, B.C.Metsch, H.R.Petry, Eur.Phys.J. A10, 395 (2001) 4. A. d' Angelo, contribution to Baryon2002, Newport-News/USA 5. see, e.g., Aker et al. Nucl.1nst.Meth.A 321, 69 (1992) 6. M.Wolf et al., Eur.Phys.J. A 9, 1 (2000) 7. e.g., J.A.Gomez-Tejedor, E.Oset, Nucl.Phys.A600, 413 (1996) 8. C.Weinheimer, M.Ostrick et al., Proposal to PAC Bonn-Mainz, 2002 9. R. Novotny, IEEE Trans. on Nucl. Sc. 38, (1991) 378

408

Mina Nozar, Ulrike Thoma, and Michael Ostrick

Andrei Afanasev and Carl Carlson

K-MESON PRODUCTION STUDIES WITH THE TOFSPECTROMETER AT COSY WOLFGANG K. EYRICH Physikalisches Institut, Universitat Erlangen-Niirnberg, E.-Rommel-Str. 1. 91058 Erlangen Germany E-mail: [email protected] FOR THE COSY-TOF COLLABORATION The associated strangeness production in elementary proton induced reactions is studied exclusively at the external COSY beam using the time-of-flight spectrometer TOF. The complete measurement of all primary and decay particle tracks allows the extraction of total and differential cross sections as well as Dalitz plots and invariant mass spectra of the subsystems for the channels p' K+&, K?E+p, K+,??p and KfFn.For all channels the full phase space is covered from the reaction threshold up to the COSY-limit of about 3.5 GeV/c. Especially the analysis of the Dalitz plots of the channel p p + K+Ap show a strong influence of N*-resonances. In parallel the production of the o - meson is studied in the reaction p'

PP 0.

1 Introduction The main interest in the investigation of the associated strangeness production in elementary reactions like pp+ KYN close to threshold is the insight into the dynamics of the Ss production. Meson exchange models appear to be the most appropriate way to describe strangeness production in the threshold region. Here the questions concern the contribution of the various strange and non strange mesons and especially the role of N*-resonances in the production mechanism. Moreover the YN final-state interaction (FSI) is known to be of special importance close to threshold. To come to conclusive results precise data are needed for different reaction channels. The measurements should concentrate on exclusive data covering the full phase space. Moreover, the data of the strangeness production in elementary nucleon-nucleon reactions are very useful as an input to explain strangeness production in nucleus-nucleus reactions including medium effects.

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2 Experiment The experiment COSY-TOF is a wide angle, non magnetic device with various start and stop detector components for time-of-flight measurement. The modular apparatus combines high efficiency and acceptance with an energy and momentum resolution of a few percent. The whole detector system together with a tiny liquid hydrogen target is installed inside a vacuum vessel. This ensures a rather precise definition of the interaction point and strongly reduced background reactions in air. The outer detector, serving as stop for the time-offlight, consists of several plastic scintillator hodoscopes. The inner detector, optimised for strangeness production, consists of two layers of thin segmented scintillators providing the start timing, a doublesided silicon micro-strip detector with a highly granulated ring and sector structure and two scintillating fibre hodoscopes. The full angular range of the reaction products is covered allowing a complete reconstruction of the p p + KYN events including the delayed decays. [I].

3 Results and discussion The reaction pp+ P A P has been investigated between 2.5 GeV/c and 3.2 GeV/c, that means from near threshold up to close to the COSY limit. For all measured momenta very clean event samples could be extracted. This is shown in fig. 1 for the momentum of 2.85 GeV/c.

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By covering the full phase space various exclusive observables can be extracted model-independently. In particular Dalitz plot analyses turned out to be a powerful tool to investigate the reaction mechanism. This is demonstrated in figure 2 where the experimental data at 2.85 GeV/c are compared with a calculation of Sibirtsev [2]. where contributions from non resonant meson exchange are combined coherently with contributions from the N*(1650, 1710, 1720)resonances and the PA-FSI. Whereas the combination of the phase

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unique way. This can be seen from fig. 3, where the projections of the Daltiz plot from fig. 2 are shown together with the calculations and a pure phase space. Obviously also here only the full calculation is reproducing the data in a satisfactory way. The distribution of the KAmass follows by "accident" the phase space, clearly showing that it is not sufficient to analyse the projections of the Dalitz plot.

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1.85

mu [GeV/cZ]

Figure 3. Invariant masses of the pA-(left) and KA-(right) subsystems at 2.85 GeVk together with calculations within the resonance model of Sibirtsev (drawn), resonances only (dotted), FSI only (dashdotted) and phase space (dashed).

Preliminary analyses of the Dalitz plots at 3.2 GeVk show that the influence of the N*( 1710)-resonancestrongly increases. As mentioned above the TOF detector for the first time also allows the measurement of the Z+-production in the channels pp+ p2?p and K + c n in the threshold region. Clean samples of a few hundred events could be extracted. The next steps will be the use of a polarized beam and the strangeness production in neutron proton scattering using a d-target. We gratefully acknowledge support by the l?L-Julich and the berman BMBF.

Keferences 1. A.Bilger et al., Strangeness Production in the Reaction pp+ K'Ap in the Threshold Region, Physics Letters B420 (1998) pp. 217-224 2. A. Sibirtsev, private communication (2002)

FIRST SIMULTANEOUS MEASUREMENTS OF THE TL AND TL‘ STRUCTURE FUNCTIONS IN THE r*P + A REACTION A.M. BERNSTEIN PHYSICS DEPARTMENT AND LABORATORY FOR NUCLEAR SCIENCE MASSACHUSETTS INSTITUTE O F TECHNOLOGY, CAMBRIDGE, MA 02139, USA

The first simultaneous measurements of both longitudinal-transverse structure functions (TL and TL’) in the p(Z, e‘p).lrOreaction in the A region are presented on behalf of the MIT-Bates OOPS Collaboration1. Measurement of the deviation of the proton shape from spherical symmetry is fundamental and has been the subject of intense experimental and theoretical interest2. This determination has focussed on the measurement of the electric and Coulomb quadrupole amplitudes (E2, C2) in the predominantly Ml(magnetic dipole -quark spin flip) y * N + A transition. The difficulty is the small E2/M1 and C2/M1 amplitudes (typically N -2 to -8 % at, low Q2). In this case the non-resonant (background) and quadrupole amplitudes are the same order of magnitude. This combination of small signal and signal/noise ratio requires both sensitive and accurate observations. The d state admixtures in the nucleon and A wave functions are caused in the quark model by the hyperfine tensor interaction between quarks3. In pion cloud model^^?^^^ it is caused by the p wave pion emission. This in turn is caused by the spontaneously broken symmetry of QCD in which the pion is an almost Goldstone Boson which primarily interacts with nucleons in the p wave. It has been shown that at low Q2 the pion cloud contributes significantly to the M1 amplitude and dominates the E2 and C2 contribution^^,^*^^ to the y*N Aitransition. The present experiment is performed near the predicted maximum of the pion cloud contribution6. To precisely determine the resonant quadrupole amplitude in the y * N A transition at low Q2, while addressing the issue of background contributions, a program has been developed at the MIT-Bates Linear Accelerator. For this purpose we have developed an out-of-plane magnetic spectrometer system (OOPS)7 in which the spectrometers are deployed symmetrically about the momentum transfer 1.32 GeV. The 4*-dependences of the beam spin asymmetry at W = 1.54 GeV are shown in Fig. 2. Although MAID2000 describes the cross sections well, the experimental and calculated beam spin asymmetries do not match, and even have opposite signs. The CLAS data set can be used to adjust the appropriate

463

u-Op*lto

~

........ ... .. ...

0.5

0

1

1.5

2

wK-Wh

2.4

3

1.5

a', G.!

Figure 3. A1/2 photon coupling amplitudes for Sll(1.535). The large full square is from the CLAS combined data analysis. The full circles only include CLAS data on n+n channel. The open markers are from previous analyses 9,10.

parameters in the MAID model by fitting both the cross sections and the beam spin asymmetries. The combined data set from CLAS was fitted with a program based on the MAID model to obtain the optimal value for the multipole amplitudes. The preliminary result for the All2 amplitude for ,511 (1535) is shown in Fig 3. One can see that the points from CLAS pion production data are in a good agreement with the q-meson production results. This is in contrast with the earlier results a t the Q2 = 0, where the pion and q production analyses gave different results

'

'.

References

1. D. Drechsel, 0. Hanstein, S.S. Kamalov, L. Tiator, Nucl. Phys. A 6 4 5 , 145 (1999). 2. F. Foster and G. Hughes, Rept. Prog. Phys. 46, 1445 (1983). 3. M.D. Mestayer et al, Nucl. Inst. and Meth. A 4 4 9 , 81 (2000). 4. G. Adams et al, Nucl. Inst. and Meth. A 4 6 5 , 414, (2001). 5. E.S. Smith et al, Nucl. Ints. and Meth. A 4 3 2 , 265 (1999). 6. M. Amarian et al, Nucl. Inst. and Meth. A 4 6 0 , 239 (2001). 7. I. Aznauryan, S. Stepanyan, JLab Analysis of Nucleon Resonances (JANR); Private communications. 8. H. Egiyan, Ph.D. Thesis, unpublished, (2001) 9. V. Burkert in Perspectives in the Structure of Hadronic Systems, ed. M.N. Harakeh et a1 (Plenum Press, New York, 1994); Private communications. 10. R. Thompson et al, Phys. Rev. Lett. 86, 1702 (2001)

ELECTRON BEAM ASYMMETRY MEASUREMENTS FROM EXCLUSIVE no ELECTROPRODUCTION IN THE A(1232) RESONANCE REGION K. JOO FOR THE CLAS COLLABORATION Jefferson Lab, 1ZOO0 Jeflerson Avenue, Newport News, VA 23606, USA E-mail: kjoo Qjlab.org The polarized longitudinal-transverse structure function U L T ~ in the p ( S , e'p)nO reaction has been measured for the first time in the A(1232) resonance region for invariant mass W = 1.1 - 1.3 GeV and at four-momentum transfer Q 2 = 0.40 and 0.65 GeV2. Data were taken at the Thomas Jefferson National Accelerator Facility with the CEBAF Large Acceptance Spectrometer (CLAS) using longitudinally polarized electrons at an energy of 1.515 GeV. This newly measured o ~ provides new and unique information on the interference between resonant and nonresonant amplitudes in the A(1232) resonance region. The comparison to recent phenomenological calculations shows sensitivity to the description of non-resonant amplitudes and higher resonances.

1

Introduction

A precise study of the y*p + A+(1232) transition has been of special interest for many years. The transition is usually described using three electromagnetic multipoles: the magnetic dipole ( M I + ) ,and the electric (El+)and scalar (&+) quadrupoles. SU(6) symmetric quark models describe M I + as a quark spin flip , while El+ and S1+ are identically zero. Small but finite contributions to El+ and S1+ may arise from interactions with the pion cloud at large and intermediate distances. Quark models that include hyperfine interactions from one-gluon exchange also predict small contributions. In addition, there is the prediction, resulting from quark helicity conservation in perturbative QCD, that MI+ = El+ at asymptotic Q 2 , while S1+ remains constant. The p(e,e'p)xo reaction has been the major tool in probing the y*p + A+( 1232) transition. However, unpolarized experiments are unable to separate the reaction mechanisms which contribute to the excitation of the A( 1232) from non-resonant backgrounds and contributions of higher mass resonances. Spin observables, which access the imaginary parts of interfering amplitudes, provide promising new information to address these issues. The imaginary parts vanish identically if the final state is determined by a single

464

465

complex phase, which is the case for an isolated resonance. Thus spin observables are especially useful to study contributions from other resonances and non-resonant terms which may interfere with the A+(1232) amplitudes. In this report, we report a measurement of the longitudinal-transverse polarized structure function CLTf obtained in the A(1232) resonance region using the p(Z, e'p)r0 reaction. 2

Experiment

The data were taken using a 1.515 GeV beam of longitudinally polarized electrons incident on a liquid hydrogen target at 100 % duty factor. The electron polarization was measured frequently with a Mdler polarimeter and was typically 69.0 %. Scattered electron and proton were measured using the CLAS detector. Electrons were selected by a hardware trigger using a coincidence of the gas Cerenkov counters and the lead-scintillator electromagnetic calorimeters. Protons were identified using momentum reconstruction in the tracking system and time of flight from the target to the scintillators. Software fiducial cuts were used to exclude regions of non-uniform detector response. Kinematic corrections were applied to account for drift chamber misalignments. The p 0final state was identified by the missing mass cut of -0.01 5 Mz(GeV2)5 0.05. Background from elastic Bethe-Heitler radiation was suppressed to below 1% using a combination of cuts on missing mass and 4: near 4; = Oo. Target window backgrounds and proton multiple scattering were suppressed with cuts on the reconstructed e'p target vertex.

3

Data analysis

The electron beam asymmetry ALT, is directly proportional to the polarized longitudinal-transverse structure function U L T ~:

A L T ~=

-

d2a' - d 2 K d 2a+ d 2a-

+

(1)

&GJiZjaLTl 00

sin

e;

sin

4:

,

(2)

where d 'af is the differential cross section for positive and negative electron beam helicities. Experimentally, ALp was determined by scaling the measured asymmetry Am by the magnitude of the electron beam polarization P,:

466

where N,' is the number of K O events for each electron beam helicity state. Acceptance and normalization factors cancel in A,, making this observable largely free from systematic errors. Radiative correction were applied using the program recently developed by Akusevich et al. for exclusive pion electroproduction. Corrections were also applied to compensate €or cross section variations over the width of a bin. ALT, was determined for individual bins of ( Q 2 ,W,case:, 4;) then multiplied by the unpolarized cross section no. A parameterization of go was used, obtained from fitting previously measured CLAS data '. The structure function (TLTI was then extracted by fitting the r#P distributions. The major systematic errors for ( T L T ~come from the electron beam polarization P, (3%)and the measured unpolarized cross section no (5%). The systematic error for A , is negligible in comparison. Figure 1 shows the comparisons of (TLT and ( T L T ~ extracted at Q2=0.40 GeV2, where the cos 0: dependence is plotted for W bins of 1.18, 1.22 and 1.26 GeV. The top plots of each figure show OLT from our previous measurements and the bottom plots show the newly extracted (TLTJ-Also shown are recent model calculations of (TLT and (TLT' using the Sat0 and Lee (SL) dynamical model 3, the Dubna-Mainz-Taipei (DMT) model 4 , and the Mainz unitary isobar model (MAID2000) Both OLT and (TLT' measure the same combination of amplitudes, but the former probes the real part while the latter probes the imaginary part of the interference. As shown in the top row of Figures 1 and ??, the calculations of (TLT from all three models agree well with the data and with each other near the peak of the A(1232) resonance. Discrepancies become evident away from the peak, especially at W = 1.18 GeV, suggesting that while all three models describe the A(1232) resonance well, their prescriptions of non-resonant and higher-resonance contributions may differ significantly. While this effect is , shown subtle for CTLTnear the peak of the A(1232), it is amplified in o ~ pas in the bottom row of Figures 1 and ??. DMT model calculations generally describe our results well, whereas MAID2000 calculations are generally higher and those of the Sato-Lee model are lower.

'.

4

summary

In summary, the polarized structure function OLTI has been measured for p(e',e'p)7ro in the A(1232) resonance region at Q2 = 0.40 and 0.65 GeV2. This structure function is significantly different from zero in the entire range

467 W=1.18GeV

W=l.22 GeV

W=1.26 GeV

$ 4

4 2

0 r

b -2 -4

-6

-8 ~6

$ 5 i

4

.

2

3

2 1 0 -1

-0.5

0.5

CLAS Data (a2=0.4 GeV') - MAID2000

-0.5

0.5

-0.5

0.5

cosd', .....

s,,:o..L*e

--.--DMT

Figure 1. Structure functions, (TLT and ( T L versus ~ cm0; extracted at Q2= 0.40 GeV2. Various curves show model predictions. Shaded bars show systematic errors.

of the A(1232) resonance region, indicating that they are sensitive to nonresonant and higher-resonance processes in the A( 1232) resonance region. The measured structure function differentiates between recent theoretical calculations. For higher Q2, contributions from non-resonant processes and higher-resonances become more important in extracting the information of the A(1232) resonance since the strength of the A(1232) resonance decreases rapidly as Q2 increases. These new measurements will provide additional valuable information towards a more detailed understanding of the y * p + A+(1232) transition. References

1. 2. 3. 4. 5.

A. Afanasev,I. Akushevich, V.D. Burkert, K. Joo, PRD 66,074004 (2002) K. Joo et al., Phys. Rev. Lett. 88, 12 (2002). T. Sat0 and T.-S.H. Lee, Phys. Rev. C 63, 055201 (2001). S.S. Kamalov and Shin Nan Yang, Phys. Rev. Lett. 83, 4494 (1999). D. Drechsel, 0. Hanstein, S.S. Kamalov, and L. Tiator, Nucl. Phys. A 645, 145 (1999).

?rNN*(1440) A N D o N N * (1440) COUPLING CONSTANTS FROM A MICROSCOPIC N N + N N * ( 1440) POTENTIAL P. GONZALEZ Dpto. de Fisica Te6rica and IFIC Universidad de Valencia - CSIC, E-46100 Burjassot, Valencia, Spain E-mail: pedro.gonzalez8uu. es

B. JULIA-D~AZ,A. VALCARCE, F. FERNANDEZ Grupo de Fisica Nuclear lJniuersidad de Salamanca, E-37008 Salamanca, Spain E-mail: bjuliaQusal.es, ualcarceOmozart.usal.es, f d z 8 u s a l . e s

The N*(1440): or Roper resonance, plays an important role in nucleon and nuclear dynamics as an intermediate state. The excitation of a Roper may mediate pion electro- and photoproduction processes pion and double pion production in N N reaction^^:^: heavy ion collisions4, etc. In this context: the knowledge of the N N + NN*(1440) interaction and the ?rNN*(1440)and a N N * (1440) coupling constants should be of great help. The usual way to determine meson-NN coupling constants is trough the fitting of N N scattering data with phenomenological meson exchange models. Therefore: a consistent way to obtain meson-NN* (1440) coupling constants is from a transition N N + NN'(1440) potential, in particular when ratios over meson-" coupling constants are to be considered. In order to derive the transition potential we shall follow the same quark model approach previously used for N N scattering 5 : 6 : this is we shall start from a quark-quark (qq) interaction containing confinement! one-gluon exchange (OGE) one-pion exchange (OPE) and one-sigma exchange (OSE) terms and carry out a BornOppenheimer approximation. The quark treatment presents two main advantages, on the one hand once the parameters of the qq potential are fixed from N N data, there is not any free parameter: on the other hand it allows all the baryon-baryon interactions to be dynamically considered on an equal footing (actually the same framework has been applied to the A excitation case'). Explicitly, the N N + NN*(1440) potential at interbaryon distance R is obtained by sandwiching the qq potential, Vqq7between N N and N N * (1440) states: written in terms of quarks, for all the pairs formed by two quarks belonging to different baryons. The qq potential has been very much detailed elsewhere 5,6. It reads:

':

468

469

where <j is the interquark distance. VCONis the confining potential taken to be linear ( r i j ) and VOGEis the usual perturbative one-gluon-exchange interaction containing Coulomb ($): spin-spin (& Z j ) and tensor (S,) terms. For future purposes we detail the central part of the one-pion: VOPE:and exchange : interactions given by: one-sigma, V O ~ E

-

where O,-h is the chiral coupling constant and A is a cutoff parameter. The values chosen for the parameters are taken from Ref.6. The N* (1440) and N states are given in terms of quarks by IN* (1440)) =

{ fi"l(OS)2(1~))

IN) = I[31(os)3) c3 P3Ic where [l3Icis the completely antisymmetric color state: [3] is the completely symmetric spin-isospin state and 0s: Is: and Op: stand for harmonic oscillator orbitals. The transition potential obtained can be written at all distances in terms of baryonic degrees of freedom '. One should realize that a qq spin and isospin independent potential as for instance the scalar OSE, gives rise at the baryon level, apart from a spin-isospin independent potential, to a spin-spin, an isospin-isospin and a spin-isospin dependent interactions 5 . Nonet heless for distances R 2 4 fm, where quark antisymmetrization interbaryon effects vanish: we are only left with the direct part, i.e. with a scalar OSE at the baryon level. The same kind of arguments can be applied to the OPE potential. Thus asymptotically ( R 2 4 fm) OSE and OPE have at the baryon level the same spin-isospin structure than at the quark level. Hence we can parametrize the asymptotic central interactions as (the A depending exponential term is negligible asymptotically as compared to the Yukawa term)

and

-

&31~O~)(OP)2)}

@ P3Ic and

470

where g i stands for the coupling constants at the baryon level and M , is the reduced mass of the N N * (1440) system. By comparing these baryonic potentials with the asymptotic behavior of the OPE and OSE previously obtained from the quark calculation we can extract the T N N *(1440) and (rNN*(1440) coupling constants. The A2/(A2 - m:) vertex factor in expressions (4) and (5) comes from the vertex form factor chosen in momentum space as a square root of monopole

';

(

A2'$2) the same choice taken at the quark level, where chiral symmetry requires the same form for pion and sigma. A different choice for the form factor at the baryon level: regarding its functional form as well as the value of A: would give rise t o a different vertex factor and eventually to a different functional form for the asymptotic behavior. Then, the extraction from any model of the meson-baryon-baryon coupling constants depends on this choice. We shall say they depend on the coupling scheme. For the OPE and for our value of A = 4.2 fm-', ~ 2 - m = ~ ,1.0286, pretty close to 1. As a consequence: in this case the use of our form factor or a modified monopole form at baryonic level makes little difference in the determination of

*'

the coupling constant. This fact is used when fixing value of

(z)2

2from the experimental LIZ

extracted from N N data. The value we use for (x,h = ln2

&*e-* 471 4mN

2

= 0.027 corresponds to

$$ = m-2

= 14.8.

To get &"*(1440) we turn to our numerical results for the 'SO OPE potential and fit its asymptotic behavior (in the range R : 5 + 9 fm) to Eq. (4). We obtain g n N N g n N N *(1440)

&L *

grNN'(1440L

&L

A* = -3.73: A2-m:

- -0.94. Let us note that the sign comes out from the arbitrary

1.e. fi choice of the overall phase of the "(1440) wave function with respect to the N wave function. Hence it is more appropriate to quote the absolute value. Furthermore the coupling scheme dependence can be explicitly eliminated if with gn" extracted from the N N + N N potential we compare gn"*(1440) within the same quark model approximation. Thus we get

The value obtained for this ratio is similar to that obtained in Ref. and a factor 1.5 smaller than the one obtained from the analysis of the partial decay

47 1

width. By proceeding in the same way for the OSE potential we have

I

g u N N * ( 1440)

I

= 0.475.

(8)

This result agrees quite well with the only experimental available result, obtained in Ref. lo from the fit of the cross section of the isoscalar Roper excitation in p(cx,ct') in the 10-15 GeV region. Furthermore, we can give a very definitive prediction of the magnitude and sign of the ratio of the two ratios, g n N N * (1440) gnNN

= 0.53

g u N N * (1440) goNN

(9)

which is an exportable prediction of our model. We should finally notice that for dynamical applications our results should be implemented including the "(1440) width. Quantum fluctuations of the two baryon center-of-mass: neglected within the Born-Oppenheimer approach, could also play some role. Though these improvements will have a quantitative effect we think, as suggested by the values we get, our predictions will not be very much modified. In this sense they could serve either as a first step for more refined calculations or as a possible guide for phenomenological applications.

Acknowledgments We thank to E. Oset for suggesting discussions. This work has been partially funded by Junta de Castilla y Le6n under Contract No. SA-109/01, and by EC-RTN, Network ESOP, Contract HPRN-CT-2000-00130. References

1. H. Garcilazo and E. Moya de Guerra: Nucl. Phys. A 562: 521 (1993). 2. M.T. Peiia et al, Phys. Rev. C 60, 045201 (1999). 3. L. Alvarez-Ruso, Phys. Lett. B 452, 207 (1999). 4. B.A. Li et al, Phys. Rev. C 50, 2675 (1994). 5. F. Ferndndez et al, J. Phys. G 19: 2013 (1993). 6. D.R. Entem et al: Phys. Rev. C 62,034002 (2000). 7. A. Valcarce et al, Phys. Rev. C 49: 1799 (1994). 8. K. Holinde, Nucl. Phys. A 415: 477 (1984). 9. D.O. Riska and G.E. Brown: Nucl. Phys. A 679, 577 (2001). 10. S. Hirenzaki et al: Phys. Lett. B 378: 29 (1996); Phys. Rev. C 5 3 , 277 (1996).

7)

ELECTRO-PRODUCTION AT AND ABOVE THE S11(1535) RESONANCE REGION WITH CLAS HALUK DENIZLI Department of Physics and Astronomy University of Pittsburgh, Pittsburgh, PA 15260, USA E-mail: [email protected] New cross section measurements for the electro-production are reported for total center of mass energy from threshold to 2 GeV and invariant momentum transfer Q 2 between 0.13 and 3.2 ( G e V / c ) 2 . This large kinematic range and increased statistics allow to study the response functions and Q2 evolution of photo-coupling amplitude.

1 Introduction and Motivation When we look at the the inclusive excitation spectra ep->eX along with the masses of known baryon resonance, the picture is complicated. The excited states of proton are broad and overlapping above the second resonance region. This makes the extraction of their physical properties very difficult. But this situation is considerably simplified in the case of the r]p final state. There are fewer resonances involved since it couples to nucleon resonance with isospin I = 1/2 only. Therefore, this process is cleaner for distinguishing certain resonance than other processes. In addition, The cross section appears to be dominated by &(1535) resonance near the threshold. This is the only known resonance to have a large branching ratio. Past experiments1i2 showed that the photocoupling amplitude pA1/2 for the &1(1535) has an unusual slow falloff with Q2 which indicates more compact object than other resonances. A structure at W around 1700 MeV has been seen by Thompson et a12. He also showed that RTT and RLT are small compared to RT. Longitudinal amplitudes are small compared to transverse in the Mainz prediction. In this paper, I will show new measurements of r] electro-production with CLAS. This data has more than quadrupled the statistics and doubled the Q2 coverage of the first CLAS data. This experiment produces precise measurements over the range 0.13 1.7 GeV are expected to couple strongly t o yN as well as 7rA, pN,or wN. Due t o their low cross section and difficult separation from other production processes, predominantly diffractive and o/r-exchanges, these multipion channels have not yet been investigated with electromagnetic probes for s-channel contributions. The CLAS detector at Jefferson Lab has accumulated a large amount of events for Zp t e'W+.rr- and Zp t e'p7r+7r-7ro, for a large range in invariant hadronic mass (1.74 < W < 2.5 GeV) and photon virtuality Q2 (0.5 < Q 2 < 3.5 GeV2) and with complete angular coverage. The multi-pion analyses examined outgoing electron tracks detected in CLAS in coincidence with a proton and 7r+ track. Missing mass techniques were applied to identify the two-pion channel and w p channel. The following sections present results from the well elaborated analysis of the two-pion channel which will soon be published, followed by preliminary results for the wp channel which is still being analyzed. 2

The reaction channel y * p -+ X t p7r+.rr-

The two-pion channel has been analyzed for a major fraction of the accumulated data (for W = 1.4 - 1.9 GeV and Q2 = 0.5 - 1.5 GeV2) by means of a phenomenological model.2 The model describes the reaction y*p + px+fn-

489

490

as a sum of amplitudes for y*p -+ nA + pn+n- and y*p -+ pop + pm+n(at tree level) and a phase space factor representing all other possible mechanisms. The resonant part includes 12 states rated as 3' and 4* with sizeable n A and/or p p coupling^,^ based on a Breit-Wiper ansatz. Non-resonant contributions to p p (diffractive ansatz) and n A were implemented as well.4 The partial LS decay widths of the included resonances are taken from an analysis of nnN data by M. M a n l e ~ Where .~ available, the electromagnetic couplings Al l2,A3/2 are determined through parameterizations extracted from previous experiments; for the other resonances the results of Single Quark Transition Model (SQTM) fits6 and Quark Model predictions' are used. In each W and Q 2 bin, the model was fitted to the following three differential cross sections simultaneously: da/dM,,+, du/dM,+,- , and dc/dO,-. The fitting procedure was performed in two steps: (A) The model parameters representing the non-resonant and phase space contributions were fitted to CLAS data, whereas the resonant parts were kept fixed using available information on resonances in the fitted W range. (B) Restricted W ranges where we observed discrepancies between the CLAS data and the model calculation, were re-fitted by allowing for variation of the resonant coupling parameters within the SQTM fitting uncertainties of 10-20 %.

c30

E 25 b

20

15

10

5

0

O

w GeV

'

'1:4

'

'1:s

'

'$'

'

'117

'

'is' '119 ; '

' '

'

'

'2

I

W GeV

Figure 1. Total cross section for y * p + pn+s- for 3 Q 2 ranges. The curves on the left plot result from a fit using fixed resonant parameters (step A). The curves on the right plot result from a fit allowing for variation of resonance couplings (step B). The errors in the CLAS data are statistical only.

49 1

Figure 1 shows the total cross section and the model calculation for the three analyzed Q2 bins: 0.5-0.8 GeV2, 0.8-1.1 GeV2, and 1.1-1.5 GeV2. The description of the cross section is considerably improved by allowing for variations of N' couplings in step B (plot on right side). The only exception is the W range around 1.7 GeV where a reasonable variation (10-20 %) of established resonance parameters fails t o fit the CLAS data.

2 100

A

50 25

50 D

- 3 0 \

-

1

W

1.25 1.5

-

1 1.25 1.5

1 1.25 1.5

M+ ,

2

= b

(GeV)

\ 100

75

50

40

25 T J O

20 0

A

?

0.25 0.5 0.75

&..-..

40

'

..Q

0.25 0.5 0.75

I

U

0.25 0.5 0.75

M,+n-

\ 13

b

20 0

O

100

0

,

100

,

,

0

0 +CM,-

(GeV)

1 0

r d eg )

Figure 2. Differential cross sections duldM,,+, du/dM,+,- , and du/dO,- (from top t o bottom) at W=1.70-1.725 GeV and Q2 bins: 0.5-0.8 GeV2 (left), 0.8-1.1 GeV' (mid), 1.11.5 GeV2 (right). Curves show the fit result when varying either the couplings of 013(1700) (solid) or P11(1710) (dotted) or Pi3(1720) (dashed line).

Allowing for a wide variation of coupling parameters of either 013(1700) or P11(1710) or P13(1720) result in better fits t o the data as shown in Fig. 2. Whereas the variation of &(1700) parameters fails t o fit the angular distri-

492

bution and the variation of 5 1 (1710) overestimates dn/dM,, at M,+,- M 0.7 GeV, the best fit is obtained by a significant change of the p13(1720) coupling parameters. In comparison with the PDG values3 (mass: 1650-1750 MeV, r = 100-200 MeV, BR(pN)=70-85 %), we find that its coupling to .rrA clearly dominating over the pN coupling: BR(.rrA)=63f12 % and BR(pN)=19&9 % with its mass and width at mR = 1725 f 20 MeV and r = 114 f 19 MeV. Apart from such drastic changes in established resonance parameters, we considered the possibility that an unknown resonant state may couple to electromagnetic probes which has not been visible in .rrN scattering. Such a state is - according to our fits, keeping the established resonance parameters fixed - most likely a PI^ state at 1720 MeV with I? = 88 f 17 MeV and BR(nA)=41f13 %, BR(pN)=17flO %. The isospin could not be determined.

3

The reaction y'p

+ wp + .rr+r-nop

According to quark model predictions,l>gthe w N channel is another promissing channel in the search for undiscovered N*. Due to its zero isospin this vector meson only couples to I = states. Omega electroproduction data was extracted analyzing (e,e'pr+) events with cut on missing mass MMetp,+X > 2m,. As shown in Fig. 3, the w mass peak in the resulting missing mass distributions MMe,,x was sufficiently narrow ( M 30 MeV FWHM) to permit fits in the immediate omega mass neighborhood using a 3ndorder polynomial to represent the underlying 37r phase space background. 0

1 . 7 < W < 1.8 G e V

._

=-

1 . 8 < W < 1.9 G e V

~MK)

1.9<W 2mr. T h e w signal is extracted In each kinematical bin separately.

Figure 4 shows the preliminary differential cross section for selected W ranges. The angular distributions are characterized by a monotonic fall off with increasing production angle, indicating diffractive and/or T exchange process(es). However, in the W ranges around 1.8 GeV and 1.9 GeV, the

493

cross section shows additional strength in intermediate and backward direction, an indication for a strong nucleon pole (u-channel) and possible N * resonance (s-channel) contributions. Due to statistical limitations, we required in this analysis only one pion of the w decay being detected. The data set is currently being enlarged to allow for smaller W - and Q2-bins and additional investigations on d* dependence and angular momenta.

Figure 4. Preliminary results from CLAS for omega electroproduction: differential cross section for selected W ranges.

References

S. Capstick and W. Roberts, Phys. Rev. D 49, 4570 (1994). V. Mokeev et aE, Phys. of Atomic Nucl. 64, 1292 (2001). D.E. Groom et all Eur. Phys. J. C 15, 1 (2000). M. Ripani et all Phys. of Atomic Nucl. 63, 76 (2000). 5. D.M. Manley and E.M. Salesky, Phys. Rev. D 45, 4002 (1992). 6. V.D. Burkert, Czech. Journ. of Phys. 46, 627 (1996). 7. S. Capstick, Phys. Rev. D 46, 2864 (1992). 8. F. Close and Z.P. Li, Phys. Rev. D 42, 2194 (1990).

1. 2. 3. 4.

QCD CONFINEMENT A N D MISSING BARYONS P.

GONZALEZ

Dpto. de Fisica Te6rica and IFIC llniversidad de Valencia CSIC, fi-~6100 Burjassot, Valencia, Spain E-mail: pedro.gonzalezOuu.es

-

H. GARCILAZO E.S.F.M., Instituto Politicnico Nacional, Edificio 9, 07738 M k i c o D.F., Mexico E-mail: [email protected]

J. VIJANDE, A. VALCARCE Grupo de Fisica Nuclear Universidad de Salamanca, E-37008 Salarnanca, Spain E-mail: [email protected], valcarceOmozart.usal.es We show that in a quark model scheme the use of a screened confining potential: suggested by lattice and QCD non-perturbative calculations: instead of an infinitely rising one with the interquark distance may give rise to a one-teone correspondence between the predicted three-quark bound states and the observed baryon resonances. This points out to the use of the baryon spectrum as a quite stringent test of the long-range confining potential.

Constituent quark models of baryon structure are based on the assump tion of effective quark degrees of freedom so that a baryon is a three-quark color singlet bound state. Quarks are bound by means of a quark-quark (44) potential which tries to mimic QCD at the baryon energy scale. The potential may incorporate directly derived perturbative QCD contributions in the form of a one-gluon exchange (OGE) interaction and non-perturbative terms arising from multigluon quark interaction processes. Among them, confinement is usually taken for granted. The form of confinement is attached to the behavior of the running coupling, a,,at low momentum transfer (low Q 2or large distances). In lowest-order QCD a, reads: 4T

where A is the QCD scale parameter and Po = 11 - $ N j , being N j the number of flavors. As Q + A, diverges what is interpreted as a signal of strict confinement. Taking into account lattice simulations for heavy quarks in the

494

495 so-called quenched approximation (considering only valence quarks) a qq confining potential linearly rising with the interquark distance is proposed '. The consideration of this confining force altogether with OGE and/or one-meson exchange or other effective interactions turns out to be fruitful in the construction of quark potential models that provide with a precise description of baryon spectroscopy 2.3.4.5. However all the models predict a proliferation of bound states in the baryon spectrum at excitation energies above 1 GeV which are not experimentally observed as resonances. This difference between the quark model prediction and the data about the number of physical resonances is known as the missing resonance problem. An explanation for such a discrepancy was given by realizing that most of the missing states could be too inelastic to be easily observed6e7. To test experimentally this idea, in order to clarify the issue: is a current objective of the CLAS collaboration in TJNAF'. In this talk we propose as an alternative that there may be a one-to-one correspondence between the predicted bound states and the observed baryon resonances once the confinement dynamics is properly implemented by sea quark contributions. From lattice calculations for the heavy quark sector in the unquenched approximation (including light qq pairs) it has become clear that when increasing the interquark distance creation of light qq pairs out of the vacuum in between the quarks becomes energetically preferable resulting in the complete screening of quark color charges at large distances. Moreover the effective coulomb coupling turns out to be stronger in the presence of sea quarks. In the 80's a specific parametrization of these effects was given in terms of a potentialg. Regarding the confining term it looked like:

This form shows a clear Yukawa screening of the linear potential in terms of a screening length p-' typically around 1fm. u is the string tension with values around 0.16 GeVZ and u / p is the splitting energy of the heavy quark pair. These features can also be inferred from a non-perturbative QCD calculation of as.From an approximate solution of the Schwinger-Dyson equation asreadslo:

(Q2+4m2

(%)I

where Mi(Q2) = mi [In A2 s) / In is a dynamical gluon mass: and m g = 300 - 700 MeV. Hence a freezing of the infrared coupling at distances around 1 fm comes out supporting the view of a screened confinement.

496

-%

I .5z~

u, W

Figure 1: Relative energy nucleon and delta spectrum for the screened confining potential with p = 1.54 f m - ' ~ c = 512.5 MeV, R = R~ = 105.23 MeV fm, ro=0.55 fm, and mu = rnd = 337 MeV. The shaded regions represent the experimental data with their uncertainty. Lines marked with a cross correspond to experimental data for which no uncertainty is available.

To examine the consequences derived from such a screening for the light baryon spectrum we shall assume that the same form of the screening is applicable to light quarks and we shall complement the screened confinement potential with the minimal OGE interaction (coulomb plus spin-spin terms). The same model but with a linear confinement has been applied to the meson and baryon spectrum in the past 11:127 providing a reliable description except for the energies of the first radial excitations and the aforementioned proliferation of missing states. The qq potential is then written as:

where we have assumed the usual color structure for confinement (the A % are In the spirit the Gell-Mann SU(3) matrices) and c should be identified with of quark model calculations c and p should be taken as effective parameters. To get the light baryon spectrum we solve the Schrodinger equation through a Faddeev calculation. The complete resulting spectrum, up to J = $: is shown in Fig. 1 where an almost complete parallelism between predicted bound states and cataloged

E.

497

resonances can be observed avoiding the proliferation of missing states. Note that the precise position of the states very close to the (2q bound-1 free 4)state threshold is very sensitive to the particular quark model considered what could be responsible for the few remaining discrepancies. Moreover with the exception of the Roper resonances the calculated spectrum is of significantly good quality. Concerning the values of the fitted confinement parameters ,u-l = 0.65 fm and c = 0.51 GeV (or equivalently D = 0.156 GeV' ) are not far from the heavy quark case. In conclusion although our calculation is not complete (higher orbital angular momentum excitations should be also calculated and further refinements to understand the energy dependence of LI, should be considered 13) we may conjecture from our results that the confining dynamics in QCD has a clear signature in the baryon spectrum in the form of a one-to-one correspondence between 3q bound states and observed resonances: or inversely that the baryon spectrum tells us about the specific form of the confining mechanism in QCD. Acknowledgments

We thank to V. Vento: S. Noguera: J. Papavassiliou and F. Ferndndez for suggesting discussions. This work has been partially funded by COFAA-IPN (Mexico): by Junta de Castilla y Le6n under Contract No. SA-109/01, and by EC-RTN, Network ESOP, Contract HPRN-CT-2000-00130. References 1. G.S. Bali, Phys. R e p . 343: 1 (2001): and references therein. 2. N. Isgur and G. Karl: Phys. Reo. D 18:4187 (1978). S. Capstick and N. Isgur, Phys. Reo. D 34, 2809 (1986). 3. B. Desplanques e t al: 2. Phys. A 343: 331 (1992). 4. A. Valcarce et nl: Phys. Lett. B 367: 35 (1996). H. Garcilazo et al, Phys. Reo. C 63: 035207 (2001). 5. L.Ya. Glozman and D.O. Riska, Phys. Rep. 268: 263 (1996). 6. R. Koniuk and N. Isgur, Phys. R e v . Lett. 44: 845 (1980). 7. S. Capstick and W. Roberts, Phys. Reo. D 47, 1994 (1993). 8. M. Ripani, Few Body Syst. Supp. 11: 284 (1999). 9. K.D. Born e t al: Phys. Reo. D 40: 1653 (1989). 10. A.C. Aguilar et a( hepph/0109223. J.M. Cornwall and J. Papavassiliou, Phys. Rev. D 40: 3474 (1989); Phy.9. Rev. D 44, 1285 (1991). 11. R.K. Bhaduri et al: Nuovo Cimento A 6 5 : 376 (1981). 12. B. Silvestre-Brac and C. Gignoux: Phys. Reo. D 32: 743 (1985). 13. P. Gonzilez et al: work in progress.

PHOTOPRODUCTION OF THE E HYPERONS J.W. PRICE, J. DUCOTE, AND B.M.K. NEFKENS UCLA Department of Physics and Astronomy, Los Angeles, CA 90095-1547, USA E-mail: priceophysics. ucla.edu

FOR THE CLAS COLLABORATION Very little is known about the doubly-strange B hyperons. s U ( 3 ) ~ symmetry, based on QCD, implies the existence of many B states yet to he found. A complete study of the excited B spectrum can also he used to study other related areas of nuclear physics, such as the s - d quark mass difference and Bp scattering. We will report on a new approach to B physics, using the photoproduction process -p -+ K+K+B-, in which the B is cleanly tagged by the missing mass of the ( K + K + )system. We show the current status of this study with the CLAS detector at Jefferson Laboratory, and discuss how it relates to the above topics. We also comment on the future of this program.

1

Introduction

Quantum chromodynamics (QCD) describes the interactions of the quarks and gluons. An aspect of QCD that is not completely explained is the nature of the hadrons. QCD only permits the existence of color singlet states. The na'ive framework of 444 baryons leads to grouping the baryons in four multiplets: a totally antisymmetric singlet state, the A; two mixed-symmetry octets, made up of N , A, C, and E;and a totally symmetric decuplet, consisting of A, C, E,and R. Inspection of this scheme leads to the conclusion that every N* state has a corresponding octet E state, and that every A state has a corresponding decuplet S. The Review of Particle Properties lists twenty-two N* states and twenty-two A states, implying the existence of forty-four E states. To date, we have only found eleven of these states, only three of which have been fully identified by their mass, width, spin, and parity. Finding these states is of fundamental importance to nuclear physics. One aspect of the E states that will help in this search is their narrower width. As has been pointed out by Risk ', the gross features of the widths of the baryons may be understood as being due to the number of light quarks in the baryon. Since the E has only one light quark while the N* and A have three, we expect the N* and A to be nine times as broad as the S, which is seen to remarkable accuracy. We are further aided in the search for excited E states by the application of flavor symmetry. This symmetry is the consequence of the structure of the

498

499

+ C,

QCD Lagrangian, which we may write as LQCD= LO

where

4

We note that Lo depends only on the quark and gluon fields and their derivatives; Lo is independent of the quark masses. For small mq, the mass term L, is a correction to LO. To the extent that flavor symmetry is a good symmetry, we expect the mass spectrum of the octet baryons to be related to each other, and similarly for the decuplet baryons. The quality of the comparison between the N* and A states has already been demonstrated '. 2

Experimental Method

We have selected the photoproduction process on the proton, y p + K+K+E:-, to study the 8* spectrum. This has resulted in the first exclusive measurement of photoproduction on the proton, and is currently the only suitable method for studying most of the E* spectrum. We detect the two K+, and infer the E- by its characteristic peak in the missing mass of the (K+K+)system. The two positively-charged kaons in the final state ensure that the missing particle has S = -2, Q = -1, and that it is a baryon. The = is the only possibility, making for a very clean experimental signature. The measurement was carried out with the CLAS detector at the Thomas Jefferson National Accelerator Facility (JLab) The photons were individually tagged, and the range of photon energies used was 3.0 - 5.5 GeV. CLAS is a large acceptance detector with a toroidal magnetic field, oriented such that positively-charged particles are bent away from the beamline.

-_

'.

3

Preliminary Results

Figure 1 shows the missing mass spectrum of the (K+K+)system. There are two strong peaks in the figure, corresponding to the ground state E-(1321) and the first excited state 5-(1530). The positions and widths of the missing mass peaks are consistent with the known masses and widths of the states and the resolution of the CLAS detector. We find our production rate of the ground state 5-, given current CLAS data acquisition capabilities, to be several thousand per day.

500 100

Figure 1. The missing mass spectrum for r p + K+K+X. The two peaks correspond to the ground state C- at 1321 MeV and the first excited 8- at 1530 MeV.

4

Future Plans

There are several possit,,: projects we may pursue in this work, including (but not limited to) searches for higher-mass states, the neutral Eo, measuring J p for the E* states, studying the s - d quark mass difference, and using E p scattering to measure the Z - p scattering length and look for exotic baryon states. We will continue this analysis to search for as many states as our energy and statistics allow. There are several poorly-known states which need confirmation. We will also look for a proposed 5* state at approximately 1870 MeV which decays via the process E* -+Ev,which would belong to a J p = 1/2- octet with the N(1535), the A(1670), and the C(1750). We may use a similar process to study the photoproduction of the neutral Eo.Instead of the process y p + K+KoEo,which is complicated by the indeterminate strangeness of the K t , we will use the process y p + K+K+7r-S0. The loss in acceptance due to the requirement of an additional detected particle should be outweighed by the cleanliness of the signature.

501

By detecting the decay chain E*3 ET 4 A m , we can measure the spins and parities of the excited states 6. This would allow us to fill in many of the gaps in our knowledge of the E* spectrum. Finding more E* states along with their spins and parities will allow us to complete several baryon multiplets. This will allow a test of the Gell-Mann decuplet equal spacing relation and the Gell-Mann-Okubo mass relation, which are in turn related to the mass difference between the s and d quarks. Since the B is a relatively long-lived particle, we may have the opportunity to look for a secondary vertex due to the scattering of the E with a proton in the target. Elastic scattering measurements will allow us to measure the Z p scattering length and coupling constant, while inelastic measurements may point to evidence for the H dibaryon or exotic baryon states ’. 5

Conclusion

We have made the first observation of exclusive E photoproduction on the proton, and have shown that the production rate is sufficient to consider mounting a large program based on the physics of the 5 hyperon. This project is still in its infancy, and much work remains to be done. More data exist, which will allow us to improve our statistical precision, and to search for higher-mass states, as well as to broaden our knowledge of the S spectrum. Acknowledgments This work was carried out with the support of the Department of Energy. References 1. D.E. Groom et al., Eur. Phys. J. C15, 1 (2000) and 2001 off-year partial update for the 2002 edition available on the PDG WWW pages (URL: http://pdg.lbl.gov/) . 2. D.-0. Riska, in N S T A R 2001 Proceedings, Mainz, Germany, 2001, edited by D. Drechsel and L. Tiator (World Scientific, Singapore). 3. B.M.K. Nefkens and J.W. Price, in MENU 6001 Proceedings, edited by H. Haberzettl and W.J. Briscoe, TIV Newsletter 16,9 (2001). 4. W.K. Brooks, Nucl. Phys. A663-664,1077 (2000). 5. S.F. Tuan, Phys. Rev. D 46,4095 (1992). 6. N. Byers and S. Fenster, Phys. Rev. Lett. 11, 52 (1963). 7. E.L. Lomon, in Proceedings of the Conference on Advances in Nuclear Physics and Related Areas, Thessaloniki, July 1997.

OPEN STRANGENESS PRODUCTION IN CLAS G . NICULESCU Ohio University, Athens, OH, USA E-mail:[email protected] (for the CLAS Collaboration) An extensive program dedicated to the study of open strangeness systems was established in Hall B at Jefferson Lab. This program takes full advantage of the excellent characteristics of the CEBAF accelerator combined with the almost complete angular coverage of the CLAS detector. A general overview of the program is given, as well as results for the angular dependence of the electroproduction of kaon-hyperon final states.

The study of K-hyperon leptoproduction can provide new insights on many of the important issues in nuclear physics. To the lowest order, and as far as there is no significant strangeness content of the nucleon, the elementary kaon-hyperon production process involves the production of a single ss pair which breaks the flux tube (argued to be1, alongside with constituent quarks, non-perturbative bound state solutions of QCD). This is highly relevant if one wants to gain insight in the energy range where the transition between hadronic and quark degrees of freedom occurs. Due to the higher masses involved, the study of kaon production allows one to probe a higher W range (with two-body kinematics) than it is possible using pions. Furthermore, the strangeness sector might be the right place to look for some of the so-called “missing resonances”, predicted (but not (yet) observed experimentally) by some quark models2 - as some of these resonances might couple strongly to both photons and kaons. The A and Co hyperons act as natural isospin filters in the sense that only N * resonances can contribute (in an s-channel picture) t o A whereas both N* and A* resonances can contribute to the Co channel. The availability of polarized electron beams, coupled with the self-analyzing nature of the A hyperon weak decay makes single- and double-polarization observables accessible if the detection of at least one of the decay products of the hyperon is possible. A comprehensive program devoted to the study of strangeness electroproduction (hopefully addressing the issues listed earlier) was established in the experimental Hall B at JLab. This program takes full advantage of the excellent momentum and angular coverage provided by the CLAS spectrometer, as well as its multi particle final state detection capabilities. The study of ground state hyperon production (Experiment E93030) is

502

503

an important part of this program; the rest of this contribution will try to highlight some of the results of this study. The missing mass recoiling against the outgoing electron and the K+ meson in electron proton scattering, as measured in CLAS, is shown in Fig. la. Prominent peaks are observed corresponding to the A and Co hyperons, smaller peaks corresponding to the A1520 and the C1385/A1405 are also observed as well as a certain amount of background (mostly from misidentified kaons). The resolution obtained with the CLAS detector is significantly better than the spacing between the two ground state hyperons ( 4 0 MeV), allowing for a clean separation of the two peaks. At each beam energy, further analysis of the data was carried out by binning the data in Q2 (-Q2 being the 4-momentum squared of the virtual photon), W (the total energy in the hadronic center-of-mass frame), cosO;( (the angle of the k a m relative to the virtual photon direction in the K-hyperon center of mass frame), and 4 (the angle between the leptonic and hadronic production planes). The virtual photon cross-section can be written as:

where EL = &Q2/u2 is the longitudinal polarization of the virtual photon. Given the almost complete angular coverage of the CLAS detector the 4 dependence of Eq. 1 can be measured (at fixed Q 2 , W , and cosO*). Through a simple fitting procedure one can then extract the 4 independent part of the cross-section nu = OT + ELUL, as well as the two interference terms, UTT and O L T . This procedure is illustrated in Fig. l b for the A hyperon and Fig. l c for the Co hyperon for a representative kinematic bin (Q2=0.7 (GeV)2, W=1.9 GeV, and cos0°=-o.3). The vertical error bars shown are statistical only while the horizontal error bars merely show the extent of each 4 bin considered. By carrying out this fitting procedure for all available kinematic bins one can study separately the angular and energy dependence of the nu, UTT and OLT observables. In Fig. 2 the preliminarya cosO* dependence of these three observables is shown, separately for A and Co, for Q2= 0.7 (GeV)' and W = 1.9 GeV. The uncertainties shown are statistical only. The solid lines are predictions of the Regge model described in Ref. while the dashed lines are predictions from the effective Lagrangian model of Ref. There are large qualitative differences between the A and Co production. Most striking, the cos8k dependence of nu is very forward-peaked for the A and more central aAs of this writing this analysis is undergoing the final systematic checks and is expected to be finalized in the near future.

504

Figure 1. a) - Missing mass distribution in K + electroproduction as measured with th CLAS detector. b) and c) - Extraction of the uu,UTT and QLT through a fit of the 4 dependence of the differential crosssection for the A channel (top right) and the Co channel (bottom right). For both cases Q2=0.7 ( G e V ) 2 ,W=1.9 GeV, and c0s6~=-0.3.

for the Co. This points to a t*hannel domination of the A production in the forward direction, whereas this mechanism appears to be suppressed for Co. The size, and forward peaking of QLT for A production strengthens the above argument. Neither one of the two models shown is very successful in describing the data other than in its more general features. The models seem to fare worse in explaining the Co data than they do for the A data. In conclusion, the electroproduction of the ground state A and Ca was studied using the CLAS detector at JLab. The hermeticity of the detector allowed the separation of the nu, QTT, and ULT observables. Significant differences between the two hyperons are observed, pointing to different reaction mechanisms, especially in the forward direction. The interference terms are larger in the A than in the Co channel. The discrepancies between the model predictions and the experimental data warrant a revision of the basic assumptions and parameters entering the theoretical models. This work was supported in part by the National Science Foundation under Grant No. PHY-007226.

505

"ijdl

/I -

0.3 0.2

:

0.1 h

h

.r? 0.9

5 W

-0

G d , -0.1 D

d -0.2 -83 -0 -0.1

-0.2 -0.3

cos( O K )

cos( O K )

Figure 2. (TU,(TTT and (TLT observables shown as a function of the cos 8' angle (left panels) and Co hyperons (right panels). From top to bottom the three rows of panels correspond to (TU,@ T T , and OLT respectively. Theoretical predictions obtained with a Regge model (solid lines) as well as an effective Lagrangian model (dashed lines) are shown.

References

1. 2. 3. 4.

N. Isgur, JLAB-THY4O-20, (2000). S. Capstick and W. Roberts, Phys. Rev. D58, 1 (1998). M. Guidal, private communication, (2000). T. Mart, private communication, (2000).

K+ PHOTOPRODUCTION AT LEPS/SPRING-8. R.G.T. ZEGERS FOR THE LEPS COLLABORATION RCNP, Osaka Uniuersity, 10-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan At the LEPS beam line at Spring-8, K+ photoproduction off the proton is studied for 1.9 GeV < W < 2.3 GeV and O0 < O,,(K+) < 6C0. Since data are taken with transversely polarized photons, the photon-polarization assymetry can be measured. In contrast to the cross section, this observable is very sensitive to the details of the reaction process, such as the possible contribution from so-called 'missing' resonances and thus provides a good way to distinguish between various theoretical descriptions. In the paper, the current status of the analysis and expected impact of the results are discussed.

1

Introduction

The study of strangeness photoproduction on the nucleon is a potentially powerful tool t o deepen the insight into baryon structures, because of the strangeness degree of freedom involved. The p ( y ,K+)A and p ( y ,K+)Co reactions are good candidates for such studies, since they provide a way to access a rather large part of the rich excitation spectrum of the nucleon. For a number of these nucleon resonances, the branching into strange channels is well known. On the other hand, a large number of resonances predicted in quark models have so far been undiscovered and are hence referred to as 'missing resonances'. It has been prepositioned that some of these missing resonances could couple strongly to the K A and KC channels. Although the above-mentioned reaction channels had been under investigation for an extensive period of time, data taken at SAPHIR' has resulted in renewed interest. This is largely due t o the fact that structure in the total cross section spectrum of the p ( y ,K + ) A reaction near W=1900 MeV was revealed. Mart and Bennhold2 showed that this structure can be explained if an additional 0 1 3 (1895) resonance is included in the calculations. Alternatively, if from the set of possible candidates in this mass range a P13 (1950) resonance is chosen, the data is equally well3 described. Unfortunately, it is difficult to draw strong conclusions based on cross section measurements only because of ambiguities in the theoretical descriptions. In the region W < 2.5 GeV, most calculations are performed in a tree-level effective-Lagrangian approach. Ambiguities arise from the choice of included resonances, the values of the coupling constants (depending on the magnitude of SU(3)-symmetry breaking) and the choice of hadronic form factors. Further

506

507

complications are due to coupled-channel contributions4 and off-shell effects5. Moreover, different methods to suppress the strength due to the Born terms only, lead to equally good descriptions of the available data3. It can, therefore, be concluded that at present we are left with an unacceptable level of model dependence in the theoretical description of experimental results. Improvement in this situation on the theoretical side is possible by changing approaches as to reduce the number of parameters and limit the model dependencies, for example by using a consituent-quark approach5. On the experimental side, one strives to increase the amount of available data, especially by measuring previously unprobed observables. Inclusion or exclusion of certain resonances2 as well as the use of different model ingredients3 have large effects on the predictions for (double) polarization observables. Therefore, at various places in the world (GRAAL, JLAB, ELSA, MAMI, LEGS and Spring-8) experimental programs are in progress to measure these observables. It has been shown that the photon-polarization asymmetry (the asymmetry measured in the comparison between data taken with different polarizations for the incoming photon) in particular contains large sensitivities. Mart and Bennhold2 predict a sign change for the photon polarization asymmetry if the missing &(1895) resonance is present. Janssen et aL3 showed that various methods to suppress the strength of the Born terms, as well as the choice of form factor also changes the photon polarization asymmetry significantly. 2

K f photoproduction at LEPS/SPring-8

Investigation of the p ( y , K + ) A and p ( y , K + ) C o reactions at the LaserElectron-Photon beam h e at Spring-@ (LEPS) can contribute strongly to the field, because kinematical regions are probed that are not accesible elsewhere. Moreover, since the photons are produced by Compton backscattering of laser photons off electrons, polarization is automatically obtained by polarizing the laser light. Between December 2000 and June 2001, photo-production data was taken with a liquid Hydrogen target7. The photon energy range was between 1.5 GeV and 2.4 GeV (i.e. 1.9 GeV < W < 2.3 GeV) and for these energies the transverse polarization (horizontal or vertical) varies between 50% and 95%, respectively. By comparing the azimuthal dependence of cross sections for horizontally and vertically polarized photons, the photonpolarization asymmetry can be determined via the relation:

508 *

L

v)

5 4500 F 0 " 4000 ? 3500

5

3000 2500

2000 1500 1000

500 0

1

1.5

K* Missing Mass (GeV) Figure 1. Kf missing mass spectrum taken at LEPS.

where C is the photon-polarization asymmetry, P the averaged degree of polarization for the horizontal and vertical polarized data, 4 the azimuthal angle of the K+ and Nh(N,) the measured azimuthal distributions for horizontal (vertical) polarized data. In this relation, detector acceptances are divided out. Only foward K+ production angles (Oo < O,,(K+) < 60') can be probed at the LEPS facility, but with a high accuracy and good statistics. This angular range is especially important to distinguish K and K* contributions, since the former peaks and the latter vanishes at Oo. K+ particles can cleanly be selected7 from the reconstructed mass spectrum. In figure 1 the missing mass spectrum for the p ( y , K + ) is shown for about 50% of the available data. The h ( l l l 6 ) , C0(1193), A(1520) and a combined peak due to the h(1405) and CO(1385) can clearly be distinguished. In figure 2, photon-polarization asymmetries are shown for the A(1116) and C0(11Y3), for two different choices of photon energy (1.7 and 2.2 GeV). No correction for photon polarization has been applied and the plots are scattering-angle integrated. From this figures it is clear that at LEPS the photon polarization asymmetry for the K + , h and K f , C o can be accurately determined. Since the photon polarization asymmetry is expected to fluctuate rather quickly as a function of photon energy in the resonance region, it is important to determine asymmetries for as narrow energy bins as possible. It is envisioned that with the current statistics a binning of 100 MeV in E-, (corresponding to ap-

509 ,0.6

,0.6

z"

i

=0 ;'2 .

G kaO.2

? 5' 0

% 5.' 0

-0.2

-0.2

-0.4

-0.4

2.4

-0.6

0

y+p+Kt+Z0(1193)

++O. 4

2

4

6

-0.6

0

2

4

6

Figure 2. Scattering-angle and photon-energy integrated asymmetry curves for the A( 1116) (left) and CO(1193) (right). Open data points/dashed fits are for 1.6 < E, < 1.8 GeV and full data points/solid fits are for 2.1 < E , < 2.3 GeV.

proximately 50 MeV in W )can be achieved for 4 different values o f t between 0 and -0.6 (GeV/c)2.

3

Status and outlook

At present, acceptances and efficiencies for the LEPS detector are being studies. These include Monte-Carlo simulations to determine the geometrical acceptance accurately as well as detailed studies of the separate parts of the detector system, photon-beam properties and tracking errors. With the various details understood, results for the photon polarization asymmetry and the differential cross section are expected to come out in the course of 2002. References

1. M.Q. Tran et al., Phys. Lett. B 445,20 (1998). 2. T. Mart and C. Bennhold, Phys. Rev. C 61 (R) 012201 (2000). 3. S. Janssen et al., Phys. Rev. C 65,015201 (2001). 4. Wen-Tai Chiang it et al., nucl-th/0104052, 2001. 5. B. Saghai, nucl-th/0105001, 2001. 6. T. Nakano et al., Nucl. Phys. A684,71c (2001). 7. T. Nakano et al., these proceedings.

KAONPHOTOPRODUCTI0N:BACKGROUND CONTRIBUTIONS AND MISSING RESONANCES STIJN JANSSEN AND JAN RYCKEBUSCH Department for Subatomic and Radiation Physics, Ghent University, Proeftuinstraat 86, 9000 Gent, Belgium E-mail: [email protected]. be Kaon photoproduction off the proton is studied in an effective Lagrangian approach. The dominant resonance contributions in the reaction dynamics are identified, including a search for signals of “missing” resonances. SpeciaI attention is paid t o the issue of the elusive role played by background contributions.

1

Formalism

Since long, it has been known that pion production and pion induced reactions may be too restrictive to explore the complexity of the nucleon spectrum. Therefore, the study of other meson production reactions is essential to gain access to excited nucleon states which remain unobserved in pionic reactions but which are predicted by (constituent) quark-model calculations. Reactions of this type are the strangeness production processes p(y, K ) Y , where Y = A or C. Here, we present results of p(y, K ) Y calculations which adopt an effective Lagrangian approach starting from hadronic degrees-of-freedom’ . The effective Lagrangians provide the mathematical structure of the interaction vertices and the propagators of the intermediate fields. In order to account for the short-range physics of the inter-baryon interaction, form factors are introduced at the hadronic vertices. The cutoff mass of those hadronic form factors sets the typical length scale of the hidden short-range dynamics. The. reaction amplitude contains the usual Born terms and the exchange of the vector meson K* in the t-channel (also the K1 is taken into account in the case of K+A production). Apart from the lLbackgroundllcontributions, there is common agreement2 that the three nucleon resonances ,911(165O), P11(1710) and P13(1720) play a substantial role in the p(y, K ) Y reaction dynamics. Due to isospin considerations, contributions of the I = A* resonances are excluded in the K+A channel. For the KC processes, we have identified the 5’31 (1900) and P31(1910) resonances as likely candidates for intermediate A* states. Finally, we have implemented predicted “missing” resonances and investigated whether their inclusion considerably improved the overall description of the data.

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Figure 1. The extracted coupling constants for the s11(1650), p11(1710), P13(1720) and D l ~ ( 1 8 9 5 s-channel ) resonances in the p ( y , K f ) h process, using three different models for dealing with the background terms. The circles are for model A, the squares for model B and the triangles for model C.

2

Background Contributions

Assuming a moderate breaking of SU(3)-flavor symmetry, one can put forward some ranges for the g K + A p and gK+COp coupling constants starting from the value of gr". Adopting a realistic breaking of sU(S)-flavor symmetry at the 20% level, though, one finds that the predicted contribution from the Born terms largely overshoots the measured p(y, K ) Y cross sections. This observation clearly illustrates that the treatment of the background diagrams poses a serious difficulty when modeling open strangeness photoproduction reactions. We have suggested three schemes which accomplish to reduce the Born strength to realistic levels. In model A, soft hadronic form factors with a cutoff value of the order of the kaon mass (= 0.5 GeV) are introduced. Despite our reservations against the use of soft hadronic form factors, it emerges that they are absolutely necessary in order to reduce the Born strength to an acceptable level when no other ingredients are introduced in the model. Alternatively, we showed that the introduction of u-channel hyperon resonances is able to reduce the Born strength through the mechanism of destructive interferences'. This method is adopted in model B. Finally, in model C the constraints imposed by a moderate breaking of SU(3) symmetry are simply ignored and g K + A p and gK+COp are treated as free parameters. In such an approach, the optimum values for the two coupling constants correspond with a completely broken SU(3)-flavor symmetry. All three schemes succeed in providing a satisfactory description of the SAPHIR3>4data which consists of total and differential cross sections as well

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Figure 2. Model calculations for the total p ( y , K + ) hcross section. The solid curve includes the missing D13, the dashed curve includes a Pi3 resonance.

as recoil polarization asymmetries. Despite the fair agreement of the three models with the data, it has to be stressed that in some cases a substantial amount of model dependence is introduced in the extracted resonance parameters. This is made clear in Fig. 1 where the extracted coupling constants of the nucleon resonances for the p(y, K + ) Aprocess are plotted for the three different background models. For the KC counterpart, the extracted resonance coupling constants are less dramatic affected by the model dependences in the background diagrams. The model dependence in the extracted resonance couplings is rather unfortunate, given that this information can bridge the gap between the p(y, K ) Y measurements and the quark-model calculations for baryons. The same variations are also observed in the predictions of the photon beam asymmetry and other polarization observables. Here also, the KC results seem to be more stable than the K + h ones with regard to variations in the parameterization of the background diagrams.

3

Missing Resonances

With the release of the SAPHIR data back in 1998, it became clear that the energy dependence of the total p(y, K + ) h cross section exhibits a peculiar structure about 1.5 GeV photon lab energy. It was suggested by the George Washington group2 that this structure could be theoretically accounted for by the inclusion of a “missing” &(1895) resonance. Such a resonance has never been observed in pionic reactions but its existence was predicted by con-

513 stituent quark-model calculations5. As such, it appears as a good candidate for a “missing” resonance. Our calculations confirm that the description of the p ( y ,Kf)A data is significantly improved after the inclusion of this new 0 1 3 resonance and that the calculations can account for the observed structure in the energy dependence of the total cross section. With respect to the classification of the quantum numbers of this additional resonance, it should be stressed that the data can equally well be described by adding other resonant states. For example, as is made clear in Fig. 2, the inclusion of a “missing” Pl3 resonance can also produce the structure in the energy dependence of the total cross section. In the other isospin channels, p ( y ,K+)Co and p(y, Ko)CC,the quality of agreement between the model calculations and the SAPHIR data only marginally improved after the inclusion of the missing resonance. 4

Conclusion

Model calculations for the p ( y ,K+)Y observables are presented. Special attention is paid to the issue of the background contributions. It turns out that different schemes for dealing with the background can account for the available data but produce significant model dependences in the extracted resonance parameters and in the predictions for the unmeasured polarization observables. Whereas the energy dependence of the measured p(y, K + ) A cross section suggests the existence of a previously unobserved resonance, the current data does not enable one to identify unambiguously the quantum numbers of it. Indeed, both a 0 1 3 and a P13 resonance with a mass of about 1.9 GeV are able to improve the description of the p ( y , K + ) A data. There are no convincing signals for a salient role of a such an additional resonance in the p ( y , K)C channels. We are confident, however, that the upcoming data for various polarization observables and electroproduction response functions will allow to further pin down the full reaction dynamics of the strangeness photoproduction processes and remove some of the model dependences which exist to date. References 1. S. Janssen, J. Ryckebusch, D. Debruyne and T. Van Cauteren, Phys. Rev. C 6 5 , 015201 (2002). 2. T. Mart and C. Bennhold, Phys. Rev. C 61, R0112201 (2001). 3. M.Q. Tran et al., Phys. Lett. B 445, 20 (1998). 4. S. Goers et al., Phys. Lett. B 464, 331 (1999). 5. S. Capstick and W. Roberts, Phys. Rev. D 58, 074011 (1998).

DYNAMICAL DESCRIPTION OF NUCLEON COMPTON SCATTERING AT LOW AND INTERMEDIATE ENERGIES: FROM POLARISABILITIES TO SUM RULES S. KONDRATYUK TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., V 6 T 2A3 Canada E-mail: [email protected]

0. SCHOLTEN K V I , 9747 AA Groningen, The Netherlands E-mail: [email protected] Results of the Dressed K-matrix Model are presented for nucleon Compton scattering, nucleon polarisabilities and related sum rules. Effects of the meson loop dressing on the A resonance are shown.

1

Compton scattering at low and intermediate energies

The Dressed K-matrix Model has been developed to describe pion- and photon-induced reactions on the nucleon at both low and intermediate energies. In this model effects of the meson cloud around the nucleon are included by dressing the nucleon propagator and 7rNN vertices up to infinite order while obeying essential constraints from unitarity, crossing and analyticity. In what follows we will be comparing the fully dressed and the bare calculations. The latter corresponds to the traditional K-matrix models 2 , where analyticity is badly broken since the real parts of the meson loops are not included at all. Fig. 1 shows calculated differential cross sections for proton Compton scattering. Comparing this calculation as well as pion-nucleon and pion photoproduction phase shifts with data, we fixed all parameters of the model. Thus we can do a parameter-free calculation of the nucleon polarisabilities, which are found to be in a reasonable agreement with experiment. 2

Compatibility of the low-energy and sum-rule evaluations of nucleon polarisabilities

Since the present model is applicable in both intermediate and low-energy regions, it allows us to calculate nucleon polarisabilities in two distinct ways 5 , namely: 1)directly from the low-energy expansion of the scattering amplitude, and 2) by integrating calculated total cross sections in sum rules corresponding

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Figure 1. Dependence of the Compton cross section on the photon lab energy at fixed angles. The fully dressed and bare calculations are compared with the data.

to coefficients in the low-energy expansion. Such a comparison is important because the sum rules rest on only few fundamental requirements 6 : gaugeinvariance, crossing symmetry, unitarity and analyticity, the latter being of special significance. As can be seen from Table 1, the level of agreement between the low-energy calculation (method 1))and the sum-rule calculation (method 2)) is quite good at the two leading orders in the photon energy: at w,corresponding to the anomalous magnetic moment n of the proton, and at w 2 , corresponding to the sum Q ,@of the electric and magnetic polarisabilities. This means that the model obeys the essential symmetry constraints at these orders. The dressed calculation shows a closer agreement

- -

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516

since it fulfills analyticity constraints much better than the bare calculation. However, a discrepancy shows up for the forward spin polarisability yo,i. e. at

-

w3.

Table 1. Comparison between the proton polarisabilities as computed directly from the low-energy expansion of the amplitude (LE) and as computed from the sum rules (SR).

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3 Dressing the 7rNA vertex with an infinite number of loops An exploratory calculation indicated that the disagreement between the low-energy and sum-rule evaluations of yo is due to the fact that, unlike the nucleon self-energy, the self-energy of the A resonance was computed only up to one T N loop. The first step in extending the dressing procedure is to dress the A on the same footing with the nucleon in the purely hadronic sector, i. e. for pion-nucleon scattering. In particular, the T N A vertex gets dressed with an infinite number of meson loops. This improves the P33 phase shift at higher energies, as is shown in Fig. 2 (the other phase shifts are not affected). The dressing of the y N A vertex with an infinite number of loops is currently under way.

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FULL with: Dressed 7rNA . BarerNA 1

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Figure 2. The calculated P33 phase shift is improved by the consistent dressing of the A resonance up to infinite order. The data points are from the analysis.

517

References 1. S. Kondratyuk and 0. Scholten, Phys. Rev. C 59, 1999 (1070); ibid., Nucl. Phys. A 677,2000 (396); ibid., Phys. Rev. C 62, 2000 (025203). 2. P.F.A. Goudsmit et al., Nucl. Phys. A 575,1994 (673); T . Feuster and U. Mosel, Phys. Rev. C 58, 1998 (457); ibid., Phys. Rev. C 59, 1999 (460); A. Yu. Korchin, 0. Scholten, and R.G.E. Timmermans., Phys. Lett. B 438,1998 (1). 3. S. Kondratyuk and 0. Scholten, Phys. Rev. C 64,2001 (024005). 4. G. Galler et al., Phys. Lett. B 503,245 (2001); A. Hunger et al., Nucl. Phys. A 62,385 (1997). 5. S. Kondratyuk and 0. Scholten, Phys. Rev. C 65,2002 (038201). 6. A.M. Baldin, Nucl. Phys. 18,1960 (310); L.I. Lapidus, Sov. Phys. JETP 16,1963 (964); S.B. Gerasimov, Sow. J. Nucl. Phys. 2, 1966 (430); S.D. Drell and A.C. Hearn, Phys. Rev. Lett. 16,1966 (908). Phys. Rev. D 63,114010 (2001). 7. R.A. Arndt et al., Phys. Rev. C 52,2120 (1995).


Session on Hadrons in the Nuclear Medium Convenors N. Bianchi M. Sargsian


NUCLEAR SHADOWING AND IN-MEDIUM PROPERTIES OF THE po * T. FALTER, S. LEUPOLD AND U. MOSEL Institut fuer Thwretische Physik Universitaet Giessen 0-35392 Giessen, Germany We explain the early onset of shadowing in nuclear photoabsorption within a mu]tiple scattering approach and discuss its relation to in-medium modifications of the p o .

The nuclear photoabsorption cross section is known to be shadowed at large energies, i.e. O,A < Au,N. This was at first interpreted as a confirmation of the vector meson dominance (VMD) model, which assumes that the photon might fluctuate into vector meson states with a probability of order aem. To give rise to shadowing, these hadronic fluctuations must travel a t least a distance ZV that is larger than their mean free path inside the nucleus. This so called coherence length ZV can be estimated from the uncertainty principle

where k, and kv denote the momentum of the photon and the vector meson respectively and mv is the vector meson mass. Recent photoabsorption data1i2 indicate an early onset of shadowing at E, ~1 GeV. From (1) one sees that the lightest vector meson, e.g. the po, has the largest coherence length and therefore its properties determine the onset of the shadowing effect. This lead to the interpretation3 of the low energy onset of shadowing as a signature of a decreasing po mass in medium since a decrease of m, increases the coherence length I,. A quantitative description of the shadowing effect is possible within the Glauber model". The nuclear photoabsorption cross section can be related via the optical theorem to the nuclear forward scattering amplitude. In order a,, one finds the two contributions shown in Fig. 1. The left amplitude stems from forward scattering of the photon from one nucleon inside the nucleus. Summing over all nucleons this amplitude alone leads to the unshadowed cross section U,A = Au,N. Shadowing arises from the interference with the *WORK SUPPORTED BY DFG AND BMBF.

521

522

Figure 1. The two amplitudes that contribute to the nuclear forward scattering amplitude in order aem.

second amplitude in order aem.Here the photon produces some hadron X I on one nucleon inside the nucleus. This hadron then scatters through the nucleus and finally into the outgoing photon which has the same momentum and energy as the incoming photon. Since we are dealing with the forward scattering amplitude and the nucleus has to be in its ground state after the last scattering event one usually assumes that it stays in its ground state during the whole multiple scattering process (multiple scattering approximation). One sees that, in principle, shadowing can be explained without the usage of VMD . In the simple Glauber model one makes use of the eikonal approximation, assuming that all scattering events at high energies go predominantly into the forward direction. This limits the intermediate states X i to hadrons which have the quantum numbers of the photon, e.g. the vector mesons. Neglecting off-diagonal scattering ( V N -+V ' N with V # V ' ) and neglecting the widths of the vector mesons one gets for the total photon nucleus cross section

Here n ( 3 denotes the nucleon number density and frv and fv are the vector meson photoproduction and V N forward scattering amplitudes respectively. In our calculation5 we also account for two-body correlations between the nucleons. In the derivation of (2) one has made an error of order A-' by summing up infinitely many multiple scattering terms for the intermediate vector meson. This is equivalent5 to the propagation of the vector meson in an optical potential, giving rise to an effective in-medium mass and width. The momentum transfer qv = k - kv in the phase factor arises from putting the vector meson on its mass shell. A large momentum transfer qv causes a rapidly oscillating term in the integrand of (2) and reduces the shadowing

523

effect. Note that qv is just the inverse of the coherence length lv as can be seen from (1). We now relate the amplitudes frv and f v using VMD: e

f,v = fvr = -fv. sv

(3)

The pN forward scattering amplitude f, is taken from dispersion theoretical a n a l y ~ e & ~In. the energy region that we are considering the real part of f, is negative and of the same order of magnitude as the imaginary part, leading to an increase of the effective po mass in medium. Within VMD the negative real part also enters the photoproduction amplitude via (3). This enhances the shadowing effect and compensates the suppression due to the larger in-medium mass. In total one gets an increase of shadowing even with a positive mass shift of the po in medium. This can be seen from the left side of Fig. 2 where we show our results for the ratio crA/Aa,N. The calculation that includes the negative real part (solid lines) is in perfect agreement with the data. When the real part of f v is neglected, as done in most other calculations, one gets the result represented by the dotted curves and clearly underestimates the shadowing effect for all nuclei. One even gets anti-shadowing below 2 GeV for P b and 1 GeV for C. In an improved model', we explicitly sum over multiple scattering amplitudes where 1, 2, ... A nucleons participate in the scattering process. This avoids the error of order A-' that occurs in the large A limit as described above. We also take the widths of the vector mesons into account and find that the main contribution to shadowing at low energies stem from light po mesons with masses well below the pole mass. These are favored by the nuclear formfactor because their production is connected with a small momentum transfer. This is in agreement with our qualitative understanding of shadowing, since light fluctuations have a larger coherence length. We also do not hold on to the eikonal approximation any longer. Dropping this restriction leads to a new contribution to the shadowing effect due to no mesons as intermediate states. Since these cannot be produced in the forward direction without excitation of the nucleus they do not contribute to shadowing at high energies. In the shadowing onset region, however, they give rise to 30% of the total shadowing effect in the case of C and 10% in the case of P b as can be seen from the solid lines on the right side of Fig. 2. The dashed lines show the contribution from intermediate p , w and 4 mesons. In total one again gets a good description of the shadowing effect. We have presented a theoretical explanation for the early onset of shadowing as observed in nuclear photoabsorption. It can be explained by taking the negative real part of the pN forward scattering amplitude into account.

524

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Figure 2. Calculated ratio cryA/AuyN plotted versus the photon energy E7. The left side shows the result of the simple Glauber model: with real part of fp (solid lines), Refp = 0 (dotted lines). The right side shows the result of our improved model: contributions from p , w and 4 (dashed lines), including the contribution from intermediate r0 (solid lines).

This corresponds to an increase of the effective po mass in nuclear medium, in agreement with dispersion theoretical analyses. The major contribution to shadowing stems from light po with masses much smaller than the pole mass. In addition we find contributions from intermediate xo to shadowing in the onset region. References

N. Bianchi et al., Phys. Rev. C 54, 1688 (1996). V. Muccifora et al., Phys. Rev. C 60, 064616 (1999). N. Bianchi et al., Phys. Rev. C 60, 064617 (1999). T. H. Bauer et al., Rev. Mod. Phys. 50, 261 (1978). T. Falter, S. Leupold and U. Mosel, Phys. Rev. C 62, 031602 (2000). V. L. Eletsky and B. L. Ioffe, Phys. Rev. Lett. 78,1010 (1997). 7. L. A. Kondratyuk et al., Phys. Rev. C 58, 1078 (1998). 8. T. Falter, S. Leupold and U. Mosel, Phys. Rev. C 64, 024608 (2001).

1. 2. 3. 4. 5. 6.

SCALAR- AND VECTOR-MESON PRODUCTION IN HADRON-NUCLEUS REACTIONS W. CASSING’ Institut fiir Theoretische Physik, H. -Bu#-Ring 16, 35392 Giessen, Germany E-mail: Wolfgang.CassingOtheo.physik.uni-giessen.d e The production and decay of vector mesons ( p , w) in p A reactions at COSY energies is studied with particular emphasis on their in-medium spectral functions. It is explored within transport calculations, if hadronic in-medium decays like a+aor a07 might provide complementary information to their dilepton (e+e-) decays. Whereas the &a- signal from the pmeson is found to be strongly distorted by pion rescattering, the w-meson Dalitz decay to a0y appears promising even for more heavy nuclei. The perspectives of scalar meson ( f o , a o ) production in p p reactions are investigated within a boson-exchange model indicating that the fomeson is hard to detected in these collisions in the K K or m~decay channels whereas the channels p p + pna; and p p + da$ look very promising.

1

Introduction

The modification of the vector meson properties in nuclear matter has become a challenging subject in dilepton physics from T - A , p A and A A collisions. Here the dilepton (e+e-) radiation from p’s and w’s propagating in finite density nuclear matter is directly proportional to their spectral function which becomes distorted in the medium due to the interactions with nucleons. Apart from the vacuum width ;?I (V = p, w ) these modifications are described by the real and imaginary part of the retarded self energies C V , where the real part %Ev yields a shift of the meson mass pole and the additional imaginary part 9 C v (half) the collisional broadening of the vector meson in the medium. We recall that the meson self energy in the t - p approximation is proportional t o the complex forward V N scattering amplitude fvN(P,0) and the nuclear density p(X), i.e. C v ( P ,X) = -4np(X)fv~(P,O). The scattering amplitude itself, furthermore, obeys dispersion relations between the real and imaginary parts3 while the imaginary part can be determined from the total V N cross section according to the optical theorem. Thus the vector *IN COLLABORATION WITH E. L. BRATKOVSKAYA, M. BUSCHER, YE. s. GOLUBEVA, V. GRISHINA, V. HEJNY, V. METAG, J . MESSCHENDORP, G. I. LYKASOV, L. A:. KONDRATYUK, M. V. RZJANIN, S. SCHADMAND, A. A. SIBIRTSEV, H. STROHER

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meson spectral function

can be constructed once the V N elastic and inelastic cross sections are known. Note that in ( 1 ) all quantities depend on space-time X and 4-momentum P. 2

Production and decay of vector mesons at finite density

As mentioned before, the in-medium vector meson spectral functions can be measured directly by the leptonic decay V+e+e- (cf. ref^.^^^^^), the strong decay po + 7rr+n-- or the Dalitz decay w+7roy, respectively. The vector meson production in p A collisions can be considered as a natural way4y6 to study the p and w-properties at normal nuclear density under rather well controlled conditions. The transport calculations have been performed for p+A collisions at 2.42.6 GeV by introducing a real and imaginary part of the vector meson self energy and width as

in the t-papproximation. Here MO and denote the bare mass and width of the vector meson in vacuum while p ( X ) is the local baryon density and p0=0.16 fm-3. The parameter ,BY-0.16 was adopted from the models in The predictions for the w-meson collisional width rcollat density po range from 20 t o 50 MeV7- depending on the number of wN final channels taken into account - while the collisional width of the pmeson should be about 100 - 120 MeV at po due to the strong coupling to baryon resonances (cf. Fig. 6 of Ref.3). In Ref.8 it has been found that the 7r+7r- decay mode of the po in nuclei is not well suited to reconstruct the in-medium po spectral function except for very light nuclei due to the strong 7r* final state interactions (cf. also Ref.g). The situation changes for the in-medium w-meson Dalitz decay since here only a single pion might rescatter whereas the photon escapes practically without reinteraction. In this case it is foundlo that most of the w-mesons from a 12C target decay in the vacuum (92%) and consequently w decays in the medium as well as no rescattering are rather scarce. The situation changes for a Cu target where 7roy coincidences from finite density are more frequent (19% w's decay inside the target), however, also 7ro rescattering gives a substantial background. The latter can - in the invariant mass range 0.6

527

< M 5 0.9 GeV of interest - be suppressed effectively by kinematical cuts on higher T O energiesll or angular correlations between the photon and the pion12 which provides good perspectives for the n0y decay mode.

3

Scalar meson production

The structure of the lightest scalar mesons a(980) and fo(980) is not yet understood and is one of the most important topics of current hadronic physics. It has been discussed that they could be either ” qq states”, ”Four-quark cryptoexotic states”, KK molecules or vacuum scalars. Moreover, there is a strong mixing between the uncharged ao(980) and the fo(980) due to a coupling t o KK intermediate states. It is, therefore, important to study independently the uncharged and charged components of the ~ ( 9 8 0 because ) the latter are not mixed with the fo(980) and preserve their original quark content. In order t o estimate the cross section of the reactions pp + p p f z , pp + ppag, p p + p a : , p p + d a i at bombarding energies close to threshold which are available at COSY/Julich - an effective Lagrangian approach as well as the Regge pole model have been employed. The amplitudes taken into account are: i) the a,-, coupling to two nucleons through the fl(1285) and Tmeson exchanges; ii) the Q coupling through 77- and 7r-meson exchanges; iii) the production of %-mesons through pion exchange with s- and u- channel nucleon currents. The coupling constants and cut-off parameters Ai for T and 7- meson exchanges are taken from the Bonn potential model; for the a,-,- and f1(1285)-mesons the values from Ref.13 are used while the cut-off A at the nucleon exchange vertex was considered as a free parameter within the interval 1.1-1.3 GeV and fixed approximately by comparison to the LBL data for a0 production14. Within this model the mechanisms i) and ii) are of minor importance and the dominant contribution comes from the nucleon u- and s-channel exchanges. For the deuteron a: final state the two-step model (TSM) described by the triangle diagram is used15J6 employing the deuteron wave function in the parameterization from Ref.17. The results of the calculations show that in p p reactions the ppfo final state is hard to detect due to the nonresonant background from T+T- or K+K-18; a similar statement holds for the ppa: final statelg since the cross section is small due to a destructive interference between s- and u- channel diagrams. However, the p n a i or d a i final states show sizeable cross sections close t o t h r e ~ h o l d ‘which ~ dominate over the nonresonant background channels. We note, that preliminary experimental results for the p p + da: reaction have become available by now and support the calculations performed in Refs.l5~l6.

+

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4

Summary

In this contribution the production and decay of vector mesons (p,w) in p A reactions at COSY energies has been studied with particular emphasis on their in-medium spectral functions. It is found within transport calculations, that hadronic in-medium decays like T + K - or r o y might provide complementary information to their dilepton ( e + e - ) decays. However, the T+T- signal from the pmeson is strongly distorted by pion rescattering on nucleons even for light nuclei like " C . On the other hand, the w-meson Dalitz decay to 7roy appears promising even for more heavy nuclei since only the neutral pion may rescatter and 3-photon events ( K O + yy) have a very small background at high invariant mass. Furthermore, the perspectives of scalar meson (fo,ao) production in pp reactions have been investigated within a boson-exchange approach as well as the Regge pole model indicating that the fo-meson is hard to detect in the K K or T K decay channels in these collisions whereas the final channels pnaof and daof look very promisinglg. References

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

W. Cassing, E.L. Bratkovskaya, Phys. Rept. 308, 65 (1999) R. Rapp, J. Wambach, Adv. Nucl. Phys. 25, l(2000) L. A. Kondratyuk et al., Phys. Rev. C 58, 1078 (1998) Ye. S. Golubeva et al., Eur. Phys. Jour. A 7, 271 (2000) Ye. S. Golubeva et al., Nucl. Phys. A 625, 832 (1997) E. L. Bratkovskaya, NucI. Phys. A 696, 761 (2001) G. I. Lykasov et al., Eur. Phys. Jour. A 6, 71 (1999) A. Sibirtsev, W. Cassing, Nucl. Phys. A 629, 717 (1998) G. M. Huber, these proceedings A. Sibirtsev et al., Phys. Lett. B 483, 405 (2000) J. Messchendorp et al., Eur. Phys. Jour. A 11, 95 (2001) Ye. S. Golubeva et al., Eur. Phys. Jour. A 11, 237 (2001) M. Kirchbach, D. 0. Riska, Nucl. Phys. B 176, 1 (1980) M. A. Abolins et al., Phys. Rev. Lett. 15, 469 (1970) V. Yu. Grishina et al., Eur. Phys. Jour. A 9, 277 (2000) V. Yu. Grishina et al., Phys. Lett. B 521, 217 (2001) M. Lacomb et al., Phys. Lett. B 101, 139 (1981) E. L. Bratkovskayaet al., Eur. Phys. Jour. A 4, 165 (1999) E. L. Bratkovskayaet al., Jour. Phys. G 28, 2423 (2002)

HELICITY SIGNATURES I N SUBTHRESHOLD po PRODUCTION ON NUCLEI G.M. HUBER Department of Physics, University of Regina, Regina, SK S4S OA2, Canada We report a helicity analysis of subthreshold p o production on 2H, 3He h d 12C nuclei at low photoproduction energies. The results are indicative of a large longitudinal p polarization ( I = 1, m = 0 ) and are consistent with a strong helicity-flip mechanism of p production. The analysis supports an in-medium modification of the po spectral function.

Of all particles, the p has received the most attention with regard to medium modifications. Since the po carries the quantum numbers of the conserved vector current, its properties are related to chiral symmetry, and can be investigated with a variety of models. Most models predict a reduction in the renormalized vector meson mass in the nuclear medium. In addition, the in-medium width of the po may be increased by resonant interactions. Experimental evidence for po mass modification has been widespread, but all suffer from significant model uncertainties. The goal of the study reported here is to provide data which can be interpreted in a less model-dependent fashion than those presently available. We have recently published a helicity analysis of our 2Hand natC7r+7rphotoproduction data from TAGX. The most important points of this analysis are: (1) The "s~bthreshold~~ region is chosen to maximize any nuclear interaction effect. Fermi momentum is required to put po on shell, and the po is produced with low boost with respect to the nuclear medium. This choice of photon energy also suppresses diffractive po production. (2) The 7r+7rIT- are detected in the TAGX large solid angle spectrometer. The po + 7rf7r- decay channel has been selected because of its favorable M 100% decay ratio. (3) The p decay angular distribution is reconstructed in the s-channel helicity frame, where the po direction is taken as the quantization axis. 8* is the polar angle of the 7r+ in the po + d 7 r - C.M. system. (4) The geometry of the TAGX spectrometer natually favors 7r+7r- events from po decay, at the expense of the competing background processes. Non-

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po background is further suppressed by the requirement that the missing mass

< (mtaTget+125MeV), which eliminates 3n production and n - N inelastic FSI, and by the requirement that the nn opening angle > 120O. As po + ITIT is the only mechanism that emits n+n- back-to-back at a common vertex, this results in a large O,, in the lab frame. Other processes preferentially produce n+x- with smaller lab frame opening angle. These two cuts eliminate > 95% of non-p0 background, and > 90% of n - N elastic scattering FSI following p + nlT+nITdecay. 3He

*H

'*C

500-600MeV

....:.

40 .:.

0

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im

0 1

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cos en+ Figure 1. A portion of the data are displayed as a function of cosO:+ in the invariant mass range of 500-800 MeV/c2 in 100 MeV/c2 bins. For each panel, the upper line data have missing mass cuts applied, while the shaded region has in addition an opening angle cut applied, as explained in the text.

Sample data distributions from this analysis are shown in figure 1. The distributions without the O,, cut are featureless, characteristic of the superposition of the many An, N * n , N * , and AA processes dominating x+nproduction in this energy regime. The result of the opening angle cut (shaded distribution) is a dramatic reduction (- 5 : 1) in the number of surviving events in the central regions of the distributions. A pronounced p - wavelike cos20 signature is observed in the 600 5 m,, 700 MeV/c2 region and weaker ones in the 500-600 and 700-800 MeV/c2 m,, bins. This signature is consistent with n+n- production by the decay of a longitudinally polarized po (1 = 1, m = 0). n+n- production from An, N * n and other two-step processes

. These moments can be expanded, according to the operator product expansion (OPE), in powers of l/Q2, and the fall of the resonances along a smooth scaling curve with incresing Q2 was explained in terms of this QCD twist expansion. Duality is expected to hold so long as the higher twist effects (terms in (1/Q2)" in the OPE expansion) are small. In the present analysis, the Cornwal-Norton moments for nuclear structure function were calculated: M Z N ( Q 2 )= dx F:(x,Q2) x n - 2 . The structure function data used were obtained in experiments at SLAC l 1 p 4 , CERN ', Fermilab lo and JLab 5 . The quasielastic and elastic contributions, important for low Q 2 , were added to the moments. The moments for iron can be constructed (assuming that nuclear effects axe small) by adding the proton and neutron contributions, extracted from

s,"

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0

1

3

2

Q2

4

5

6

7

(GeV/c)’

Figure 2. The second moment of F2 for proton (stars), deuteron (full circles), iron (squares), and neutron (empty circles), The neutron data are obtained as the difference between the deuterium and proton moments. The solid lines are obtained by fitting the data for proton and deuteron, and using the procedure described in the text for iron.

+

proton and deuteron data: M ( F e ) = 2 x M ( p ) ( A - 2 ) x M ( n ) , where M ( n ) is taken to be M ( d ) - M ( p ) and is shown in Fig. 2 (empty circles). The differences between the moments calculated this way, and those actually measured on iron, and measured moments are smaller than 5% for Q2 above 2 (GeV/c)2, and between 5 and 10% for Q2 between 0.1 and 2 (GeV/c)2. We next examine the nuclear dependence of the EMC effect in the resonance region, and compare this to precise measurements made in the DIS regime. For this analysis, we take the cross section ratio of iron to deuterium in the resonance region for Q2 4 (GeV/c)2, requiring W 2 > 1.3 GeV2 to exclude the region very close to the quasielastic peak where the scaling violations become significant. Figure 3 shows this ratio for the SLAC measurement and for the JLab resonance region data. The resonance region measurement is consistent with the DIS measurements and is more precise in the high-z region. In conclusion, we utilized inclusive electron-nucleus scattering data for precision tests of quark-hadron duality. Duality is observed to hold for nuclei even in the low Q2 regime of Q2 FZ 0.5 (GeV/c)2, well below the DIS limit. Structure functions extracted in the resonance region appear consistent with the DIS results. In the QCD moment explanation this indicates that higher twist contributions are small or cancelling. Further, the EMC effect on the structure function in the nuclear environment is observed to hold in the resonance region. This work was supported in part by the U S . Department of Energy under Grants No. DEFG02-95ER40901 and W-31-109-ENG-38, and the National Science Foundation under Grants No. HRD-9633750 and MPS-9600208.

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Figure 3. Ratio of nuclear to deuterium cross section. The diamonds are the Jefferson lab data for iron (resonance region). The circles are data for iron from SLAC (DIS region).

References

1. E. Bloom and F. Gilman, Phys. Rev. D4, 2901 (1971). 2. I. Niculescu et al, Phys. Rev. Lett. 85, 1186 (2000); I. Niculescu et aZ, Phys. Rev. Lett. 85, 1182 (2000). 3. H. Georgi and H. D. Politzer, Phys. Rev. D14, 1829 (1976). 4. B. W. Filippone et al, Phys. RRv. C45, 1582 (1992). 5. J. Arrington et al, Phys. Rev. C64, 014602 (2001); J. Arrington et aZ, Phys. Rev. Lett. 82, 2056 (1999). 6. J. Gomez et al, Phys. Rev. D49, 4348 (1994). 7. M. Arneodo et aZ, Phys. Lett. B364:107, (1995). 8. A. DeRujula, H. Georgi and H. D. Politzer, Ann. Phys. 103,315 (1977). 9. J. J. Aubert et al, Nucl. Phys. B272, 158, (1986); Berge et al, Zeit. Phys. C49, 187, (1991). 10. Oltman. Nevis Report 270, (1989); Adams et aZ, Phys. Rev. D54, 3006, (1996). 11. S. Dasu et al, Phys. Rev. D49, 5641, (1994).

NEUTRON STRUCTURE FUNCTION AND INCLUSIVE D I S FROM 3 H AND 3 H E TARGETS AT LARGE BJORKEN-X M.M. SARGSIAN Depnrtment of Physics, Florida International University, Miami FL 33199, USA

S. SIMULA I N F N , Sezione R o m a III, V i a della Vasca Navale 84, I-00146 Roma, Italy

M.I. STRIKMAN Department of Physics, Pennsylvania State University, University Park PA 16802, USA A detailed study of inclusive deep inelastic scattering from mirror A = 3 nuclei at large values of x ~ j is ~presented. ~ k The ~ ~main purpose is to estimate the theoretical uncertainties on the extraction of FT from such measurements. Within the convolution approach we confirm the cancellation of nuclear effects at the level of = 1%for x = l 1.5- 13.4 GeV. 1 have been performed2 at JLab up to Q2 w 7 GeV2. At low Q2 values the scaling function depends strongly on Q2 due to final state interactions (FSIs). As these FSIs become small the extracted scaling function becomes nearly independent of Q2 and depends only on y, as predicted in the y-scaling picture. However, while the data show scaling in y, this by itself does not ensure that the scaling function is connected to the momentum

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lo1

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h E

v

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Figure 1. Scaling function F(y) for deuterium from E89-008 for scattering angles between 15 and 55 degrees, after subtracting a model of the inelastic contributions (large for y > 0, generally negligible for y < 0). Errors shown are statistical only. The solid line represents the expected F ( y ) based on a calculation of the deuteron momentum distribution using the Av14 NN potential.

distribution. We present here an attempt to test the assumptions of the scaling analysis and the extraction of the nucleon momentum distributions. Figure 1 shows F(y) for deuterium, as extracted from the cross sections measured in E89-0082. As the momentum distribution is related to the derivative of F ( y ) , the lack of high precision data on deuterium at large IyI makes it difficult to directly extract the momentum distribution from this data. We can, however, compare the scaling function to what we expect based on a calculation of the deuteron momentum distribution. The solid line is a calculation of F ( y ) using a momentum distribution calculated from the Argonne-vl4 N-N potential. The normalization of the scaling function extracted from the data is consistent with unity (as it must be if it is related to the momentum distribution) and the distribution is in generally good agreement with the calculation. In particular, they are in very good agreement at very large values of the nucleon momentum, (y). This region is especially important because these high momentum components are generated by short range interactions of the nucleons. It has been suggested that final state interactions in this region, where the nucleons are close together, may not disappear as Q2 increases. If there were large final state interactions that were nearly independent of Q 2 ,

569

one might see scaling but the scaling function would not yield the proper momentum distribution in the tails. The data from deuterium indicate that such Q2-independent FSIs are small or absent, although higher precision data at high Q2 and large IyI would allow a much stronger limit to be set. While the y-scaling analysis of the deuterium data appears to yield the correct deuteron momentum distribution, this is not the case for the heavier nuclei. The momentum distribution extracted from F(y) for heavy nuclei falls off much more rapidly at large y, indicating that the high momentum components in heavy nuclei are much smaller than in deuterium, which is the opposite of what one might expect. In addition, the normalizations of the scaling functions for heavy nuclei are -20-30% lower than they should be if F ( y ) is related to the nucleon momentum distribution. These problems indicate that there is a failure of some kind in the scaling analysis for heavy nuclei. The breakdown for A > 2 nuclei comes from the assumption that the residual ( A - 1) nucleus remains in an unexcited state. This is a reasonable approximation when removing a single nucleon from a shell at low missing energy. However, the high momentum nucleons are predominantly generated by short range correlations, meaning that the momentum of the struck nucleon is mostly balanced by a single nucleon, leaving a high momentum nucleon in the residual nucleus. In the following analysis, we take this into account by assuming a simple three-body breakup of the nucleus, where the struck nucleon is assumed to be one of a correlated pair of nucleons moving within the residual ( A - 2 ) nucleus. The scaling variable in this case is y* = k K2N/2, where y* is the total momentum of the struck nucleon, coming from the relative momentum of the two correlated nucleons, k , and the momentum of the pair within the residual nucleus, K ~ N . Figure 2 shows F ( y * ) from iron, along with the fit to the deuterium scaling function (note that for deuterium there is no ( A- 2 ) residual nucleus, so y* = y). The high momentum behavior is identical for deuterium and heavy nuclei (carbon, iron, and gold), indicating that the two-nucleon correlations that dominate in deuterium are the main source of high momentum components in heavy nuclei. Using the modified scaling variable, the normalization of F ( y * ) is also consistent with unity, as it should be if the scaling function is related to the nucleon momentum distribution. While this data indicates that the modified scaling analysis is valid and allows extraction of the nuclear momentum distributions, the data at large nucleon momentum is somewhat limited, especially for few-body nuclei where the extracted distributions can be compared to essentially exact calculations of nuclear structure. Future measurements are planned with 6 GeV beam3 which will significantly increase the amount of data in the scaling region at

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.1.0

-0.8

-0.6

-0.4

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0.0

0.2

0.4

Y* [GeVl Figure 2. Scaling function F ( y * ) for iron from E89-008, after subtracting a model of the inelastic contributions which dominate for y > 0. The solid line is a fit to the measured F ( y * ) for deuterium. The dashed line is the tail of the deuteron fit, scaled up by a factor of six.

large nucleon momenta. This data will significantly improve the data at large IyI and Q 2 , and will include measurement on 3He and 4He. We can then use this to extract information on the momentum distributions in heavy nuclei, and study in more detail the nature of their short range correlations. This work is supported (in part) by the U.S. DOE, Nuclear Physics Division, under contract W-31-109-ENG-38. References

1. G. B. West, Phys. Rep. 18, 263 (1975) ; Y. Kawazoe, G. Takeda and H. Matsuzaki, Prog. Theo. Phys. 54, 1394 (1975). 2. J. Arrington et al., Phys. Rev. Lett. 82, 2056 (1999). 3. Jefferson Lab experiment e02-019, J. Arrington, D. B. Day, B. W. Filippone, A. Lung, spokespersons.

MEDIUM EFFECTS IN A(,??,E‘P) REACTIONS AT HIGH Q2 D. DEBRUYNE AND J. RYCKEBUSCH Ghent University, Proeftuinstraat 86, B-9000 Gent, Belgium E-mail: [email protected]. be Medium dependencies of bound nucleons are studied in a fully relativistic and unfactorized framework for the description of exclusive A(S, e’fi processes. The theoretical framework, which is based on the eikonal approximation, can accommodate both optical potential and Glauber approaches for the treatment of final state interactions. It is discussed how both approaches compare to one another. Calculations for 12C(e,e’p) nuclear transparencies are presented. The issue of measuring the predicted medium modifications for the bound nucleon’s electromagnetic form factors is addressed by presenting 4He(S, e’fi results.

Exclusive A(Z,e’p3 reactions at high Q2 [Q2 >_ 1 ( G ~ V / C )are ~ ] a tool to study several aspects of nuclear and nucleon structure in a region where one expects that both hadronic and partonic degrees-of-freedom may play a role. Amongst the physics issues which can be investigated with electromagnetically induced proton knockout reactions is the short-range structure of nuclei. Here, one wants to find out if there are any hadronic components in the nucleus that carry large momenta, or whether the high momentum components in the nuclear wavefunction are entirely governed by the partonic degrees-of-freedom. Exclusive A(> Ikil. Solving the relevant Dirac

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equation with scalar and vector potentials in this approach, leaves us with a wave function that ressembles a relativistic plane wave,

but for two extra ingredients. First, there is the dynamical enhancement of the lower component through the presence of the scalar (Vs)and vector (Vv) potentials, and, second, there is the extra phase factor zS(g, z). At higher energies the highly inelastic nature of p p and p n collisions makes that a potential based description of FSI effects appears no longer feasible and one can make use of the Glauber approach, which is a multiple-scattering extension of the eikonal approximation. In the Glauber model one assumes that the struck proton undergoes subsequent collisions with the spectator nucleons, and each of these collisions is then treated in the eikonal approximation. One assumes that spectator nucleons are frozen, and that only elastic or mildly inelastic collisions occur. The Glauber wave function can be formally written as

with 8 the Glauber phase shift function. The reader is referred to Refs.lp2 for more details. Within the context of exclusive A(Z, el$ reactions, color transparency stands for the suggestion that at sufficiently high values of Q2 the struck proton may interact in an anomalously weak manner with the spectator nucleons in the target nucleus. The Q2 and A dependence of the nuclear transparency can provide information about the non-hadronic, small-sized components in the nucleon, and is thus a direct measure for the occurence of color transparency. The nuclear transparency basically expresses the likelihood that a nucleon, after absorption of a virtual photon, escapes the nucleus. Results of relativistic calculations for the nuclear transparency in the 12C(e,e'p) reaction are shown in Fig. 1. Neither the data nor the model calculations give any evidence for the predicted onset of color transparency. At high Q2 the nuclear transparency saturates at a value of 50-60 %. A recent re-analysis of the world's 12C(e,e'p) database5 resulted in spectroscopic factors of the order of 50-60% of the sum rule value for Q2 values below 0.8 (GeV/c)2. At higher values of Q2, spectroscopic factors approaching the sum rule value were extracted. It should be stressed, though, that at low Q 2 an analysis based on optical potentials was used, whereas at high Q2 a Glauber method was adopted. In view of the apparent discrepancy

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05 0.6 0.7 0.809 I

3

4

5

6

1

8

Qz [(&V/c)’]

Figure 1. Nuclear transparency for 12C(e,e’p) as a function of Q2. The curves are from relativistic calculations within the optical model eikonal approximation (OMEA) and the relativistic multiple-scattering Glauber approach (RMSGA) with or without short-range correlations (SRC). All calculations use the CC1 current operator in the Coulomb gauge. The displayed curves assume full occupancy of the single-particle levels. The data are from ref^.^,^

between the extracted spectroscopic factors at low and high Q2, one may wonder whether a typical optical potential and Glauber approach actually lead to comparable spectroscopic factors when applied to the same l 2C ( e ,e’p) data set. The summed spectroscopic factors for the s (SlS) and p (5’1,) shell can be deduced from the transparency results of Fig. 1 through the following formula : SIZC z (251, 4$,)/6 N Tezp/Ttheo.From Fig. 1 one observes that at moderate values of Q2 the optical potential calculations and correlated Glauber calculations produce similar nuclear transparencies, and, hence, similar summed spectroscopic factors. From this observation one may conclude that in the kinematical regime where both the Glauber and optical potential approach are plausible descriptions of FSI effects, there is a reasonably smooth transition from the low to the high Q2 regime. The steady rise of the spectroscopic factors as a function of increasing Q2, manifesting itself as an overshoot of the data at low values of Q 2 , can also b e inferred from this figure. Recently, it has been suggested that the electric and magnetic form factors of a bound nucleon may deviate considerably from those of the free nucleon6. Double polarization experiments of the A(Z, e’p3 type provide excellent opportunities to probe these effects. We have compared our model calculations for the 4He(Z,e’p3 double polarization ratio at Q2 M 0.4 (GeV/c)2 with data collected at Mainz. From the results displayed in Fig. 2 it can be seen that

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the inclusion of medium modified form factors has a considerable impact on the double ratio results. Implementing the effect of short-range correlations (SRC) only marginally affects the results. A study of the Q2 dependence of this ratio, performed recently at JLab, confirms these findings’. 4

He(e,e’p) at Q2 = 0.38 (GeV/c)2

.

RMSGA

X

RMSGA + QMC

A

0.81, 0

, , , , 1

2

3

4

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RMSGA + QMC + SRC

, , , , , , ,j 6

7

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9 1 0 1 1 1 2

Theoretical Model Adopted Figure 2. Double polarization ratio for the ‘He(Z, e’p3 reaction. Shown are calculations in the Glauber approach (RMSGA), with and without the effect of medium modification included (QMC), and with or without the inclusion of SRC. Each set of four calculations shows the results for the CC1 current operator, once in the Coulomb gauge, and once in the Weyl gauge, and for the CC2 operator, also in both gauges. Data are from Ref.7

References

1. D. Debruyne and J . Ryckebusch, NPA 699, 65c (2002). 2. D. Debruyne, J . Ryckebusch, S. Janssen and T. Van Cauteren, PLB 527, 62 (2002). 3. T. O’Neill et al., PLB 351,87 (1995). 4. D. Abbott et al., PRL 80, 5072 (1998). 5. L. Lapikas, G. van der Steenhoven, L. Frankfurt, M. Strikman and M. Zhalov, PRC 61, 064325 (2000). 6. A.W. Thomas, contribution to this conference. 7. S. Dieterich et al., PLB 500, 47 (2001). 8. S. Strauch, contribution t o this conference.

STUDY OF NUCLEON SHORT RANGE CORRELATION IN A(E,E') REACTION AT X , > 1 K. EGIYAN, H. BAGDASARIAN, N. DASHYAN Yerevan Physics Institute, 2 Brother Alikhanyon Street, Yerevan 375036, Armenia E-mail: egiyanajereuanl. yerphi. a m

For the CLAS Collaboration The cross section ratios of inclusive electron scattering from the nuclei 4He, 12C, 56Fe and 3He are measured for the first time. It is shown that these ratios as a function of Q2 and zg are scaled in Q2 > 1.4 (GeV/c) and ZB > 1.5 range. This scaling was predicted within Short Range Correlation (SRC) model. The values of these ratios in the scaling region can be used to derive the probabilities of SRC in heavy nuclei. Our analysis demonstrate that for nuclei with A 2 12 these probabilities are 4.5-5.2times larger than in deuterium, while for 4He it is larger by factor of 2.6-3.3only.

High energy inclusive electron scattering off nuclei can be used for investigation of high momentum component of the nuclear wave functions where contribution of short range correlations (SRC) is dominant. To suppress the contribution from the inelastic events one should study the lower energy transfer ( v ) part of the scattered electron spectra, which corresponds to the condi> 1 Furthermore, from kinematic relation of quasielastic e A tion X B = scattering one can evaluate the X B dependence of the magnitude of minimal missing momentum contributing in the reaction at the given values of Q2 (see Fig.1). As it follows from Fig.1 one can identify a value xg(Q2) such that at X B > 2; the missing momenta involved in the reaction exceed the average Fermi momenta (- 250 M e V / c ) characteristic for uncorrelated nucleons in nuclei. Additionally, to remove nucleons from SRC the energy transferred, v, should exceed the missing energy characteristic to SRC (- 250 - 270 M e V ) 2, therefore, v > 300 M e V . If these conditions are met one can expect that inclusive (e,e') reactions off nuclei will proceed through the interaction of the incoming electron with the correlated nucleon in SRC. In Ref. it was shown that the dominance of SRC contribution in the above mentioned kinematic region can be checked if to study the normalized" ratios of A(e,e')X cross

&

'.

'

~

OHereafter, by the ratio of the cross sections we will mean the ratios normalized by A. We will separately discuss effects due to uep > men which are important for 3He due to Z not equal to N.

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sections defined as follows:

Here ffe.41 and CleA1 are the inclusive cross sections of the electron scattering from nuclei with atomic numbers A1 and A2, respectively. For practical purposes it was chosen A1 > Aa, with A2 = 2,3. The basic prediction of

A0 0.8

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02

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Figure 1. The minimum d u e of nucleon Fermi momentum as a function of zg . a) For twonucleon system at several Q2 in (GeV/c)2;b) - For different nuclei at Q2 = 2.0 (GeV/c)2. Horizontal lines indicate the Fermi momentum characteristic to uncorrelated motion of nucleons in nuclei ( w 300 MeV/c).

SRC model for R ( Q 2 , z g )is that they are expected to scale as a function

of 28 > 2; and Q2 > 1. Previously, the predictions for scaling have been checked in using the existing SLAC data for deuterium (as a light nucleus) and heavier nuclei and it was indicated the existence of the scaIing regime at Q2 > 1 and x 2 1.5. However, the data are not purely experimental, since they include the theoretical calculations, and the ratios may have 33475

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been affected by the fitting and interpolation procedures used. In this talk we present the experimental studies of the cross section ratios of inclusive electron scattering from the 4 H e 12C 56Fe and 3 H e measured for first time.

m3

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Figure 2. SRC Model predictions for the normalized inclusive cross section ratio as a function of X B for several values of Q2 (in (GeV/c)2). a) - 12C to 3He, b) - 56Fe to 3He.

We study the ratio:

Using the data from

it is possible to calculate the predictions for the ratio

R i e 3 defined in Eq. (2). The results of these calculations are shown in Fig.2 for 12C and 56Fe nuclei. The primary goal of this work is to check the existence of the scaling for the ratio defined in Eq. (2).

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The measurement was performed with the CLAS detector in Hall B at Thomas Jefferson Accelerator Facility. The 2.261 GeV and 4.461 GeV electron beam was incident on a cylindrical 1cm diameter 4 cm length target cell filled by the liquid 3 H e or 4 H e and/or 1x1 cm2 plates of 12C(lmm thick) or 5sFe (0.15 mm thick) solid targets. The scattered electron was detected in wide kinematic range. The data were binned in X B and Q2 and the cross sections

g 4 3.5

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Figure 3. The ratios Eq. (2) for 12C. a)- circles - Q2= 0 . 7 5 f 0 . 1 ; squares - Q2 = 1 . 0 f 0 . 1 ; triangles - Q2 = 1.20 f 0.1 and at incidant energy 2.261 GeV. b) - circles - Q2 = 1.5 f 0.1 with incident energy 2.261 GeV; squares - Q2 = 1 . 7 f 0.3; triangles - Q2 = 2.30 f 0.3,both with incident energy 4.461 GeV.

were calculated as a function on these variables. We study the ratios of obtained cross section in the 1 < X B < 2 range for H e , 12Cand 56 Fe targets. In Fig.3a,b these ratios are shown for 12Ctarget at several values of Q2. The similar data were obtained for 56Feand 4 H e targets. Based on these data one can draw the following important conclusions: (i) there is a clear Q2 evolution of &),3(XB) shape - at low (< 1.3 (GeV/c)2)Q2, the R$,,(xB) ratios increase with X B in all 1 < X B < 2 range (see Fig.Sa),

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(ii) as Q2 increases the saturation (scaling) effect is observed (see Fig.3b), (iii) these behaviors do not depend on neither the target-nucleus nor the incident energy. (iiii)there is a good agreement in shapes between the theoretical ) calculations based on pair SRC model and the experimental R i e 3 ( z ~(see Fig.2). Based on the obtained data on R i e 3 ( z 8 ) within , the SRC model of

" ,2.8

1.5 (GeV/c)2for each nuclei. ) over this Q2region are shown in Figda The ratios R i e 3 ( z ~averaged with the blue rectangles. Using these values we then evaluate the ratios r i e 3 ( z B ) = a2 A which are shown FigAa by the red circles. One can con-

=

580

clude that the probabilities of pair correlation per nucleon are approximately 2.2-2.5 times larger in “C and 56Fe than in 3 H e , while for 4 H e this ratio is approximately 1.5-1.6 only. The absolute values of a 2 , ~ can be extracted if one knows the a 2 , ~ ~ The 3 . only experimental value of a 2 , ~ is ~ 3 known to be l . 7 f 0.3 from Ref. On the other hand this parameter can be evaluated using the realistic wave functions of the deuteron and 3 H e nucleus. These calculations yield, a 2 , ~ = ~ 32 f 0.1. The our extracted values of a 2 , as ~ well as results from are shown in Fig.4b which demonstrate that for A < 12 nuclei there is a sizeble Adependence of a 2 , parameter, ~ while at A 12 this dependence is very weak. The absolute values of a 2 , parameters ~ for A 12 are in the interval of 4.55.3, while for 4 H e it is in 2.7-3.2 interval. Within the error bars our data are consistent with the results of previous SLAC ( e , e / )data analysis in Ref.

’.

>

>

’.

References

1. L.L. Frankfurt, M.I. Strikman, D.B. Day, M.M. Sargsian, Phys. Rev. C48, 2461, (1993). 2. L.L. Frankfurt and M.I. Strikman, Pys. Rep., 76, 215 (1981); ibd 160, 235 (1988). 3. W.P. Schutz et al., Phys.Rev.Lett., 38, 8259 (1977). 4. S. Rock et al., Phys.Rev.Lett., 49, 1139 (1982). 5. R.G. Arnold et al., Phys.Rev.Lett., 61, 806 (1988). 6. D. Day et al., Phys. Rev. Lett., 59, 427 (1979). B 343, 47 (1995).

N N CORRELATIONS MEASURED IN 3He(e,e’pp)n R. A. NIYAZOV, L. B. WEINSTEIN FOR THE CLAS COLLABORATION Physics Dept., Old Dominion University, Norfolk,

VA 23529, USA E-mail: [email protected]. edu [email protected]. edu We have measured the 3He(e,e’pp)n reaction at 2.2 and 4.4 GeV over a wide kinematic range. The kinetic energy distribution for ’fast’ nucleons ( p > 250 MeV/c) peaks where two nucleons each have 20% or less and the third or ‘leading’ nucleon carries most of the transferred energy. These fast nucleon pairs (both pp and pn) are back-to-back and carry very little momentum along f, indicating that they are spectators. Experimental and theoretical evidence indicates that we might have measured N N correlations in 3He(e,e’pp)n by striking the third nucleon and detecting the spectator correlated pair.

1

Introduction

One signature of correlations is finding two nucleons with large relative momentum and small total momentum in the initial state. Unfortunately, the effects of N N correlations are frequently obscured by the effects of two body currents, such as meson exchange currents (MEC) and isobar configurations (IC) l. In order to disentangle these competing effects, a series of comprehensive measurements are needed. In order to provide this, we measured electron scattering from nuclei, A(e,e’X), using the Jefferson Lab CLAS (CEBAF Large Acceptance Spectrometer), a 47r magnetic spectrometer. These measurements were part of the ’EZ’ run group that took data in Spring 1999. This paper will concentrate on the results from the 3He(e,e’pp)n reaction which exhibit a signature for N N correlations. 2

The 3He(e,e’pp)nMeasurements

We studied electron induced two proton knockout reactions from 3He using the CLAS detector and made a cut on the missing mass M, = to select 3He(e,e’pp)n events. Figure 1 shows the electron acceptance and undetected neutron missing mass resolution for Ebeam= 2.2 GeV. The threshold of the CLAS is approximately 0.25 GeV/c for protons.

581

582 Figure 1. a) Q2 vs w for 3He(e,e'pp)n events. b) Missing mass for 3He(e,e'pp) events. We cut on the peak at M z = M , to isolate (e,e'pp)n events.

0

0.5

1

2

1.5

0.5

3

1.1

Missing Mass (GeVlc') b)

a)

0

1

0.9

Omega (GeV)

1

Iel

-1

-0.5

0

0.5

1

cowp")

b)

Figure 2. a) Kinetic energy balance distribution for 2.2 GeV electrons with cut p , > 250 MeV/c. The boxes correspond to cuts used in later figures. b) Opening angle of the fast p n pairs corresponding to the cut in the upper left and lower right corners of a). The shaded histogram shows the fireball phase space distribution (with arbitrary normalization).

In order to understand the energy sharing in the reaction, we plotted the kinetic energy of the first proton divided by the energy transfer ( T p l / w )versus that of the second proton (Tp2/w)for each event. We eliminated events with p , < 0.25 GeV/c, which are mostly dominated by hard final state rescattering, and focussed on events where all three nucleons are 'active', i.e p~ > 0.25 GeV/c (see Figure 2a). In this case we see three peaks at the three corners of the plot, corresponding to events where two nucleons each have less than 20% of the energy transfer and the third 'leading' nucleon has the remainder. We call the two nucleons 'fast' because p >> p f e r m i . Then we looked at the opening angle of the two fast nucleons. Figure 2b shows fast pn pairs with a leading proton. Note the large peak at 180 degrees (cosOpn x -1). The peak is not due to the cuts, since we do not see it in a fire ball phase space simulation assuming three body absorption of the virtual photon and phase space decay. It is also not due to the CLAS acceptance since we see it both for leading protons and leading neutrons. This back-to-back peak is a strong indication of correlated N N pairs.

583 Figure-3. a) Total momentum of the fast pn pair at 2.2 GeV. b) The same for pair relative momentum.

2 F

m N 2 m, e 1215 MeV where the inelastic pion production process, not included in this work, starts. The missing higher order range terms in the S11 phase are expected to be induced by additional inelastic channels or by the nucleon resonances N(1520) and N(1650). In the right panel of Fig. 1 we confront the s- and p-wave Kf-nucleon phase shifts with the most recent analyses by Hyslop et a1.8 and Hashimoto’. The phase shifts are reasonably close to these single energy phase shifts except the Po3 phase for which we obtain much smaller strength. Note however, that at higher energies the single energy phase shifts of Hashimoto’ are reached smoothly. In Fig. 2 we compare the empirical ratios A1/Ao and A2/Ao of the elastic and inelastic K - p scattering with the results of the X-BS(3) approach. For plab < 300 MeV the empirical ratios with n 2 3 are compatible with zero within their given errors. A large A1/Ao ratio is found only in the K - p + 7roA channel demonstrating the importance of p-wave effects in the isospin one channel. The dashed lines of Fig. 2, which are obtained when switching off d-wave contributions, confirm the importance of the A( 1520) resonance for the angular distributions in the isospin zero channel. The latter resonance is included in the X-BS(3) approach as part of a baryon nonet resonance field. For details we refer to’.

+

References

1. M.F.M. Lutz and E.E. Kolomeitsev, Nucl. Phys. A 700,193 (2002). 2. N. Kaiser, P.B. Siegel, W. Weise, Nucl. Phys. A 594,325 (1995). 3. E. Oset, A. Ramos, Nucl. Phys. A 635,99 (1998). 4. G.F. Chew, S. Mandelstam, Phys. Rev. 119,467 (1960). 5. U.-G. MeiDner, J.A. Oller, Nucl. Phys. A A 673,311 (2000). 6. S. Kondratyuk, A.D. Lahiff, H.W Fearing, Phys. Lett. B 521,204 (2001). 7. R.A. Arndt et al., Phys. Rev. C 52,2120 (1995). 8. J.S. Hyslop et al., Phys. Rev. C 46,961 (1992). 9. K. Hashimoto, Phys. Rev. C 29, 1377 (1984). 10. T.S. Mast et al., Phys. Rev. D 11,3078 (1975); R.O. Bangerter et al., Phys. Rev. D 23, 1484 (1981).

MEASUREMENT OF THE WEAK PION-NUCLEON COUPLING CONSTANT, H:, FROM BACKWARD PION PHOTO-PRODUCTION NEAR THRESHOLD ON THE PROTON R. SULEIMAN Jefferson Lab, MS 12H, 12000 Jefferson Ave, Newport News VA 23606, USA E-mail: [email protected]

The longest range weak pion-nucleon coupling constant, h:, is important for nuclear parity violation. However, after considerable effort in the past two decades, its value is still poorly known largely due to many-body theoretical uncertainties. Prospects of a new measurement of h: in a theoretically clean process are presented. A measurement of the parity-violating asymmetry in pion photoproduction off the proton is related to h: in a low-energy theorem for the photon polarization asymmetry at threshold in the chiral limit. At present two completed experiments - photon circular polarization for 18F and the anapole moment of 133Cs- have been interpreted to give very different values of h i . This experiment will be the first attempt to measure h: in the single nucleon system. A reliable measurement of h i provides a crucial test of the meson-exchange picture of the weak N N interaction. Such a test of the meson-exchange picture will shed light on low energy QCD.

1

Introduction

The nucleon-nucleon ( N N ) weak interaction is the last sector of the weak interaction where the main aspects of the electroweak theory have not been verified. In the presence of the nuclear interaction, the weak N N interaction can be isolated via parity violation. The most comprehensive theoretical treatment t o date t o describe the weak N N interaction is given in a review by Desplanques, Donoghue, and Holstein (DDH) '. Their best guess value of the weak pion-nucleon coupling constant is h i = 4.6 x The determination of hk from experimental measurements in nuclei are discussed in Reference '. There are substantial uncertainties in interpreting most experiments in nuclei because one can not make reliable calculations of the amplitudes of the weak meson-nucleon exchange potential operators. This measurement is free from nuclear structure uncertainties and is a clean measurement of hi.

607

608

---E,

= 160

MeV

E - = 180 MeV

-E, =

230 MeV

Y

0

30

60

90

120

150

180

elLab [degl Figure 1. Asymmetry of the differential cross section for T p pion Lab angle (h; = 4.6 x lo-').

2

+ nn+

as a function of the

Pion Photoproduction at Threshold

The weak interaction induced parity-violating asymmetry in low energy pion photoproduction was calculated by Chen and Ji '. They found that the photon helicity asymmetry:

A T

d o ( & = +1) - d o ( & = -1) = +I) d a ( & = -1)

- d+,

+

(1)

at the first non-vanishing order (NLO) in heavy-baryon chiral perturbation theory (HBxPT) at threshold is:

where fr is the pion decay constant and gA is the neutron decay constant. There is an extended threshold region in which the effective theory description remains effective and, at the same time, the cross section is appreciable. This region is between 180 and 230 MeV in laboratory photon energy. The higherorder corrections are expected to be O ( E T / M ~ )20%.

-

609 Table 1. Experimental conditions for the proposed measurement. Beam Energy Beam Current Beam Polarization

230 MeV 400 pA 80%

Radiator Thickness Photon Energy ( E , ) f (N7INe) Photon Polarization

3% r.l. Cu (0.043 cm) 230-180 MeV 0.006 75%

Target Luminosity (Is) Average Cross Section % ( y p Solid Angle Acceptance

80 cm LH2 0.5 x lo3' cm-2 sec-' 5x cm2/sr 1.0 sr

4

Experimental Asymmetry ( A )

ma+)

1.7x 1 0 - ~

The asymmetry A,(O") in the differential cross section for T p mr+ as a function of the pion Lab angle is shown in Fig. 1. Note the strong dominance of the photon polarization asymmetry at forward and backward angles in the threshold region. Only at angles near 90" and E-, > 200 MeV does the modification from high partial waves become significant.

3 Experimental Considerations

A polarized electron beam will be used to produce a circularly polarized photons by hitting a radiator. The electron beam will be deflected away through a chicane to a beam dump. The photon beam will be incident on a liquid hydrogen target. A toroidal magnet will bend the backward produced pions to a total absorption plastic scintillator detector. The expected counting rate is approximately 250 MHz. The detector will be out of direct view of the target and will operate in current mode. The experimental conditions are listed in Table 1. 1000 hours of beam time are required for 20% statistical accuracy. A high quality electron beam will be used to produce the photon beam with no amplification of any of the helicity correlated differences in beam parameters (energy, angle, and position). The total systematic uncertainty is anticipated to be smaller than the statistical one.

610 15

10

P

Y

5

k

r 0

-5

Figure 2. The projected error bar from this experiment compared to DDH theoretical estimate and other completed and planned experiments.

4

Summary

The weak pion-nucleon coupling constant will be measured in pion photoproduction to a high level of accuracy in a reasonable beam time. Fig. 2 shows values of h i : (from left to right) DDH theoretical estimate, 18Fexperiments 4 , 133Cs experiment 5 , and expected statistical uncertainty from LANSCE experiment (it will achieve this uncertainty in 9 months of data taking). The last value represents the expected statistical uncertainty from this experiment in 1.5 months of data taking. References

1. B. Desplanques, J. Donoghue, and B.R. Holstein, Ann. Phys. 124, 449 (1980). 2. E.G. Adelberger et al, Ann. Rev. Nucl. Part. Sci. 35, 501 (1985). 3. J.W. Chen and X. Ji, Phys. Rev. Lett. 86, 4239 (2001). 4. S.A. Page et al, Phys. Rev. C 35,1119 (1987). 5. C.S. Wood et al, Science 275, 1759 (1997). 6 . J.D. Bowman (Spokesperson) et al, “Measurement of the Parity-Violating Gamma Asymmetry A, in the Capture of Polarized Cold Neutrons by Para-Hydrogen, n’ p -+ d + y”, Proposal for DOE, 17 April 1998.

+

TO

+ yy TO NLO IN CHPT

JOSE L. GOITY Department of Physics, Hampton University, Hampton, VA 23668, and Thomas Jefferson National Accelerator Facility, Newport News, VA 23606. The x o + yy width is determined to next to leading order in the combined chiral and l/Nc expansions. It is shown that corrections driven by chiral symmetry breaking produce am enhancement of about 4.5% with respect to the width calculated in terms of the chiral-limit amplitude leading to rno+-,-,= 8.10 f 0.08 MeV. This theoretical prediction will be tested via T O Primakoff production by the PRIMEX experiment at Jefferson Lab.

1 Introduction

In QCD there are predictions whose character is fundamental: one of them is the 7ro -+ yy decay width. In the limit of exact s U ~ ( 2x) s U ~ ( 2chiral ) symmetry, i.e. when the u- and d-quark masses vanish, the decay amplitude is predicted by the chiral anomaly induced by the EM interaction on the axial current associated with 7ro Goldstone mode. This amplitude results in the width rnO+-,? = = 7.73 eV. Although this prediction agrees well with the world averaged experimental value, this has a generous error of about 7% that prevents the observation of deviations from the chiral limit prediction resulting from explicit chiral symmetry breaking by the quark masses. This situation will change with the PRIMEX experiment at Jefferson Lab that aims at a more precise measurement in the 1 to 2% range '. This talk reports on the theoretical prediction for such deviations including next to leading order corrections in the low energy expansion, and shows that indeed these deviations would be observable in that experiment. As shown in 2 , the non-vanishing u-and d-quark masses induce corrections to the 7ro -+ yy amplitude that can be predicted in the framework outlined below. These corrections are of two types: i) Mixing corrections induced by isospin breaking implying that the physical 7ro is not a pure isospin eigenstate having a projection on the pure U ( 3 ) states associated with the 77 and the 7'. They are controlled by the ratios (mu- md)/ms and N,(m, - m d ) / A , (A, is the chiral expansion scale, and N , the number of colors). ii) corrections controlled by the ratio m / A x , where 7fi = (mu+ m d ) / 2 . Since the first type of corrections turn out to be dominant, it is natural to work in a framework where the q and rf are included as active degrees of freedom. Such a framework is indeed available and consists in chiral pertur-

($-)2(q)3

61 1

612

bation theory (ChPT) with three light flavors supplemented with the l/Nc e x p a n s i ~ n ~In? this ~ . framework, the corrections i) start at leading order (LO), while the corrections ii) are of next-to-leading order (NLO). In this talk the calculation of the rate rrro+y7 including NLO corrections is outlined and the results discussed. 2

The decay amplitude

The two-photon decay amplitudes of the self-conjugate pseudoscalars are obtained from the Ward identity satisfied by the associated axial currents:

where M , is the quark mass matrix, eQ is the electric charge operator, FF = ~ E , , , , ~ ~ Fand ~ ” similarly F ~ ~ , GG = Considering the matrix elements of Eqn.(l) between the vacuum and two-photon states and selecting the pole terms generated by the physical K O , y and y’, it is possible to extract the twophoton transition amplitudes for these states. At NLO these matrix elements require a NLO calculation of the masses and the decay constants, as well as contributions due to excited states and continuum that are of type ii) and thus of NLO. The NLO masses and decay constants are calculated in the mentioned framework of ChPT and l/Nc expansion, while the contributions due to excited states are represented by an U ( p 6 )unnatural parity Lagrangian, the O ( p 6 ) Wess-Zumino (WZ) term. With the low energy counting in which l/Nc is a quantity of order p 2 , the NLO evaluation of masses and decay constants requires the chiral Lagrangian up t o order p4, which with standard notation reads: c = p )+ c(4)+ . . .

+ x t u ) - 21 ~ ; 7 T ; c(4) = Ls(DpUtDpU(xtU+ U t x ) )+ Lg(xUtxUt + h . ~ . ) + $A D , ~ T ~ D , T-~-iFoAz - - ~ T ~ ( x-ux ~ u ) , c(2)=

~F~(D,uD+ ~ u-1F ~ : ( X)U ~ 4

4

2 6

(2)

where only terms relevant for masses and decay constants are kept. Here U is the U (3 )matrix parametrized by the pseudoscalar nonet, where ~ T , Jis the singlet member whose mass in the chiral limit is MO when l/Nc corrections are disregarded. Note that terms such as the L4 and others are not included because they are O(p4 x l/Nc) = O(p6),and thus of NNLO. The terms A1,z represent l/Nc corrections. Since one-loop corrections with L(’)are of order O(p4 x l/Nc) O(p6),they ought to be neglected as well. The masses and decay constants are then extracted by calculating the two-point function of axial currents, and are given by:

613 Fo

where L58

+4L5Bo 3Fo ( m u+ md + 4ms); FOO= Fo(l+ -) + 8L5Bo (mu+ md + ms); 2 3Fo A1

2L8

- L5 and p

+ 2A2 - 8L5-L). FO MZ

-A1

The Oh6)WZ term relevant here is determined in terms of a single low energy constant t l , and reads:

L$Q7 = -i7ratl(X-Q2)FF;

u=

fi,X -

=u t p t

- uxtu.

(4)

The low energy constants are determined by fitting to the masses in the nonet, to F,+ and F K + , and to the two-photon decay widths of the q and q'. Corrections to Dashen's theorem are included for the extraction of isospin breaking by the quark masses. Unfortunately, tl cannot be determined from the fit and its estimate via QCD sum rules is used: t l _N -+(F," +), where m y _N m p . The term 7%

proportional to

T

+Md

involving the excited pion pole is small

and can be neglected.

3 Results and conclusions The two-photon amplitudes of the physical states for N, = 3 finally reads:

(77I R I T = ~ ~-)i o (-CaFG1 1 47r

+ ~ Bo - t i B a e ( { ~ " , M q } Q 2 )(77 ) I F F I O), FO

m,

(5)

where 7rg = 7ro, 7rg = q, and q=j = q', and c3 = 1 , c8 = I / & and CO= 0 is the mixing matrix determined from the mass matrix in the 7ro-71-77' subspace. The decay constant matrix in this subspace is defined by: ( r a , p I A; I 0) = -ippFaa,

614 where 8, = eSbFba,with Fat, the decay constant matrix in the basis of pure u(3) states as given in Eqn.(S). At LO only the first term in Eqn.(5) is left with Fa, = F&,, where 0 is determined from the LO mass formulas. At LO the 7ro width is enhanced as a result of the mixing by 4.5% from 7.73 to 8.08 eV, an effect first noted in Ref. '. The mixings with the 77 and 77' give similar contributions that add up; this is the reason why an analysis where the 77' is explicitly included is important for understanding the effect. The NLO result for the width is almost identical to the LO one: 8.10 eV. This stability is however non-trivial. The mixing matrix 0 is affected in the entries involving the 7ro by corrections of the order of 20%, but at the same time the decay constant matrix in the U(3) basis receives corrections that tend to undo those leaving the relevant decay constant matrix elements FToa almost unchanged. In the abscense of the O@) WZ term these NLO corrections amount to a 0.5% further increase in the width, which is then largely compensated by the estimated cointribution of the said WZ term. There are several sources of theoretical errors. The most important one is the uncertainty in the ratio R = ms/(md - m,) that largely determines the corrections due to mixing; this ratio is determined from MK0 - M K + after removing the EM contribution determined using the corrected Dashen theorem; this leads to R = 3 7 f 5 and an uncertainty in the T O width of 0.6%. Other uncertainties such as EM corrections and NNLO corrections are estimated to be in the 0.2-0.3% range. In all, it is expected that the overall uncertainty is below 1%. In conclusion, the theoretical prediction rTo+rr= 8.10 eV obtained in the framework of ChPT@l/N, indicates a substantial enhancement of about 4.5% over the prediction based on the chiral limit decay amplitude. The magnitude of this enhancement is such that it should be observed in the forthcoming 7ro lifetime measurement by the PRIMEX collaboration at Jefferson Lab where a measurement with a precision better that 2% is expected.

Acknowledgments The work reported here was done in collaboration with A. M. Bernstein and B. R. Holstein, and was in part supported by NSF grant PHY-9733343 and by DOE contract DE-AC05-84ER40150.

References 1. A. Gasparian, these proceedings. 2. J. L. Goity, A. M. Bernstein and B. R. Holstein, JLAB-THY-02-15. 3. P. Herrera-Siklbdy, J. I. Latorre, P. Pascual and J . Taron, Nucl. Phys. B497 (1997) 345, and Phys. Lett. B419 (1998) 326. 4. R. Kaiser and H. Leutwyler, Eur. Phys. J. C17 (2000) 623. 5. B. Moussallam, Phys. Rev. D51 (1995) 4939. 6. Fayyazuddin and Riazuddin, Phys. Rev. D37 (1988) 149.

THE DEPENDENCE OF THE "EXPERIMENTAL" PION NUCLEON SIGMA TERM ON HIGHER PARTIAL WAVES J.STAHOV Abilene Christian University, Abilene, T X , 79699, U S A E-mail: stahov@physics. acu. edu and Unzversity Tuzla, 35000 Tuzla, Bosnaa and Herzegovina A dependence of the value of the pion-nucleon sigma term on higher partial waves is discussed. Two recent predictions of a high value of the sigma term are scrutinized. It has been concluded that tha main reason for obtaining high values of the sigma term are input D waves that are not consistent with analyticity.

1

Introduction

The value of the 7rN sigma term C is given in terms of the D+amplitude (bar indicates that the pseudovector Born term is subtracted) at the Chang-Dashen (CD) point Y = 0, t = 2m:: C = F,2D+(V = 0, t = 2m,), 2 where F,=92.4 MeV is the pion decay constant. For details concerning the 7rN kinematics we refer to reference'. Generally, there are two kinds of methods used to calculate the D+amplitude at the CD point. The first method uses dispersion relations to calculate 2m:) directly. The second method determines the coefficients in the subthreshold expansion of the D+ amplitude:

o+(O,

D+(O,2m2,) = (c7,:o+d&t+Z$2t2+..); C = (c7,~o+Z~'t-t~~~t2+..)F,2 3 CD+AR, where C D denotes contributions from the first two terms, and AR is so a called curvature term that includes contributions of quadratic and higher terms. Obtained values for C range from 60 M e V to 93 MeV. It is of interest to understand which partial waves give important contributions to D+ in each of the above mentioned methods. It is clear that the leading contributions come from the input S and P waves, but earlier evaluations(see reference' and references therein) show that contributions from D and higher partial waves must not be neglected. 2

The role of the higher partial waves

In order to demonstrate the importance of the higher partial waves in determination of the C term, let's briefly describe two methods, that have produced

615

616

dramatically different results in the past few years. Gasser, Leutwyler, Locher, and Sainio(GLLS)2, proposed a method to improve results for Co previously derived from the KH80 solution by taking into account newer, mutually consistent meson factory data below pion lab. momentum k~ = 185 MeV/c. The method is based on six forward dispersion relations for the invariant amplitudes D + , B’, E* e &D’. D waves and higher partial waves are needed as a part of the input below a cutoff momentum ko. Above ko, results from one of the existing PW solutions are used. As a result, GLLS machinery predicts coefficients &o and in the subthreshold expansion. The curvature term was determined using another method3. Several further updates were made by Sainio. In reference4 a value C = 62 MeV was reported. Higher partial waves below cutoff momentum ko were taken from Ka85 solution’. It was pointed out that “results are rather insensitive to the choice of PW solution above the cutoff momentum”. The most recent update w a given in reference6. Results from SpOO solution7, including D waves below ko, were used. Obtained value, C = 93 MeV, is more than 50% higher than previously reported values. One concludes that GLLS machinery is sensitive to the input for D waves and higher partial waves below the cutoff momentum. Starting from the fixed-t dispersion relations for t = 2m:, Olsson’ derived a sum rule in which the value of the Df amplitude at the CD point is expressed in terms of the S, P, D-and higher partial waves threshold parameters. Using Koch’s values for the D-and higher partial wave scattering lengths, Olsson obtained value C = (71 f 9)MeV. Using D-and higher partial waves scattering lengths ,from VPI/GW solution SrnO17, Olsson and Kaufmanng recently obtained significantly higher values ranging from 80 MeV to 88 MeV. Common to both of these high evaluations of the sigma term was the use of the higher partial waves at low energy from the latest VPI/GW solutions. It is important to point out that below the GLLS cutoff momentum ko = 185 MeV/c reliable values for D and higher partial waves can not be obtained from experimental data only. One has to start from first principle in 7rN physics-Mandelstam analyticity and the analytic structure of the 7rN partial waves. Consistency of a given partial wave with analyticity can be tested using one of the methods developed in the past (see referencelo end references therein). In the hyperbolic partial wave relations (HPWR) a given s-channel partial wave is expressed in terms of other s-channel partial waves and the t-channel partial waves, multiplied by corresponding s-channel and t-channel kernels. Kernels, that are explicitly known, reproduce the analytic structure of the T N partial waves. In addition, there is also a contribution from nucleon exchange term that is explicitly known as well. The method is superior compared to

617

_"

0

0.1

0.2

Figure 1. Comparison of F+ :

0.3

0.4

0.5

0.6

form HPWR to input from SpOO

other methods when predicting higher partial waves (D waves and higher) in the low energy region ( k 5 500 MeV/c). In that case, there are two leading contributions-the nucleon exchange and the t-channel contribution. Due to behavior of the t-channel kernels, contributions from higher values of t are strongly suppressed, so that input available today makes it possible to obtain reliable predictions for the higher T N partial waves. For example, the main contribution to the isospin even combinations of D waves, FZ*, comes from the region t< 25m;. Recent calculation" shows that our input from the tchannel in that kinematical region is fairly well known. Results from HPWR for isospin even combinations of reduced partial waves ( F L = qZ/q1+' , see ref.') are shown in Fig.1 and Fig.2. It is evident that D waves from VPI/GW solution SpOO are not consistent with analyticity at low energies. For instance, the isospin even combination F$+ (shown in Fig.1) has the wrong sign.

3

Conclusions

D waves in the VPI/GW SpOO partial wave solution are not consistent with analyticity in the low energy region and are evidently wrong. Methods sensitive to the input D waves produce high values of the pion nucleon sigma term because of the low energy D waves from VPI/GW solutions. A high "experimental value" of the sigma term could be accepted as reliable only if partial waves from the input partial wave solution are consistent with analyticity.

618

loo 80

khan

+

0

0.1

0.2

0.3

0.4

0.5

0.6

Figure 2. Comparison of F$- from HPWR to input from SpOO

I wish to thank Prof. G. Hohler for his continuous support and valuable discussions. This work was supported by DOE project DE-FGO3-94ER40860 References

1. G. Hohler, Landolt-Bornstein, Vol. I/9b2, Pion-nucleon Scattering, Springer 1983. 2. J. Gasser, H. Leutwyler, M. Locher, and M.E. Sainio, Phys. Lett. B213, 85,(1988). 3. J. Gasser, H. Leutwyler, and M.E. Sainio, Phys. Lett. B253, 252(1991). 4. M.E. Sainio, 7rN Newsletter 13, 144(1997). 5. R. Koch, Z. Phys. C 29, 597(1985). 6. M.E. Sainio, Proc. from the Inst. for Nuclear Theory, Vol.l1,346, A.M. Bernstein, J.L. Goity, Ulf-G. Meifher, Editors, World Scientific 2000. 7. SAID 7rN database, http://gwdac.phys.gwu.edu. 8. M.G. Olsson, Phys. Lett. B428, 50 (2000). 9. M.G. Olsson, W.B. Kaufmann, will be published in 7rN Newsletter 16. 10. J. Stahov, will be published in 7rN Newsletter 16. 11. J. Stahov, In preparation.

FIRST BEAM-TARGET DOUBLE-POLARIZATION MEASUREMENTS USING POLARIZED HD AT LEGS A. LEHMANN', K. ARDASHEV', C. BADE', M. BLECHER3, C. CACACE4, A. CARACAPPA4, A. CICHOCKI', C. COMMEAUX', I. DANCHEV7, A. D'ANGELO', A. D'ANGELO', R. DEININGER', J.P. DIDELEZ', R. DI SALVO', C. GIBSON', K. HICKS', S. HOBLIT4, A. HONIG', T. KAGEYA3, M. KHANDAKER", O.C. KISTNER4, A. KUCZEWSK14, F. LINCOLN4, M. LOWRY4, M. LUCAS2, J. MAHON', H. MEYER3, L. MICEL14, D. MORICCIANNI', B. NORUM', B.M. PRJ3EDOM7, T. SAITOH3, A.M. SANDORF14, C. SCHAEdF', C. THORN4, K. WANG5, X. WE14, AND C.S. WHISNANT'. (THE LEGS SPIN COLLABORATION) 'James Madison U.'Ohio U., Virginia Tech., 4Brookhaven National Lab., U. Virginia, U. de' Paris-Sud (Orsay), U. of South Carolina, U. d i Roma 11 and INFN-Sezione di Roma, 'Syracuse U., lo Norfolk St. U

'

'

'

A new polarized target using HD in the solid phase has been developed for studies of the nucleon spin structure at Q 2 = 0 using pion photo-production. In combination with the high quality LEGS photon beam and a large solid angle spectrometer this target allows practically background-free measurements on the proton and on the neutron. The first beam-target double-polarizationdata taken with this target are reported here.

1

Introduction

With the development of the Strongly Polarized Hydrogen deuteride ICE target (SPHICE), LEGS (the Laser Electron Gamma Source) has started a program of double-polarization measurements. This unique target is complemented by the high quality polarized Compton backscattered photon beam at LEGS and the large acceptance Spin ASYmmetry (SASY) detector system built for these experiments. With the combination of SPHICE and SASY at LEGS, we are beginning a detailed study of pion photo-production and nucleon spin structure. The goal of these experiments is the measurement of the Gerasimov-DrellHeard (GDH) and the forward spin polarizability2 sum rules on the proton and on the neutron, from pion threshold to 470 MeV. The dominant contributions to these sum rules are contained in this energy region. In addition, these measurements will allow the extraction of double-polarization asymmetries, putting significantly stricter constraints on the multipole amplitudes of pion photo-production.

619

620

2

Experiment

2.1 LEGS Photon Beam

The photon beam at LEGS is produced by Compton backscattering of laser light from the 2.8 GeV electron beam at the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory. This electron energy, in combination with a new frequency quadrupled laser and a conventional ArIon laser, permits the production of tagged photons from pion threshold up to 470 MeV. The polarization of the photon beam is determined by the polarization of the incoming laser beam and known to an accuracy of better than 1%. This also allows a “random” flipping through various polarization states, linear and circular ones, by changing the polarization of the laser beam. A complete specification of the laser polarization is obtained by the measurement of the Stokes vector, Sl = (01, Ul, K}. The three components of this vector are Q 1 , the intensity of a 0’ polarized beam, Ul,the intensity of the beam polarized at +45”, and K , the intensity of a right circularly polarized beam. With the known polarization transfer functions, Pli,,,, (E,) or Pcircz,lar (E,), Sl can be transformed into the photon beam Stokes vector, S, ( E T )= {Qr (E,) , U, (E-,),V, (E,)}. The photon polarization is typically 270% throughout the tagging range.

2.2 Strongly Polarized Hydrogen deuteride ICE Target (SPHICE) SPHICE represents a new technology using molecular HD in the solid state3. These targets are very pure, with only 2 protons and 1 neutron per molecule. The sole background reactions stem from the ~ 2 0 % (by weight) of aluminum wires which are needed for cooling purposes. SPHICE is polarized in a low temperature (15-20 mK) and high field (1517 T) environment. The spin-lattice relaxation time TIof HD is long, but by adding a small concentration of ortho-H2 to the HD gas, the H (and D ) in HD can be polarized via spin-spin coupling4. Eventually, with a time constant of a few days, ortho-Hz decays into the magnetically inert para-Hz, and after typically ~ 4 days 0 the spins of HD are “frozen in”. The target used for the experiment reported here was polarized at ~ 1 8 mK and 15 T for 40 days. The TImeasured in-beam (1.25 K/0.65 T) was 13 days for l? and 36 days for 8 . The initial polarization obtained for hydrogen was 71%. However, due to numerous tests and manipulations done on this first target, the hydrogen polarization was 30 f3% when in-beam. This large drop in polarization is the result of, among other things, the equivalent of

621

five transfers of the target between the dilution refrigerator and the in-beam cryostat (IBC), and a detailed mapping of the relaxation time as a function of temperature and field. 2.3 Spin-ASYmrnety Array (SASY)

The Spin-Asymmetry detector array, SASY, determines angle, energy, and particle identity for all reactions induced by photons on hydrogen and deuterium over the entire LEGS energy range. In this way, a simultaneous measurement of the four pion photo-production channels n+n , n - p nop , and ,On is possible. The major detector subsystems are: the crystal box (an array of 432 NaI(T1) crystals), and a forward wall of plastic scintillator :.( 30% neutron efficiency) and Pb-Glass Cerenkov counters. Atomic events are rejected by a gas Cerenkov counter at 0" and an Aerogel detector covering angles out to 30". The space between the IBC and the crystal box is filled with a plastic scintillator, azimuthally segmented in 32 sections, extending the neutron coverage to 90". The pion solid angle coverage of SASY is about 3n.

3

Results

With the specifications of the photon polarization, the most general expression for the cross section on a longitudinally polarized target can be written as

where C (0; E,) is the 0"/90" beam polarization asymmetry on an unpolarized target, G (0; E,) is the f 4 5 " beam polarization asymmetry with longitudinal target polarization, E (0;E,) is the helicity cross section asymmetry, and P, is the longitudinal target polarization. To disentangle these asymmetries from data obtained with beam polarizations less than 100%requires measurement with four linear (OD, go", k45")as well as left and right circular polarizations. This is readily done at LEGS by randomly cycling the laser polarization through all six states. Data collected in this way with a longitudinally polarized target permits the extraction of and E (0; E,) simultaneously. (0; E,), C (0; E,), G (0;

622

With the help of the Eq. (1) asymmetries can be constructed from the beam polarization states Oo/900 linear, f45" linear, and left/right circular. The results are plotted in Figure 1, dependent on the pion azimuthal angle 4. The solid lines are the calculated distributions fitted simultaneously to the data in the three panels, with C,E , and G as the only free parameters.

0

:*

-0.5

+

Figure 1. Inclusive 7 G D + ?yo azimuthal angle dependence of the three asymmetries constructed from the data. The bottom panel shows the Oo/900beam polarization asymmetry, the center panel shows the asymmetry for f45' linear polarization and the top panel contains the left/right circular polarization asymmetry. The curves are simultaneous fits to the data.

As an example, in Figure 2 the results of these fits are shown for the inclusive pion photo-production reactions 9 + f i D + 7 ~ ' and 7 f i D + rTf as a function of the polar angle at E-, = 317 MeV. Both reaction channels were taken in the same data run. Note the quality of the results after a data taking period of only 3.5 days. These are the first simultaneous measurements of the double-polarization observables E and G.

+

623

Figure 2. Pion polar angle dependence for the beam asymmetry C (top) and the doublepolarization asymmetries G (center) and E (bottom) at E , = 317 MeV. The left panel is for the reaction 7 I?D --t T O , the right one for 7 f i D + T * .

+

+

Acknowledgments This work is supported by US Dept. of Energy under contract DE-ACO298CH10886 and by the US National Science Foundation. References

1. S.B. Gerasimov, Sou. J. Nucl. Phys. 2, 430 (1966); S.D. Drell and A.C. Hearn, Phys. Rev. Lett. 16,908 (1966). 2. V. Bernard, N. Kaiser, J. Kambor, and Ulf-G. Meissner, Nucl. Phys. B 38,315 (1992). 3. A. Honig, Q. Fan, X. Wei, A.M. Sandorfi and C.S. Whisnant, Nucl. Instrum. Methods A 356,39 (1995). 4. A. Honig, Phys. Rev. Lett. 19,1009 (1967).


Session on Lattice QCD and Heavy Quarks Convenors K.-F. Liu S. Ohta


LATTICE CALCULATION OF BARYON MASSES USING THE CLOVER FERMION ACTION D.G. RICHARDS Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA M. GOCKELER, P.E.L. RAKOW Institut fur Theoretische Physik, Universitat Regensburg, 0-93040 Regensburg, Germany R. HORSLEY, C.M. MAYNARD Department of Physics & Astronomy, University of Edinburgh, Edinburgh EH9 SJZ, Scotland, UK

D. PLEITER, G. SCHIERHOLZ Deutsches Elektronen-Synchrotron DESY, John von Neumann Institute for Computing NIC/Deutsches Elektronen-Synchrotron DESY, D-15738 Zeuthen, Germany We present a calculation of the lowest-lying baryon masses in the quenched approximation to QCD. The calculations are performed using a non-perturbatively improved clover fermion action, and a splitting is found between the masses of the nucleon and its parity partner. An analysis of the mass of the first radial excitation of the nucleon finds a value considerably larger than that of the parity partner of the nucleon, and thus little evidence for the Roper resonance as a simple three-quark state.

1

Introduction

The calculation of the excited nucleon spectrum provides a theatre to explore many of the central questions in hadronic physics, including the applicability of the quark model, the r61e of excited glue, and the existence of “molecular” states. Recently, several lattice calculations of the masses of lowest-lying nucleon states have appeared, using a variety of fermion actions. In this talk, I describe a calculation of the mass of the lowest-lying negative-parity state using an O(a)-improved clover fermion action. By using a variety of volumes and lattice spacings, we are able to estimate finite-volume and finitelattice-spacing effects; further details of this calculation are provided in earlier papers. 5 ) 6 For a subset of our lattices, we also determine the mass of the first radial excitation of the nucleon. 1~29374

627

628

2

Calculational Details

There are two interpolating operators that we will consider in our measurement of the low-lying J = 112 nucleon spectrum:

Nii2’

=~ijk(uTCygdj)uk,

Nii2’ = ~ i j k ( u T C d j ) 7 5 ~ k . (1) These operators have an overlap with particles of both positive and negative parity; on a lattice periodic or anti-periodic in time, the best delineation that can be achieved is that of a forward-propagating postive-parity state, and a backward-propagating negative-parity one. The “diquark” piece of Nl couples upper, or large, spinor components whilst that of Nz couples an upper and a lower spinor component and hence vanishes in the non-relativistic limit. Thus we expect N1 to have a better overlap with the positive-parity ground state than N2. The expectation is that N2 couples primarily to the lightest radial excitation of the nucleon, which experimentally is the so-called Roper resonance ”(1440). The calculation is performed in the quenched approximation to QCD, using the the standard Wilson gluon action and the non-perturbatively improved “clover” fermion action. The quark propagators are computed using both local and smeared sources. Where possible, errors on the fitted masses are computed using a bootstrap procedure, but simple uncorrelated x2 fits are employed in the chiral extrapolations. 3

Results

The masses of the nucleon and its parity partner are obtained from fourparameter fits to the two-point correlators of N1. For the chiral extrapolation of the masses, we adopt the ansatz

+

(arnxl2= ( u M ~ )b z~( ~ r n , ) ~

(2)

where X is either N1I2+ or N1i2-. The leading non-analytic term in the quenched approximation is linear in rn,, but results for a M x are insensitive to this term, and indeed in the case of N112+ we find a coefficient whose central value differs in sign from that predicted. In order to compare our data to experiment, we show in Figure 1 the masses of the nucleon and its parity partner at each lattice spacing; we find good consistency between the lattice calculation and the physical values, despite systematic uncertainties due to the chiral extrapolation, finite-volume and the use of the quenched approximation.

629 I1

LO

3

I

I

-

GI-

t a

%l

I

I

nl

-

L

-

N(939) 0 Jacobi 0 Fuzzed

-

-

Figure 1. Masses of nucleon and its parity partner in units of TO’ where TO 0.5 fm. The labels “Jacobi” and “Fuzzed” refer t o two different nucleon smearing techniques used t o improve the signal for the ground-state masses.

The nature of the Roper, the first nucleon excitation, has long been debated. In Figure 2, we show the effective masses of the positive- and negativeparity states constructed from N l , and of the positive-parity state constructed using Nz for a quark mass around that of the strange; it is clear that the latter mass is considerably higher than that of the negative-parity state, and therefore much heavier than the Roper (1440). The ordering of the masses at each quark mass is also shown in the figure, revealing a mass splitting between the radial excitation and the nucleon parity partner comparable to that between the parity partner and the nucleon, in accord with other lattice calculations. 1,2,3 4

Conclusions

We have seen that the low-lying excited nucleon spectrum is accessible to lattice calculation, and that lattice calculations are already providing valuable insight, most notably through the lack of evidence for the Roper resonance as a naive three-quark state. Increasingly energetic excitations are subject to increasing statistical noise, and thus further precise calculations will require the full panoply of lattice technology, such as the use of anisotropic lattices. 2,8 Such lattice calculations will provide the vital theoretical complement to the experimental programme at Jefferson Laboratory and elsewhere.

630

1-

$ -

I

v

% +

* *

vNY ANY-

8 8 05-

a a = =

0 Ni"'

-

0 N:"'

I

OQ

u

s

tu

IS

1u

01

2s

I

Figure 2. The left-hand plot shows the effective masses of the positive-parity states using Ni (circles) and N2 (bursts), and negative-parity using N1 (diamonds). The right-hand plot shows the corresponding fitted masses at ( a / ~ o ) 0.02, ~ the middle points in Figure 1.

-

Acknowledgements This work was supported in part by DOE contract DEAC05-84ER40150 under which the Southeastern Universities Research Association (SUM) operates the Thomas Jefferson National Accelerator Facility, by EPSRC grant GR/K41663, and PPARC grants GR/L29927, GR/L56336 and PPA/P/S/l998/00255. MG acknowledges financial support from the DFG (Schwerpunkt "Elektromagnetische Sonden").

References

1. F.X. Lee and D.B. Leinweber, Nucl. Phys. (Proc. Suppl.) 73, 258 (1999). 2. F.X. Lee, Nucl. Phys. (Proc. Suppl.) 94, 251 (2001). 3. S. Sasaki (RBC Collaboration), Nucl. Phys. (Proc. Suppl.) 83 (2000) 206; S. Sasaki, T. Blum and S. Ohta, Phys. Rev. D65, 074503 (2002). 4. W. Melnitchouk et al., hep-lat/0202022. 5. D.G. Richards (LHPC and UKQCD Collaboration), Nucl. Phys. (Proc. Suppl.) 94, 269 (2001). 6. M. Gockeler et al. (LHPC/QCDSF/UKQCD Collaborations), Phys. Lett. B532, 63 (2002). 7. J.N. Labrenz and S.R. Sharpe, Phys. Rev. D54, 4595 (1996). 8. LHP Collaboration (R. Edwards et d.), in preparation.

NUCLEON MAGNETIC MOMENTS, THEIR QUARK MASS DEPENDENCE AND LATTICE QCD EXTRAPOLATIONS

A

T.R. HEMMERTA AND W. WEISEAlB Theoretische Physik, Physik Department, T U Miinchen 0-857‘7 Garching, Germany ECT*, Villa Tambosi, I-38050 Villazzano (Trento), Italy

1

Introduction

The chiral symmetry of QCD is spontaneously broken at low energies, leading to the appearance of Goldstone Bosons. For 2-flavor QCD we identify the resulting 3 Goldstone Bosons with the 3 physical pion states, the lowest lying modes in the hadron spectrum. In addition to being spontaneously broken, chiral symmetry is broken explicitly via the non-zero quark mass 7jl. in the QCD lagrangian. This explicit breaking is responsible for the non-zero masses m, of the pions. In the now experimentally established large-condensate scenario with parameter Bo one obtains m: = 2 7jl. Bo (1

+ O(hB0))

(1)

for this connection. At low energies QCD is represented by a chiral effective field theory (xEFT) with the dynamics governed by the Goldstone Bosons, coupling to matter fields and external sources. The important aspect for this work i s the fact that this xEFT incorporates both the information on the spontaneous and on the explicit breaking of chiral symmetry. We report on recent work utilizing xEFT to study the quark mass (pion mass) dependence of the magnetic moments of the nucleon. 2

The Calculation

We use xEFT with pions, nucleons and deltas as explicit degrees of freedom. When including matter fields with differing masses-as is the case between A(1232) and the nucleon-one has to make a decision on the power counting one employs. Throughout this work we follow the so called Small Scale Expansion (SSE) of refs.2. However, in one crucial aspect we differ from refs2: For the leading order N A transition lagrangian we employ

631

632

Figure 1.

which treats vector and axial-vector couplings C V , C A to this transition on a symmetric footing. Usually the (leading order) N A vector coupling is relegated to subleading order based on standard (“naive”) power counting arguments. Nevertheless, we find it necessary to resort to Eq.(2) to capture essential quark-mass dependent effects in the anomalous magnetic moments already at leading one-loop order, resulting in a better behaved perturbative expansion. Our goal is to study the quark (pion) mass dependence of the magnetic moments of the nucleon. Treating the electromagnetic field as an external vector source, to leading one-loop order-according to SSE-one has to evaluate 11 diagrams, displayed in Fig.1.

3

Isovector Anomalous Magnetic Moment

For the isovector anomalous magnetic moment one obtains

633

+N~LO,

(3)

where A is the nucleon-delta mass difference. Most of the parameters in this expression are known and specified in ref. ', except for K:, c v 1El. At a chosen regularization scale X we fit these 3 parameters to reproduce quenched lattice results for K , reported in ref. 3 . Note that these lattice data correspond to lattice pions heavier than 600 MeV. With the parameters now fixed one obtains the full curve in Fig.2, which at m, = 140 MeV comes very close to the physical isovector anomalous magnetic moment, indicated by the full circle. A priori it is not guaranteed that this extrapolation curve over such a wide range of quark (pion) masses would come anywhere near to the physical value, but remarkably it does so, albeit with a large error band (dashed curves). We also note that our approach rests on the assumption that for lattice data with effective pion masses larger than 600 MeV the differences between quenched and fully dynamical lattice simulations are small ', allowing us to utilize "Standard" instead of LLQuenchedl' xEFT methods. 4

Isoscalar Anomalous Magnetic Moment

To the same leading-one loop order in SSE one only obtains analytic quark mass dependence for the isoscalar anomalous magnetic moment K ~ : K,

= K:-- 8 E 2 M m ;

+N2L0.

(4 1

The 2 unknown couplings &t1Ez-parameterizing short-distance physics beyond the realm of XEFT-can again be fitted to lattice data

'.

5

Comparison with Pade-Formula

Combining isovector and isoscalar results one obtains the quark (pion) mass dependence of the magnetic moments of proton and neutron, as shown in the full line of Fig.3. Surprisingly our result is rather close-at least within the present error band-to the Pade-fit extrapolation formula of the Adelaide group 3 , shown as the dashed curve.

Acknowledgments The authors acknowledge partial support by BMBF and DFG.

634

6 5

4 Kv

3 2 1

0

0.2

0.6 m, [GeVI

0.4

0.8

1

Figure 2.

Figure 3.

References 1. T.R. Hemmert and W. Weise, preprint no. [hep-lat/0204005]; submitted to EPJA. 2. T.R. Hemmert, B.R. Holstein and J. Kambor, J. Phys. G24, 1831 (1998); Phys. Lett. B395, 89 (1997). 3. D.B. Leinweber, D.H. Lu and A.W. Thomas, Phys. Rev. D60, 034014 (1999).

HEAVY QUARK SPECTRUM FROM ANISOTROPIC LATTICES X. LIAO AND T. MANKE Physics Dept., Columbia University, New York, N Y 10027, USA

We present our results for the heavy meson spectrum from quenched lattice QCD calculations. By employing a fully relativistic anisotropic lattice action with very fine temporal resolution, we are able to calculate the heavy quark spectrum for a wide range of quark masses including both charm and bottom. Higher excitations such as the exotic hybrids and orbitally excited mesons are also obtained for the charmonium spectrum. Using several different lattice spacings, we perform a continuum extrapolation of the spectrum.

1

Introduction

The rich phenomenology and abundant accurate experimental data make the heavy quark system an ideal test bench for QCD and lattice QCD technique. It is crucial that we reproduce the observed hadron spectrum from first principles to justify predictions for more complicated quantities such as the weak matrix elements. However, the large separation of energy scales in the heavy quark system makes it difficult to study heavy quarks on a conventional isotropic lattice. This intrinsic space-time asymmetry of a system containing heavy quarks motivated the non-relativistic QCD However, the difficulty in controlling the systematic errors of NRQCD, including relativistic corrections, radiative corrections, and lattice discretization errors, calls for a fully relativistic study. The relativistic anisotropic lattice QCD 3,4 can be used to address these problems. In addition to bound states of quarks and anti-quarks, QCD also predicts the existence of states with explicit gluonic excitations such as glueballs and hybrids. The observation of such states will provide additional insight into the gluonic degrees of freedom in the non-perturbative regime of QCD.

635

636

2

Simulation details

We use a lattice gauge action in which the spatial-temporal and spatial-spatial plaquettes are weighted differently corresponding t o an explicit anisotropy:

where p and t o are the bare coupling and bare anisotropy. Similarly, we employ an anisotropic fermion action SgloVer= C,q(z>Q Q(Z) with Q given by

Q

= mo f vt

a, w070-tvs wiyi - 2 [Ct g o k p o k f Cs ‘ J k l F k l ] .

(2)

We choose Wilson’s combination of first and second order derivative, W, = V, - (a,/2)y,A,, to ensure the full projection property and to remove all doublers. For the clover coefficients, we use tree-level mean-field improved values t o remove the leading O ( a ) errors. We fix vs = l(or vt = 1 alternatively) and tune vt non-perturbatively by requiring that the lowest S-wave meson satisfy the relativistic dispersion relation at low momentum. The bare quark mass mo is tuned to reproduce the experimental mass value of the lowest spin-averaged S-wave meson. Our action is a generalization of the “Fermilab action” 6 , which can be considered as the special case with = 1. We construct meson operators using bilinears in the form of O i j k ( z ) = q(z) riAjAk q(z) ( ri is one of the 16 y matrices and Ai is lattice derivative). To vary the overlap of meson operator with the states of interest, we apply various smearing techniques for both the quark and gluon fields. As expected, we find link fuzzing quite important in suppressing the excited states of the hybrid mesons. The simulations we performed are listed in table 1. The lattice scales are set by 1P - 1s splitting.

3

Results and conclusions

We obtained a fairly complete charmonium spectrum (Fig. 1) including both the low lying mesons below the OD threshold and higher excitations such as the exotic hybrids ( J p c = l-+,Of-, a+-) and orbitally excited mesons (with orbital angular momentum up to 3). It has been shown that the velocity expansion of NRQCD has poor convergence for charmonium spin splittings. Our result for the P triplet splitting ratio R f s = ( 3 P-~’Ps)/(~S - 3P0)is

’

637 Table 1. Charmonium and Bottomonium Quenched Simulations. ~

Charmonium simulations

(6I ) Lat. Size ( N , , N t ) # Configurations - a;' [Gev]

(5.7, 2) (8, 32) 1950 1.945(26)

(5.9, 2) (16, 64) 1080 3.021(34)

(6.1, 2) (16, 64) 1010 4.292(49)

Bottomonium simulations

(P,0 Lat. Size ( N , , N t ) # Configurations a;' [Gev]

(5.9, 4) (8, 96) 700 6.76(24)

(6.1, 4) (16, 96) 660 10.57(31)

(6.3, 4) (16, 128) 450 15.15(81)

(6.5, 4) (16, 160) 710 20.9(2.2)

0.47(13) in the continuum limit, which agrees well with the experimental value of 0.478(5). This ratio removes the systematic errors from fixing the scale in a quenched calculation, but it is highly sensitive to relativistic corrections. A selection rule analysis shows that the width of a charmonium hybrid meson is narrow if it lies below the D**D ( S P wave) threshold which is 1.220 Gev above 1s. Our result for the 1-+ hybrid excitation is 1.361(41) Gev, slightly above the D**D threshold. However, the conclusion is not final due to known ambiguities in the the scale setting procedure for quenched simulations. We compare our 1-+ result to previous lattice results in Fig. 2 (left). We study in detail the spin splittings for bb states. Fig. 2 (right) shows the continuum extrapolation of the hyperfine splitting 3S1- 'So. Our result deviates significantly from NRQCD results, which we attribute partly to relativistic corrections. A linear fit gives 58.7(5.5) MeV, while a quadratic fit(assuming no O(au) errors) gives 51.1(3.1) MeV. For more detailed discussions, please refer to Ref. '. We demonstrate that a fully relativistic treatment of the heavy quark system is well suited to control the large systematic errors from isotropic lattices (Mat errors) and NRQCD simulations (Mwn corrections). In addition, the high temporal resolution of anisotropic lattices has dramatically reduced the statistical error of highly excited states. Remaining discrepancies with experiment should be addressed in full QCD calculations.

+

Acknowledgments

This work is supported by the U.S. Department of Energy. The numerical simulations were conducted on the QCDSP machines at Columbia University and Brookhaven's RIKEN-BNL research center.

638 References

1. G. Lepage et al., Phys. Rev. D, 46:4052, 1992. 2. C.T.H. Davies, The heavy hadron spectrum. hep-ph/9710394. 3. F. Karsch, Nucl. Phys. B, 205:285, 1982. 4. Colin Morningstar., Nucl. Phys. (Proc.SuppZ.), 53:914, 1997. 5. T.R. Klassen, Nucl. Phys. (Proc.SuppZ.), 73:918, 1999. 6. A.X. El-Khadra et al., Phys. Rev. D, 55:3933, 1997. 7. N.H. Shakespeare and H.D.Trottier, Phys. Rev. D, 58:034502, 1998. 8. P.R. Page et al., Phys. Rev. D, 59:034016, 1999. 9. P.R. Page, Nucl. Phys. A , 663:585, 2000. 10. X. Liao and T. Manke, Phys. Rev. D, 65:074508, 2002.

4.8 L::0

32

2.8

0- 1JPC

Figure 1. Charmonium spectrum from anisotropic lattice.

0

relativistic.5=5, N,=O

9

NRCICD, 5=1. N,=O [23]

4

NRCICD, +I.

N,=2

[a

45

20 I

0

0.1

,

,

,

,

0.2

as (fm)

Figure 2. Comparison to previous lattice results of charmonium hybrid meson 1-+ mass above 1.9 (Left) and bottomonium hyperfine splitting 3S1 - 'So (Right).

THE DOUBLY HEAVY BARYONS IN THE NONPERTURBATIVE QCD APPROACH I.M.NARODETSKI1 AND M.A.TRUSOV ITEP, Moscow, Russia E-mail: naro @heron.itep.ru We present some piloting calculations of the masses of the doubly heavy baryons in the framework of the simple approximation within the nonperturbative string approach. The simple analytical results for dynamical masses of heavy and light quarks and eigenvalues of the effective QCD Hamiltonian are presented.

The purpose of this talk is to present the results of the calculation of the masses and wave functions of the heavy baryons in a simple approximation within the nonperturbative QCD (see and references therein). The starting point of the approach is the Feynman-Schwinger representation for the three quark Green function in QCD in which the role of the time parameter along the trajectory of each quark is played by the Fock-Schwinger proper time. The proper and real times for each quark related via a new quantity that eventually plays the role of the dynamical quark mass. The final result is the derivation of the Effective Hamiltonian, see Eq. (1) below. In contrast to the standard approach of the constituent quark model the dynamical mass mi is not a free parameter but it is expressed in terms of the current mass m,(O)defined at 1 GeV from the condition of the minimum of the appropriate scale of p = 0. Technically, this has the baryon mass MB as function of mi: been done using the einbein (auxiliary fields) approach, which is proven to be rather accurate in various calculations for relativistic systems. This method was already applied to study baryon Regge trajectories and very recently for computation of magnetic moments of light baryons ‘. The essential point of this talk is that it is very reasonable that the same method should also hold for hadrons containing heavy quarks. As in we take as the universal parameter the QCD string tension CT fixed in experiment by the meson and baryon Regge slopes. We also include the perturbative Coulomb interaction with the frozen coupling a s ( l GeV) = 0.4. Consider the ground state baryons without radial and orbital excitations in which case tensor and spin-orbit forces do not contribute perturbatively. 5survives in the perturbative approximation. The EH has the following form N

639

640 where Ho is the non-relativistic kinetic energy operator, m y ) are the current quark masses and mi are the dynamical quark masses to be found from the minimum condition, and V is the sum of the perturbative one gluon exchange potential V, and the string potential Vstring. The string potential has been calculated in as the static energy of the three heavy quarks: K t r i n g ( T 1 , ~ 2T Q , ) = DRmin, where Rminis the sum of the three distances Iril from the string junction point, which for simplicity is chosen as coinciding with the center-of-mass coordinate. We use the hyper radial approximation (HRA) in the hyper-spherical formalism approach. In the HRA the three quark wave function depends only on the hyper-radius R2 = p2 X2, where p and X are the three-body

+

Jacobi variables: pij = f

i ( ~ i - ~ j ) X, i j

=

@(

m i mi+mj ri+mjrJ

- T k ) , where

(mi+m.)mc

mim. mi+,&

and p is an arbitrary parameter with the = ? k j , k = mi+mj;mk 7 dimension of mass which drops off in the final expressions. Introducing the reduced function x ( R ) = R5I27)(R)and averaging V = V, -t over the six-dimensional sphere one obtains the Schrodinger equation

b j

'(

)+2p

2 dR2R

a E,+--bR-R

[

where

We use the same parameters as in Ref. 5 : o = 0.17 GeV, as = 0.4, m$) = 0.009 GeV, mLo)= 0.17 GeV, mio)= 1.4 GeV, and mp) = 4.8 GeV. We solve Eq. (2) by the variational method introducing a simple variational Ansatz x ( R ) N R5/2e-ppZR2, where p is the variational parameter. Then the threequark Hamiltonian admits explicit solutions for the energy and the ground state eigenfunction: E M min E(p),where P

The dynamical masses mi and the ground state eigenvalues Eo are given for various baryons in Table 1 of Ref. '. The dynamical values of light quark mass m, N &?I 450 - 500 MeV ( q = u, d , s ) qualitatively agree with the results of Ref. obtained from the analysis of the heavy-light ground state mesons. For the heavy quarks (Q = c and b ) the variation in the values of their dynamical masses mQ is marginal. This is illustrated by the

-

641 Table 1. Comparison of results of analytical and numerical variational calculations for Ab and Ac baryons (all quantities are in units of GeV)

Baryon

0.56 4.84

mn

0.52 1.50

0.56 4.82

0.53 1.47

simple analytical results for Qud baryons. These results were obtained from = 0 in the form of expansion in the approximate solution of equation

I

P=Po

the small parameters [ = &/m$) and a,. Omitting the intermediate steps one has

E~ = 3 6

( n-5 )

mQ = m$) (1

114

(1

+ A . [ - -53B

. ff,

+ . ..

)

+ 2A.E2-t. . . )

fi.

(8)

where for our variational Anzats A = Accuracy ‘I4, B = of this approximation is illustrated in Table 1. To calculate hadron masses we, as in Ref. 3 , first renormalize the string C Ci, where the constants Ci take into account potential: ---f

+

i

the residual self-energy (RSE) of quarks. In what follows we adjust the RSE constants Ci to reproduce the center-of-gravity for baryons with a given flavor. As a result we obtain C, = 0.34, C, = 0.19, C, Cb 0. We keep these parameters fixed to calculate the masses given in Table 2, namely the spin-averaged masses (computed without the spin-spin term) of the lowest double heavy baryons. In this Table we also compare our predictions with the results obtained using the additive non-relativistic quark model with the power-law potential 6, relativistic quasipotential quark model ’, the Feynman-Hellmann theorem and with the predictions obtained in the approximation of double heavy diquark ’. In conclusion, we have employed the general formalism for the baryons, which is based on nonperturbative QCD and where the only inputs are u , N

N

642 Table 2. Masses of baryons containing two heavy quarks

State E{qcc} fl{scc} Z{qcb} R{scb} E{qbb} R{sbb}

present work 3.69 3.86 6.96 7.13 10.16 10.34

Ref. 3.70 3.80 6.99 7.07 10.24 10.30

Ref. 3.71 3.76 6.95 7.05 10.23 10.32

Ref. 3.66 3.74 7.04 7.09 10.24 10.37

Ref. 3.48 3.58 6.82 6.92 10.09 10.19

a, and two additive constants, C, and C,, the residual self-energies of the light quarks. Using this formalism we have also performed the calculations of the spin-averaged masses of baryons with two heavy quarks. One can see from Table 2 that our predictions are especially close to those obtained in Ref. using a variant of the power-law potential adjusted to fit ground state baryons. Acknowledgements

This work was supported in part by RFBR grants ## 00-02-16363 and 0015-96786. References

1. 1.M.Narodetskii and M.A.Trusov, Yad. Fiz., 65, in press [hepph/0104019] 2. Yu.A.Simonov, Lectures given at the XVII International School of Physics ”QCD: Perturbative or Nonperturbative” , Lisbon 1999 [hep-ph /9911237] 3. M.Fabre de la Ripelle and Yu.A.Simonov, Ann. Phys. (N.Y.) 212, 235 (1991). 4. B.O.Kerbikov, Yu.A.Simonov, Phys. Rev. D62, 093016 (2000). 5. Yu.S.Kalashnikova and A.Nefediev, Phys. Lett. B 492, 91 (2000). 6. E.Bagan et al. Z.Phys. C 64, 57 (1994). 7. D.Ebert et al., Z. Phys. C 76, 111 (1997). 8. R.Roncaglia et al., Phys. Rev. D 52, 1248 (1995). 9. A.K.Likhoded and A.I.Onishchenko, hep-ph/9912425

EXCITED BARYONS AND CHIRAL SYMMETRY BREAKING OF QCD FRANK X. LEE Center for Nuclear Studies, George Washington University, Washington, DC 20052, USA and Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, USA N* masses in the spin-l/Z and spin-3/2 sectors are computed using two nonperturbative methods: lattice QCD and QCD sum rules. States with both positive and negative parity are isolated via parity projection methods. The basic pattern of the mass splittings is consistent with experiments. The mass splitting within the same parity pair is directly linked to the chiral symmetry breaking QCD.

1

Introduction

There is increasing experimental information on the baryon spectrum from JLab and other accelerators (as tabulated in the particle data group I ) , and the associated desire t o understand it from first principles. The rich structure of the excited baryon spectrum provides a fertile ground for exploring how the internal degrees of freedom in the nucleon are excited and how QCD works in a wider context. One outstanding example is the parity splitting pattern in the low-lying N* spectrum. The splittings must be some manifestation of spontaneous chiral symmetry breaking of QCD because without it, QCD predicts parity doubling in the baryon spectrum. 2

Lattice QCD

Lattice QCD plays an important role in understanding the N* spectrum. One can systematically study the spectrum sector by sector, with the ability to dial the quark masses, and dissect the degrees of freedom most responsible. Given that state-of-the-art lattice QCD simulations have produced a ground-state spectrum that is very close to the observed values 2 , it is important to extend the success beyond the ground states. There exist already a number of lattice studies of the N* spectrum focusing mostly on the spin-1/2 sector. All established a clear splitting from the ground state. Here, we focus on calculating the excited baryon states in the spin-312 sector. We consider the 334,5967778,

following interpolating field with the quantum numbers I ( J p ) =

643

(:+),

644

The interpolating fields for other members of the octet can be found by appropriate substitutions of quark fields. Despite having an explicit parity by construction, these interpolating fields couple to both positive and negative parity states. A parity projection is needed to separate the two. In the large Euclidean time limit, the correlator with Dirichlet boundary condition in the time direction and zero spatial momentum becomes

where f,,is a function common to both terms. The relative sign in front of provides the solution: by taking the trace of GCly(t) with (1f y4)/4, one can isolate M+ and M-, respectively. It is well-known that a spin-3/2 interpolating field couples to both spin312 and spin-1/2 states. A spin projection can be used to isolate the individual contributions in the correlation function G,, g . Numerical test of spin projection in the spin-3/2+ channel reveals two different exponentials in G ( t )from the spin-3/2+ and spin-1/2+ parts, with the spin-3/2+ state heavier than the spin-1/2+ one, which is consistent with experiment. One would mistake the dominant spin-1/2+ state for the spin-3/2+ state without spin projection. Figure 1 presents preliminary resuIts for mass ratios extracted from the correlation functions for the 3/2+ N* states to the nucleon ground state as a function of ( ~ / p ) Mass ~ . ratios have minimal dependence on the uncertainties in determining the scale and the quark masses, so that a more reliable comparison with experiment can be made. These ratios appear headed in the right direction compared to experiment where available] but more study is needed to address the systematics. Figure 2 shows the similar plots for the 3/2- N* states.

74

3

QCD sum rules

The QCD Sum Rule method l o is a time-honored method that has proven useful in revealing a connection between hadron phenomenology and the nonperturbative nature of the QCD vacuum via only a few parameters (the vacuum condensates). It has been successfully applied to a variety of observables in hadron phenomenology, providing valuable insights from a unique, QCDbased perspective, and continues an active field. The method is analytical (no path integrals!)] is physically transparent (one can trace back to the QCD

645 2.2 2.0 1.8

l.8

I

I

2.2

1

-*

-

- 1720+/938

+ 1.4 -

ih$

c 1.2 1.0

-

0.8

-

-

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-

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-

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-

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. . " . ..... ".*

A,

*.

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22

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~

1.8

h + 1.6

h + 1.6

2

12

e 1.2

w

1.0

k

N 1.4 \

N 1.4

1.0 0.8

0.6

..-

nu

0.6

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A.

$ 1.2 -

2.0 ~

1.6

N 1.4

*

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I

0.6

1

2.0

0.2

0.4

0.8

1.0

0.0

0.2

0.4

0.8

1.0

Figure 1. Mass ratios for the 3/2+ N* states as compared to experimental values where available.

operators responsible), and has minimal model dependence. The accuracy of the approach is limited due to limitations inherent in the operator-productexpansion (OPE), but well understood. One progress in this area is the use of Monte Carlo-based analysis to explore the predictive ability of the method for N* properties The idea is to probe the entire QCD parameter space and map the error distribution on the OPE side to the phenomenological side. It is found that some QCD sum rules are truly predictive for N* masses, while others are marginal. Another progress is that a parity separation similar to that in lattice QCD can be performed in the QCD sum rule approach, resulting in the so-called parity-projected sum rules which has the general structure 11712713.

14115t16

A(M,w+)+ B(M,w+)

646 2.2 2.0 1.8

>=1 1.8 \

1.4

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k

1.0 0.8

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I

2.0

€

-*

-

1620-/938

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*A*

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-

-

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-

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I

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8

-

,

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,

-*

1.8 -1820-/938 - h 1.6 - NI 1.4 1.2 - IZI 1.0 0.8 -

$

.A

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-

%

2.2

' a

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0

1520-/938

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-

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-*

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*

,

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hI 1.8 -k30-/938

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-

2

>=I 1.6

0.8 I

2.0

0.8

*,

-

2.2

0.8

-

a .

0.6

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2.2

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€ li i

0.8

1

. I

Figure 2. Similar to Figure 1, but for the 3/2- N* states.

A(M,w-)- B(M,w-)= A-exp -2

(5)

where M is the Bore1 mass parameter, (mB,X2,w) are the phenomenological parameters (mass, coupling, threshold). The term B controls the mass splitting: if B = 0, then m+ = m-. Term B involves only dimension-odd condensates, such as the quark condensate (ijq) and the mixed condensate (ijgu . Gq). So a direct link is established between the mass splitting of parity pairs and dynamical chiral symmetry breaking of QCD. Fig. 3 shows a numerical confirmation in the case of nucleon. As (44)is decreased, both masses decrease, but with a different rate. N L - falls faster than N ; + . As a result, the mass splitting decreases. In the fimit that chiral-symmetry is restored ((qq)=O), it is expected that N;+ and N + - become degenerate. In conclusion, we can compute the baryon spectrum in the spin-1/2 and spin-3/2 sectors for all particle channels using two methods: lattice QCD and QCD sum rules. Parity projection further reveals that the mass split-

647

2.0

-

T

-1

I

I

I

I

I

1.8

A

% 0

-

1.6

/ /

ul K!

/

/

4 1.4 FI

s

1.2

ZZ

1.0

d

; 0.8 0.4

I\

/

1/;

/

I

I

0.6

I

0.8 1.0 1.2 1.4 Quark Condensate Ratio

1.6

Figure 3. Mass splitting between N L - and N I

as a function of the quark condensate. The ratio is relative to the standard value of a = - ( 2 7 ~ ) (~q q ) = 0.52 GeV3. 2

z+

ting within the same baryon pair is directly controlled by spontaneous chiral symmetry breaking of QCD.

Acknowledgments

This work is supported in part by U S . Department of Energy under grant DE-FG02-95ER40907.

648

References

1. Particle Data Group, Eur. Phys. J. C 15,1 (2000). 2. S. Aoki, et al., Phys. Rev. Lett. 84,238 (2000). 3. D.B. Leinweber, Phys. Rev. D 51,6383 (1995). 4. F.X. Lee, D.B. Leinweber, Nucl. Phys. B (Proc. Suppl.) 73, 258 (1999), 5. F.X. Lee, Nucl. Phys. B (Proc. Suppl.) 94,251 (2001). 6. S. Sasaki, Nucl. Phys. B (Proc. Suppl.) 83,206 (2000); hep-ph/0004252; T. Blum, S. Sasaki, hep-lat/0002019; S. Sasaki, T. Blum, S. Ohta, heplat/0102010. 7. D. Richards, Nucl. Phys. B (Proc. Suppl.) 94,269 (2001) 8. M. Grokeler, R. Horseley, D. Pleiter, P.E.L. Rakow, G. Schierholz, C.M. Maynard, D.G. Richards, hep-lat/0106022. 9. F.X. Lee, D. Leinweber, L. Zhou, J. Zanotti, S. Choe Nucl. Phys. B (Proc. Suppl.) 106, 248 (2002). 10. M.A. Shifman, A.I. Vainshtein and Z.I. Zakharov, Nucl. Phys. B147, 385, 448 (1979). 11. D.B. Leinweber, Ann. of Phys. (N.Y.) 254,328 (1997). 12. F.X. Lee, Phys. Rev. D57,1801 (1998); Phys. Rev. C57,322 (1998) 13. F.X. Lee, X. Liu, Phys. Rev. D66, 014014 (2002). 14. D. Jido, N. Kodama, and M. Oka, Phys. Rev. D54,4532 (1996). 15. D. Jido and M. O h , hep-ph/9611322. 16. F.X. Lee, X. Liu, t o be submitted to Phys. Rev. D.

649

Reception at the Mariner's Museum

Dinner at the Mariner's Museum


List of Participants Afanasev, Andrei Jefferson Lab 12000 Jefferson Avenue Newuort News. VA 23606. USA afan&Mab.org (757) 269-725 1

Agbakpe, Peter Jefferson Lab 12000 Jefferson Avenue Newuort News, VA 23606, USA pagbakuekjlilablorg (757) 269-5028

Ahmidoueh, Abdellah North Carolina A&T State University Department of Physics 1601 East Market Street Greensboro, NC 27407, USA abdellah@,ilab.org (336) 334-7646

Alessandro, Braghieri INFN-Pavia 6, Via Bassi Pavia, 27100 Italy braghieri@,uv.infn.it +39 0382 507628

Anderson, Bryon Kent State University Physics Department 105 Smith Hall Kent. OH 44242. USA anderson@huaca:kentedu (330) 672-4899

Arrington, John Argonne National Lab 9700 S Cass Avenue Building #203 Areonne .IL 60439 joL*,ah, gov (630) 252-3619

Avagyan, Harut Jefferson Lab 12000 Jefferson Avenue Newuort News. VA 23606 [email protected] (757) 269-7764

Baker, Keith Hampton University 130 East Tyler Street Hampton ,VA 23668 USA baker@,ilab.org (757) 727-5239

Barnes, Peter Los Alamos National Lab Physics Division, MS H846 Los Alamos ,NM 87545 USA [email protected] (505) 667-2000

Beeher, Thomas SLAC, MS81 2575 Sand Hill Road Menlo Park, CA 94025 USA tpbecher@,SLAC.stanford.edu (650) 926 4415

Beise, Elizabeth University of Maryland Department of Physics College Park. MD 20742 USA beise&hvsics.umd.edu (301) 405-6109

Bennhold, Cornelius George Washington University Department of Physics Washington, DC 20052 USA bennhold@,m.edu (202) 994-6274

651

652 Bernstein, Aron MIT 26-419 Cambridge, MA 02139 USA [email protected] (617) 253-2386

Bertin, Pierre Universite Blake Pascal 28 rue des Meuniers Clermont Ferrand, 63000 France [email protected] +33 73 40 72 76

Bianchi, Nicola INFN Frascati Casella Postale 13 Frascati ,00044 Italy bianchi@hermes,desV.de +39 0694 032320

Bisplinghoff, Jens University of Bonn Inst. her Strahlen- u. Kernphysik Nussallee 14-16 BOM.D 53115 Germanv [email protected] +49 228 i3 2543

Black, Deirdre Jefferson Lab Theory Group MS 12H2 12000 Jefferson Avenue Newport News, Va 23606 USA [email protected] (757) 269-7412

Bloch, Frederic Basel University Department of Physics and Astronomy Klingelbergstrasse 82 Basel ,CH-4056 Switzerland frederic.bloc~unibas.ch +41 61 267 37 31

Borasoy, Bugra Technische Universitaet Muenchen Institut h e r theoretische Physik T39 Physik Department Garching -, D-85747 Germanv borasov@,Dhvsik.tu-muenchen.de +498928912390

Boyarinov, Sergey Jefferson Lab 12000Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-5795

Brash, Edward University of Regina Department of Physics 3737 Wascana Parkway Regina. SK S4S OA2 Canada brash@,urepinaca (306) 585-4201

Briscoe, William George Washington University Department of Physics 725 21st Street, NW Washington ,DC 20052 USA briscoe(ii,gwu.edu (202) 994-6788

Brooks, Will Jefferson Lab 12000 Jefferson Avenue NewDort News. VA 23606 USA [email protected] (757) 269-7391

Bruell, Antje MIT 26-551 77 Massachusetts Avenue Cambridge, MA 02139 USA [email protected] (617) 253-3208

-

~

-

I

653 Burkert, Volker Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7540

Butuceanu, Cornel College of William &Mary P.O. Box 8795 Williamsburg ,VA 23187-8795 USA [email protected] (757) 221-1987

Capstick, Simon Florida State University Department of Physics Tallahassee, FL 32306-4350 USA [email protected] (850) 644-1724

Cardman, Lawrence Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA cardman@ I ab.org (757) 269-7032

Carlini, Roger Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255

Carlson, Carl College of William and Mary Physics Department P.O. Box 8795 Williamsburp.. VA 23187 USA [email protected] (757) 269-7376

Cassing, Wolfgang Universitaet Giessew Institut h e r Theoretische Physik Heinrich-Buff-Ring 16 Giessen ,35392 Germany Wolfgang.Cassm4xheo.Dhvsik.uni-giessen.de +49 6419 933310

Cha, Jinseok Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-5326

Chen, Jian-ping Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA jpchenO,ilab.org (757) 269-7413

Christy, Micheal Hampton University 130 East Tyler Street Hamoton. VA 23668 USA CHR~STYQJLAB.ORG (757) 269-5327

Chudakov, Eugene Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-6959

Coon, Sidney National Science Foundation 1015N 4201 Wilson Avenue Arlington ,VA 22201 USA [email protected] (703) 292-7382

654 Cords, Dieter Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7526

Covrig, Silviu Caltech 12000 Jefferson Ave. MS16,Rm116 Newport News, VA ,23606 USA covrig@,ilab.org (757) 269-5804

Crannell, Hall The Catholic University of America Physics Department Washington. DC 20064 USA crannell@cuaedu (202) 319-5313

D'Angelo, Annalisa Universita' di Roma Dip. di Fisica Via della Ricerca Scientifica, 1 Rome, 1-00133 Italy [email protected] + 39 06 72594562

Davies, Christine University of Glasgow Department of Physics and Astronomy Glasgow , G62 6BB UK [email protected] +44 141 3304710

De Jager, Kees Jefferson Lab 12000 Jefferson Avenue Newport News , VA 23606 USA [email protected] (757) 269-5254

De Vita, Raffaella INFN Genova Dipartimento di Fisica via Dodecaneso 33 Genova , 16146 ltaly devit&,ge.infn.it +390103536382

Debruyne, Dimitri University of Ghent Institute for Nuclear Sciences (INW) Proeftuinstmat 86 Gent, OVL 9000 Belgium dimi~talvin6.rug.ac.be +32 9264 6553

Denizli, Haluk University of Pittsburgh 5831 Walnut Street ApHl Pittsburgh, PA 15232 USA [email protected] (412) 624-8868

Desplanques, Bertrand ISN-Grenoble 53, Av. des Martyrs Grenoble ,F-38026 FRANCE desuIana@,isn.fr +33 476284172

Dew, Alexandre University of Virginia Department of Physics 382 McCormick Road Charlottesville , VA 22903 USA [email protected] (434) 924 768 1

Diakonov, Dmitri NORDITA Blegdamsvej 17 Couenhaaen ,DK-2100 Denmark diakonov&ordita.dk +45 35 32 53 12

-

I

-

655 Diehl, Markus RWTH Aachen lnst. f. Theoret. PhysikE Aachen ,52056 Germany mdiehlf&hysik.rwth-aachen.de +49 241 8027 049

Domingo, John Jefferson Lab 12000 Jefferson Avenue Newoort News. VA 23606 USA dom&ol@ilab:org (757) 269-7124

Dreher, Patrick MIT 77 Massachusetts Avenue Cambridge, MA 02139 USA [email protected] (617) 258-5446

Edwards, Robert Jefferson Lab 12000 Jefferson Avenue MS 12H2 Newport News, VA 23606 USA [email protected] (757) 269-7737

Egiyan, Hovanes Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA hovanes@,iIab.org (757) 269-5356

Elouadrhiri, Latifa Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA latif@,ilab.org (757) 269-7303

Ernst, David Vanderbilt University Department of Physics and Astronomy Nashville, TN 37235 USA david.i.erns@,vanderbilt.edu (615) 322-2828

Eugenio, Paul Florida State University Department of Physics Keen Building Tallahassee, FL 32306 USA eugenio@,il&.org (850) 644-2585

Eyrich, Wolfgang University of Erlangen-Nuernberg. PhysikalischesInstitut Erwin-Rommel-Str. 1 Erlangen, D91058 Germany evrich6hhvsikuni-erlangen.de +49 9131 852 7086

Falter, Thomas Justus Liebig Universitaet Giessen Institut fuer Theoretische Physik Heinrich-Buff-Ring 16 Giessen ,35392 Germany [email protected] +49 641 9933322

Fenker, Howard Jefferson Lab 12000Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255

Fonvielle, Helene Clermont Ferrand Labo. de Physique Colpusculaire IN2P3/CNRS University of Blaise Pascal Clermont-11 AUBIERE Cedex .63177 France helene(@clermont.iIi2~3.fI +33 4 73 40 72 66

656 Fox, Brenda Riken-BNL Research Center Building 510A Physics Upton, NY 1 1973 USA deni@,bnl.~ o v (631) 344-8595

Freund, Andreas University of Regensburg Institute of Theoretical Physics Universitaetsstr.31 Regensburg ,Germany andreas.freund@,uhvsik.uni-regensbum.de +499419432018

Freyberger, Arne Jefferson Lab 12000 Jefferson Avenue NewDort News. VA 23606 USA frevderp@iI ab.orp (757) 269-7625

Fries, Rainer Duke University Department of Physics P.O. Box 90305 Durham .NC 27708 USA [email protected] (919) 660-2590

Garutti, Erika NIKHEF Kruislaan 409 1098 SJ Amsterdam, Netherlands p98IZiInikhef.nl +3 1 205 925003

Glozman, Leonid University of Graz

Gomez, Javier Jefferson Lab 12000 Jefferson Avenue Newuort News. VA 23606 USA [email protected] (757) 269-7498

Griesshammer, Harald TU Muenchen Institut h e r Theoretische Physik (T39) Garching ,85747 Germany [email protected] +49 89 289 14403

Hansen, Ole Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7627

Institute for Theoretical Physics Universitatsplatz 5 Graz ,A-8010 Austria 1eonid.pIozman~kfUniaraz.ac.at +43 3 16 3805226 Gonzalez, Pedro Universidad de Valencia Departamento Fisica Teorica C. Dr. Moliner, 50 Burjassot(Valencia),46100 SPAIN Pedro.Gonzala@,uv.es +34 963 98 31 93 Gross, Franz Jefferson Lab Theory Group, MS 12H2 12000 Jefferson Avenue Newport News, VA 23606 USA -g (757) 269-7537 Henner, Victor Perm State University Theoretical Physics Department Bukireva str. Perm, 614600 Russia [email protected] +7 3422 33 1595

657 Higa, Renato Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA hin&,ilab.org

Higinbotham, Doug Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7851

Huber, Garth University of Regina Department of Physics Regina, SK S4S OA2 Canada [email protected] (306) 585-4240

Ibrahim, Hassan Old Dominion University 1049 W 49 th Street Apt 317 Norfolk, VA 23508 USA [email protected] (757) 683-3484

Ilieva, Yordanka George Washington University 344C Street Thomas Drive Newport News, VA 23606 USA jordanka@,ilab.org (757) 269-6671

Ito, Mark Jefferson Lab 12000 Jefferson Avenue Newoort News. VA 23606 USA [email protected] (757) 269-5295

Janssen, Stijn Ghent University Dep. of Subatomic & Radiation Physics Proeftuinsttaat 86 Gent, 9000 Belgium [email protected] +32 9 265 65 53

Jenkins, David Virginia Tech Physics Department Blacksburg, VA 24061-0435 USA jenkins@,ilab.org (540) 552-3747

Jeschonnek, Sabine The Ohio State University 310 A, Science Building 4240 Campus Drive Lima. OH 45804 USA [email protected] (419) 995 8201

Jiang, Xiaodong Rutgers University/JLab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-70 1 1

Jones, Mark Jefferson Lab 12000 Jefferson Avenue Newport News ,VA 23606 USA jonesO.ilab.org (757) 269-7255

Joo, Kyungseon Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7764

658 Kaiser, Ralf University of Glasgow Department of Physics and Astronomy Kelvin Building Glasgow , G 12 SQQ UK r. kaiser@,~hvsics.ala.ac.uk +44 141 3305287

Kasagi, Jirohta Tohoku University LNS Mikamine 2-1-2, Taihaku Sendai ,982-0826 Japan kasagi@,lns.tohoku.ac.iu +81 22 743 3420

Keppel, Cynthia Hampton U. I Jefferson Lab Physics Department, Olin 102 Hamoton. VA 23668 USA ketmel@,ilab.org (757) 269-7580

Klein, Fritz University of Bonn Physikalisches lnstitut Nussallee 12 Bonn , D-53 1 I5 Germany

.

>

kleint&hvsik.uni-bonn.de +49 228 73 2340,-234

Klein, Franz Catholic University of America Physics Department Hannon Hall 210 Washington, DC 20064 USA kleinf@,cua.edu (202) 319-6190

Klempt, Eberhard University of Bonn Institut fuer Strahlen- u. Kemphysik Nussallee 14-16 Bonn. ~, D 531 15

Klimenko, Alexei Old Dominion University 1134 Bolling Ave, Apt 21 1C Norfolk, VA 23508 USA [email protected] (757) 683-5806

Kolomeitsev, Evgeni European Centre for Theoretical Studies Villa Tambosi Strada delle Tabarelle 286 Villazzano(TN),1-38050 Italy [email protected] +390461314745

Kondratyuk, Sergey TRIUMF 4004 Wesbrook Mall Vancouver, B.C. ,V6T 2A3 Canada [email protected] (604) 222 1047(ext:64

Kudryavtsev, Aleksander ITEP 25 B. Cheremushkinskaia Street Moscow. RU 117259Russia25 kudryavt@,heron.iteo.ru +70953349354

Kuhn, Joaehim RPI 110 8th Street Troy, NY 12180 USA [email protected] (5 18) 276-6918

Kuhn, Sebastian Old Dominion University 1021 47th Street Norfolk. VA 23508 USA [email protected] (757) 683-5804

klemot@,isko.uni-bonn.de +49228732202

659 LeRose, John Jefferson Lab 12000 Jefferson Avenue Newport News. Va 23606 USA [email protected] (757) 269-7624

Lehmann, Albert James Madison University Brookhaven National Laboratory LEGS Group, Bldg. 5 10A Upton, 11973 NY [email protected] (631)344-8137

Liao, Xiaodong Columbia University 538 West 120th Street #74 New York ,NY 10027 USA xdliao&hvs.columbia.edu (212) 854-3801

Ligterink, Norbert University of Pittsburgh Department Physics & Astronomy 3941 O'Hara Street Pittsburgh ,PA 15260 USA no1 l&itt.edu (4 12) 624-9041

Liu, Keh-Fei University of Kentucky Department of Physics and Astronomy Lexineton . KY 40506 USA [email protected] (859) 257-4849

Liyanage, Nilanga University of Virginia 12000 Jefferson Ave MS 12H Newoort ews , VA 23693 [email protected] (757) 269-7254

Lomon, Earle MIT 6-302 77 MassachusettsAvenue Cambridge, MA 02140 USA lomon@,ns.mit.edu (617) 253-4877

Lung, Allison Jefferson Lab 12000Jefferson Avenue Newport News, VA 23606 USA lung@,iIab.org (757) 269-7255

Lutz, Matthias GSI Planckstrabe 1 Darmstadt ,D-6429 1 Germany m.lutz@,gsi.de +496159 71 0

Lvov, Anatoly Lebedev Physical Institute Leninsky Prospect, 53 Moscow, 119991Russia Ivov@,x4u.loi.mheo.ru

LlJring, Ulrich UniversiUt Bonn Institut Air Theoretische Kernphysik Nussallee 14-16 Bonn .53115 Germanv loenng~itku.uni-bonn.de +49228732374

Maas, Frank Maim University Institut h e r Kernphysik Johann-Joachim-Becher-Weg45 Maim. D-55099 Germanv maas@,koh.uni-mainz.de +49 6131 3925807

660 Mack, David Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255

Madey, Richard Kent State University Physics Department Jefferson Lab Newport News, VA 23606 USA madey@uhvsicskentedu (757) 269-5510

Manley, Mark Kent State University Physics Department 105 Smith Hall Kent, OH 44242 USA manlev@,kent.edu (330) 672-2407

Markowitz, Pete Florida International University CP 208 /Physics Department Miami, FL 33199 [email protected] (305) 348-1710

Mecking, Bernhard Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7561

Melnitchouk, Wally Jefferson Lab Theory Group, MS 12H2 12000 Jefferson Avenue Newoort News. VA 23606 USA meIr;ita,i.ilab.o& (757) 269-5854

Menze, Dietmar Physikalisches Institut University Bonn BOM, 53115 Germany menze0.Dhvsik.uni-bonn.de +49 228 733248

Merkel, Harald Universitaet Mainz Institut h e r Kernphysik Bechenveg 45 Mainz, 55099 Germany

Merkel@,kuh.uni-mainz.de +49 6131 39 25812

Messchendorp, Johan University of Giessen I1 Physikalisches Institut Heinrich-Buff-Ring 16 Giessen , D-35392 Germanv Johan.Messchendo&uhyii k.uni-eiessen.de +49 6419 933272

Mestayer, Mac Jefferson Lab 12000 Jefferson Avenue Newport News ,VA 23606 USA mestaver@,ilab.org (757) 269-7252

Meb, Andreas Free University, Amsterdam Division of Physics and Astronomy, Faculty of Science De Boelelaan 1081 Amsterdam ,1081 HV The Netherlands [email protected] +31204447851

Michaels, Robert Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA romO.ilab.org (757) 269-7410

661

+33473407272

Miller, Gerald University of Washington Department of Physics P.O. Box 351560 Seatle ,WA 98195-1560 USA [email protected] (206) 543-2995

Minehart, Ralph University of Virginia Physics Department Charlottesville ,VA 22901 USA rcm4v@,vir~inia.edu (434) 924-6785

Miskimen, Rory University of Massachusetts Department of Physics LGRT 417L Amherst. MA 01003 USA [email protected] (413) 545-2400

Morel, Danielle Florida State University Physics Department Tallahassee. FL 32306-4350 USA [email protected] (850) 644-1257

Nakano, Takashi RCNP, Osaka University 10-1 Mihogaoka Ibaraki .Osaka 567-0047 Jauan [email protected] +81 6 6879 8938

Nanda, Sirish Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA nand@,iIab.org (757) 269-7176

Narodetskii, Ilia ITEP BCheremushkinskaya 25 Moscow, 117218 Russia [email protected] +7 095 1299547

Niculescu, Gabriel Ohio University/JLab MS28F 12000 Jefferson Ave Newuort News. VA 23606 USA [email protected] (757) 269-7310

Niculescu, Ioana Jefferson Lab 12000 Jefferson Avenue Newuort News. VA 23606 USA [email protected] (757) 269-7255

Niyazov, Rustam Old Dominion University 1110 Bolling Ave #11A Norfolk, VA 23508 USA [email protected] (757) 683-5807

Noguera, Santiago Universidad de Valencia Departamento de Fisica Teorica C. Dr. Moliner, 50 Burjassot (Valencia) ,46100 SPAIN [email protected] +34 963 86 45 11

Michel, Bernard Clermont-Ferrand Laboratoire de Physique Corplsculaire Universite Blake Pascal de Clermont-Ferrand Aubiere ,63177 France

michelb@,clermont.in2u3.fr

662 Normand, Kristoff Basel University Institut h e r Physik Klingelbergstrasse82 Basel, 4056 Switzerland [email protected] +41612673746

Norvaisas, Egidijus Institute of Theoretical Physics and Astronomy Gostauto 12 Vilnius ,2600 Lithuania [email protected] +370 2 612906

Nozar, Mina Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA nozarm@,ilab.org (757) 269-7175

Ostrick, Michael Physikalisches lnstitut University Bonn Nussallee 12 BOM , 5 3 1 15 Germany

Page, Philip Los Alamos National Laboratory T-16, MS B283 Los Alamos ,NM 87545 USA p r o a l an].gov (505) 667-4835

Paris, Mark Los Alamos National Laboratoly T-16, MS B283 Los Alamos ,NM 87545 USA [email protected] (505) 667 0673

Pasquini, Barbara European Centre for Theoretical Studies Villa Tambosi, Strada dellaTabarelle, 286 Villazzano (Trento) ,I-38050 Italy pasauini@,ect.it +39 0461 314729

Pasyuk, Eugene Arizona State University Jefferson Lab, MS16B 12000 Jefferson Avenue Newport News , VA 23606 USA [email protected] (757) 269-6020

Price, John UCLA 14340 Addison Street #210 S h e w Oaks .CA 91423 USA [email protected] (310) 206-4943

Protopopescu, Dan University of New Hampshire Physics Department DeMeritt Hall 205 Durham. NH 03824 US protooo&ilab.org (603) 862-1685

Qattan, Issam Northwestem University/JLab 12000 Jefferson Avenue Newport News ,VA 23606 USA aattan@,ilab.org (757) 269-5794

Radici, Marco INFN - Sezione di Pavia via Bassi 6 Pavia, I 27100 Italy [email protected] +39 0382 507451

[email protected] +49228732447

663 Radyushkin, Anatoly Jefferson Lab Theory Group MS 12H2 12000 Jefferson Avenue NewDort News. VA 23606 USA radv;[email protected] (757) 269-7377

Reichelt, Tilmann Physikalisches lnstitut Uni Bonn Nussallee 12 Bonn, 53 I15 Germany [email protected] +49 0228 73 36 96

Reinhold, Joerg Florida Internatioml University &Jefferson Lab Department of Physics Miami, FL 33199 USA reinhold@,fiu.edu (305) 348-6422

Reitz, Bod0 Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA reitz@,ilab.org (757) 269-5064

Richards, David Jefferson Lab Theory Group, MS 12H2 12000 Jefferson Avenue NewDort News. VA 23606 USA

Roberts, Winston Jefferson Lab Theory Group, MS 12H2 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7062

& (757) 269-7736 Roche, Julie The College of William and Mary Physics Department P.O. Box 8795 Williamsburg ,VA 23187 USA jroche@,ilab.org (757) 269-7735

Ronchetti, Federico INFN-Frascati 40, Via E. Fermi Frascati ,Rome 00044 Italy ronchetti@,ilab.org +39 069 4032569

Sadler, Michael Abilene Christian University ACU Box 27963 Abilene .TX 79639 USA sadler@,Dhvsics.acu.edu (915) 674-2189

Saez, Jorge Jefferson Lab 12000 Jefferson Avenue Newport News ,VA 23606 USA isaez@ iI ab.org (757) 269-5387

Saha, Arun Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA saha(iiilab.org (757) 269-7605

Santopinto, Elena INFN-Genova v. Dodecaneso 33 Genova, 1-16146 Italy [email protected] +39 0103 536219

664 Sargsian, Misak Florida International University Department of Physics Miami, FL 33199 USA sarpsian(ii,fiu.edu (305) 348-3954

Sato, Toru Osaka University Department of Physics, Graduate School of Science Machikaneyama 1-1 Tovonaka .Osaka 560-0043 Jaoan tsato~ehvs.sci.osaka-u.ac.io +81668505345

Schat, Carlos Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-5839

Schicrholz, Gerrit DESY Notkestr. 85 Hamburg. 22603 Germanv Gerrit.Schierholz~desv.de +49 175 9346213

Schoch, Berthold University of Bonn Physikalisches InstiM Nussallee 12 Bonn ,NRW 53 115 Germany schoch0.ohvsik.uni-bonn.de +49228732344

Seimetz, Michael University of Mainz Institut fuer Kemphysik Becherweg 45 Maim ,55099 Germany seimetzmkoh.uni-mainz.de +49 6131 3922935

Sharabian, Youri Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-5829

Simonov, Yuri Jefferson Lab Theory Group MS 12H2 12000Jefferson Avenue Newoort News, VA 23606 USA simoiovmiIab.&g (757) 269-6051

Simula, Silvano

Sirca, Simon MIT Room 26-402 77 Massachusetts Avenue Cambridge, MA 02139 USA sirc@,rnitlns.mit.edu (617) 258-5438

INFN - Sezione Roma 111 Via della Vasca Navale 84 Rome, Italy 1-00146Italy [email protected] +39 06 5517 7053

Smith, Elton Jefferson Lab 12000 Jefferson Avenue Newoort News. VA 23606 USA eltonkhlab.org (757) 269-7625 '

Smith, Cole University of Virginia Physics Department 382 McCormick Road Charlottesville ,VA 22904-4714 USA cole@,nstar.ohvs.virginiaedu (434) 924-6806

665 Smith, Greg Jefferson Lab 12000Jefferson Avenue Newport News, VA 23606 USA smithe@,ilab.org (757)269-7255

Stahov, Jugoslav Abilene Christian University 320 Foster Science Building, ACU Box 27963 Abilene , TX 79699 USA stahov@,Dhvsics.acu.edu (915)674-2166

Stibunov, Victor Institute for Nuclear Physics at Tomsk Politechic INP, Lenina 2A Tomsk ,634050Russia stib@,noi.tou.ru +7 3822 423992

Strakovsky, Igor George Washington University Physics Department 725 21st Street, NW Washington ,DC 20052 USA [email protected] (703)726-8344

Strauch, Steffen George Washington University Department of Physics 725 21st Street, N.W. Washington, DC 20052 U.S.A. strauch@,ewu.edu (202)994-6579

Suleiman, Riad MITlJLab 12000 Jefferson Avenue Newport News ,VA 23606 USA [email protected] (757)269-6990

Tang, Liguang Hampton University 130 East Tyler Street Hampton, VA 23668 USA [email protected] (757)269-7255

Tatischeff, Boris Institut de Physique Nucleaire Orsay Cedex, France Orsay, 91406 France tati@,iono.in2o3.fr +33 1691 55182

Taylor, Simon Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757)269-7130

Thoma, Ulrike Jefferson Lab 12000Jefferson Avenue Newuort News. VA 23606 USA

Thomas, Anthony Adelaide University Director CSSM Adelaide, SA 5005 Australia [email protected] +61 8 8303 3547

Tireman, William Kent State University 480-KYoung's Mill Lane Newport News, VA 23602 USA [email protected] (757)269-7035

uthoinailab.o&

(757)269-7432

666 Todor, Luminita Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213 USA [email protected] (757) 269-5538

Ulmer, Paul Old Dominion University Department of Physics Norfolk, VA 23529 USA [email protected] (757) 683-5851

Urban, Jozef University of Bonn IKP FZ Juelich Leo Brand Str. 1 Juelich ,52425 Germany [email protected] +492461615884

Van Hoorebeke, Luc University or' Gent Dept. of Subatomic and Radiation Physics, RUG Proelbinstmat 86 Gent, 9000 Belgium luc@,inwfsunl .rup.ac.be + 32 9 2646543

Van der Steenhoven, Gerard NIKHEF P.O. Box41882 Amsterdam NL 1009 DB Netherlands [email protected] +31205922145

Vanderhaeghen, Marc University Mainz lnstitut fuer Kemphysik J.J. Becher Weg 45 Mainz ,55099 Germany

Vassallo, Andrea INFN-Genova Via Dodecaneso 33 Genova.,Italv,116146 Italv vassallo(ii~e.infn.it +39 010 3536468

Walcher, Thomas Universitn Mainz lnstitut f i r Kemphysik J.J. Becher-Weg 45 Mainz ,55099 Germany walcher@k&.uni-mainz.de +49 6131 3925197

Warren, Glen University of Basel Jefferson Lab,MS 16B-107 12000Jefferson Avenue NewDort News . VA 23606 USA [email protected] (757) 269-5797

Weise, Wolfram ECT* Trento Physics Department Technical University of Munich Garching ,D-85747 Germany [email protected] +39 0461 314760

Weiss, Christian Universitat Regensburg Institut fuer Theoretische Physik Regensburg, - . D-93053 Germanv christian.weiss(~hvsik.uni-repensburg.de +49 941 943 2187

Weygand, Dennis Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA wevgand(ii,ilab.org (757) 269-5926

marcvdh(ii,keh.uni-mainz.de +49 613 1 3924277

667 Wojtsekhowski, Bogdan Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA bogdanw(dilab.org (757) 269-7191

Wood, Steve Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255

Workman, Ron George Washington University Virginia Campus 20101 Academic Way Ashburn, VA 20147 USA [email protected] (703) 726-8345

Yamazaki, Hirohito Tohoku University Kakuriken Mikamine 1-2-1, Taihaku-ku Sendai ,Miyagi 982-0826 JAPAN [email protected] +81227433433

Yan, Chen Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255

Yoshida, Rik Argonne National Lab 9700 S Cass Ave Argonne ,IL 60439 USA rik.voshida@,anl.gov (630) 252-7874

Zegers, Remco

RCNP Osaka University 10-1 Mihogaokq lmbaraki Osaka, 567-0047 Japan zegers@s~rineS.or.io +7915808083116


Author Index HERMES, 392, 558 LEGS, 619 LEPS, 234, 506 Neutron EDM, 443 TAPS, 545 Crowder, J., 550

ACUS,A., 359 Arrington, J., 338, 550, 567 Aruga, Y., 541 Avakian, H., 319 Aznauryan, I., 460 Bacchetta, A., 311 Bagdasarian, H., 575 Barnes, P. D., 443 Becher, T., 102 Belitsky, A., 371 Belozerova, T. S., 480 Bennhold, C., 456 Bernstein, A. M., 413, 595 Biselli, A., 323 Boffi, S., 367 Borasoy, B., 599 Brash, E., 256 Braun, V. M., 363 Burkert, V., 29, 489

d’Angelo, A., 140 Dashyan, N., 575 Davies, C., 53 Debruyne, H., 571 Denizli, H., 472 Desplanques, B., 417, 421 De Vita, R., 210 Diakonov, D., 153 Diehl, M., 280 Dohrmann, F., 585 Drechsel, D., 396 Ducote, J., 498 Dugger, M. R., 476

Capstick, S., 17, 448 Cassing, W., 525 Christy, M. E., 307 Cole, L. C., 327 Cano, F., 417 Cohen, T. D., 425 Collaboration A1, 346 A2, 545 CLAS, 323, 327, 460, 464,476, 489, 498, 502, 575, 581 COSY-ToF, 409 Go, 355 Hall A, 332 Hall A E98-108, 332 Hall A/VCS, 268, 430, 434 Hall C E89-009, 589

669

Edwards, R., 43 Egiyan, H., 460 Egiyan, K., 575 Elouadrhiri, L., 384 Ent, R., 550 Eyrich, W., 409 Falter, T., 521 Fernhdez, F., 468 Fonvieille, H., 268 Forest, T., 303 Frick, P. G., 480 Fries, R. J., 363 Friman, B., 533 Funsten, H., 489 Garcilazo, H.,

494

670

Garrow, K., 562 Garutti, E., 558 Giannini, M. M., 438 Glozman L., 367, 425 Gockeler, M., 627 Goity, J. L., 611 Gonzalez, P., 417, 468, 494 Gorchtein, M., 396 GrieBhammer, H. W., 452 Hemmert, T. R., 631 Henner, V. K., 480 Hirota, K., 541 Horsley, R., 627 Huber, G. M., 529 Iijima, A., 541 Ito, Y., 541 Janssen, S., 510 Jeschonnek, S., 222 Joo, K., 464 Julia-Diaz, B., 468 Kaiser, R., 392 Kanda, H., 541 Kasagi, J., 541 Katoh, A., 541 Katsuyama, T., 541 Keppel, C., 550 Kino, K., 541 Kinoshita, T., 541 Klein, F., 489 Klempt, E., 198 Klink, W., 367 Kolomeitsev, E. E., 603 Kondratyuk, S., 514 Konno, O., 541 Kuhn, J., 323 Kundu, R., 311

Lee, F. X., 643 Lehmann, A., 619 Lenz, A., 363 Leupold, S., 521 Liao, X., 635 Lomon, E., 342 Lutz, M. F. M., 533, 603

Maas, F., 165 Madey, R., 350 Maeda, K., 541 Mahnke, N., 363 Manke, T., 635 Markowitz, P., 332 Maynard, C. M., 627 Merkel, H., 115 Messchendorp, J. G., 545 Metz, A., 311, 396 Miller, J., 65 Morel, D., 448 Mosel, U., 521 Mulders, P., 311 Muller, D., 371 Nakabayashi, T., 541 Nakano, T., 234 Narodetskii, I. M., 639 Nefkens, B. M. K., 498 Nicolet, A., 421 Niculescu, G., 502 Niculescu, I., 550 Niyazov, R. A., 581 Noguera, S., 417 Noma, T., 541 Norvaisas, E., 359 Oset, E., 456 Osipenko, M., 315 Ostrick, M., 403 Page, P., 243

67 1

Pasquini, B., 396 Pasyuk, E. A., 476 Pleiter, D., 627 Plessas, W., 367 Price, J. W., 498 Rackow, P. E. L., 627 Radici, M., 367 Ramos, A., 456 Reinhold, J., 589 Ricco, G., 315 Richards, D. G., 627 Ripani, M., 489 Riska, D. O., 359 Ritchie, B. G., 476 Roche, J., 355 Ryckebusch, J., 510, 571 Sadler, M., 189 Santopinto, E., 438 Sargsian, M. M., 554 Sato, T., 178 Schat, C. L., 485 Schierholz, G., 126, 627 Scholten, O., 514 Seimetz, M., 346 Shimizu, H., 541 Simula, S., 315, 554 Stahov, J., 615 Stein, E., 363 Strauch, S., 537 Strikman, M. I., 554

Suleiman, R., 607 Taiuti, M., 315 Tajima, Y., 541 Takahashi, T., 541 Terasawa, T., 541 Theussl, L., 421 Thomas, A., 3 Todor, L., 434 Trusov, M. A., 639 Valcarce, A., 468, 494 Vanderhaeghen, M., 396 van der Steenhoven, G., 78 van Hoorebeke, G., 430 van Orden, J. W., 222 Vasallo, A., 438 Vijande, J., 494 Wagenbrunn, R. F., 367 Weinstein, L. B., 581 Weise, W., 290, 631 Weiss, C., 388 Wolf, GY., 533 Yamazaki, H., 541 Yorita, T., 541 Yoshida, H. Y., 541 Yoshida, R., 90 Zegers, R. G. T., 506


Baryons 2002 gth INTERNATIONAL CONFERENCE

ON THE STRUCTURE OF BARYONS Jefferson Lab Newport News, Virginia March, 3 - 8, 2002

Agenda Sunday, March 3 18:OO Reception and Registration

Monday, March 4 Plenary Session (Chair: P. Barnes) 8:30 8:45 9:40 10:25 10:50 11:35 12:20

L. Cardman A. Thomas S. Capstick V. Burkert R. Edwards

Welcome Successes and Open Issues in Baryon Physics Baryon Spectroscopy in the Quark Model Break Electroexcitation of Nucleon Resonances Baryon Spectroscopy on the Lattice Lunch

Plenary Session (Chair: B. Schoch) 14:OO C. Davies 14:45 G. Miller 15:30 16:OO Yu. Simonov 16:30 G . v.d. Steenhoven 17:15 R. Yoshida

Heavy Quark Physics on the Lattice Hadrons in the Nuclear Medium Break Baryon Spectrum and Magnetic Moments in Non-perturbative QCD Polarized Structure Functions Proton Structure Results from the HERA Collider

673

674

Tuesday, March 5 Plenary Session (Chair: D. Ernst) 8:30 9:15 1o:oo 10:30 11:15 12:oo

T. Becher H. Merkel G. Schierholz A. d’Angelo

Baryon Chiral Dynamics Experimental Tests of Chiral Symmetry Break Hadron Structure from Lattice QCD Photoexcitation of N* Resonances Lunch

Session on Structure Functions and Form Factors I

- I1

Convenors: E. Beise, A. Bruell, X. Ji, and M. Vanderhaeghen 13:30 G. Cates 13:50 T. Forest 14:lO M.E. Christy 14:30 A. Metz 14:50

S. Simula

15:lO H. Avagyan 15:30 S. Liuti 15:50 16:30 J. Kuhn 16:30

L.C. Smith

16:30 P. Markowitz 16:30 I. Niculescu 16:30

J. Arrington

16:30 E. Lomon

The Spin Structure of the Neutron and 3He at Low Q2and the Extended GDH Sum Rule The Q2-Dependence of Polarized Structure Functions Measurement of R = u ~ / inu the ~ Nucleon Resonance Region The Collins Fragmentation Function in Hard Scattering Processes Leading and Higher Twists in the Proton Polarized Structure Function GY at large Bjorken X Single-Spin Asymmetries at CLAS Signals of Local Duality from a Perturbative QCD Analysis of Inclusive ep Scattering Break Study of the A( 1232) Using Double-Polarization Asymmetries CLAS Measurement of Electroproduction Structure Functions Kaon Electroproduction at Large Momentum Transfer Moments of the Proton F2 Structure Function at Low Q2 Are Recoil Polarization Measurements of Gg /GL Consistent with Rosenbluth Separation Data? Effect of New Data on Extended VDM/GK Nucleon Form Factors

675

Session on Baryon Structure and Spectroscopy I

- I1

Convenors: T.S. Harry Lee, Mark Manley, Berthold Schoch, and Silvano Simula 13:30 13:45 14:15 14:30 14:45

15:OO 13:15 15:30 15:45 16:30 16:45 17:OO

17:15 17:30 17:45 18:OO 18:15

First Measurement of the GDH Integral Between 200 and 800 MeV The GDH-Experiment at ELSA T . Michel Meson-Photoproduction with the Crystal-Barrel M. Ostrick Detector at ELSA W. Eyrich K-Meson Production Studies with the TOFSpectrometer at COSY A. Bernstein First Simultaneous Measurements of the T L and TL' Structure Fhnctions in the y* + A Reaction P. Gonzalez Photoproduction of Resonances in a Relativistic Quark Pair Creation Model Relationship of the 3P0 Decay Model to Other B. Desplanques Strong Decay Models Partial wave analysis of the J / Q + p-fiand X. Ji Other Channels Break L. Glozman Do We See Chiral Symmetry Restoration in Baryon Spectrum? L. Van Hoorebeke Virtual Compton Scattering: Results From Jefferson Lab Virtual Compton Scattering and Neutral Pion L. Todor Electro-production from the Proton in the Nucleon Resonance Region The Hypercentral Constituent Quark Model E. Santopinto A Relativistic Quark Model of Baryons with U. Loering Instanton Induced Forces New Search for the Neutron Electric Dipole P. Barnes Moment D. Morel qQ Loop Effects on Baryon Masses H. Griesshammer Learning from Dispersive Effects in the Nucleon Polarisabilities A. Braghieri

676

Session on Hadrons in the Nuclear Medium I - I1 Convenors: Nicola Bianchi and Misak Sargsian

13:30 T. Falter

Nuclear Shadowing and In-Medium Properties of the po Scalar- and Vector-Meson Production in Hadron13:50 W. Cassing Nucleus Reactions Helicity Signatures in Subthreshold po Production 14:lO G. Huber on Nuclei From Meson- and Photon-Nucleon Scattering to 14:30 M. Lutz Vector Mesons in Nuclear Matter Polarization Transfer in the 4He(E',e ' g 3 H Reaction 14:50 S. Strauch S11(1535) Resonance in Nuclei Studied with the 15:lO H. Yamazaki C(y, Q) Reaction 15:30 J. Messchendorp Double-Pion Production in y A Reactions Break 15:50 Quark-Hadron Duality in Inclusive Electron-Nucleus 16:30 I. Niculescu Scattering Neutron Structure Function and Inclusive DIS 13:50 S. Simula From 3Hand 3He Targets at Large Bjorken-X Search for a Possible Nuclear Dependence in 17:lO M.E. Christy R ( x, Q 2)= ( T L / ( T T at Small x and Q2 Hadron Formation in Nuclei in Deep-Inelastic 17:30 E. Garutti Lepton Scattering Nuclear Transparency from Quasielastic A(e, e'p) 17:50 K. Garrow Reactions up to Q2 = 8 . 1 ( G e V / ~ ) ~ Deuteron Photodisintegration at High Momentum 18:lO X. Jiang Transfer

+

Wednesday, March 6 Plenary Session (Chair: J. Kasagi) 8:30 9:15

D. Diakonov F. Maas

1o:oo 10:30 T. Sat0 11:15 M. Sadler 12:OO E. Klempt

Instantons and Baryon Dynamics The Strangeness Contributions to the Form Factors of the Nucleon Break Electromagnetic Production of Pions in the Resonance Region - Theoretical Aspects Hadronic Production of Baryon Resonances Baryon Resonances and Strong QCD

677

Session on Structure Functions and Form Factors I11 14:OO G. Warren G; via $z,efn)p 14:15

M. Seimetz

14:30 14:45

R. Madey J. Roche

15:05

S. Covrig

15:25

E. Norvaisas

15:45

R. Fries

16:05

M. Radici

Measurement of the Electric Form Factor of the Neutron at Q2 = 0.6 - 0.8 (GeV/c)2 Neutron Electric Form Factor via Recoil Polarimetry The GoExperiment: Measurement of the Strange Form Factor of the Proton Status of SAMPLE Deuterium Experiment at 125 MeV The Nucleon Form Factors in the Canonically Quantized Skyrme Model Soft Contribution to the Nucleon Electromagnetic Form Factors Electroweak Properties of the Nucleon in a Chiral Constituent Quark Model

Session on Baryon Structure and Spectroscopy I11 14:OO C. Bennhold 14:15

H. Egiyan

14:30

K. Joo

14:45

P. Gonzalez

15:OO

H. Denizli

15:15 15:30

E. Pasyuk D. Ernst

15:45

V. Henner

16:OO C. Schat

Dynamical Baryon Resonances with Chiral Lagrangians Pion Electroproduction in the Second Resonance Region Using CLAS Electron Beam Asymmetry Measurements From Exclusive K O Electroproduction in the A (1232) Resonance Region K N N *(1440) and a N N *(1440) Coupling Constants from a Microscopic N N + N N * (1440) Potential q Electroproduction at and Above the Sll(l535) Resonance Region with CLAS 11 Photoproduction From the Proton Using CLAS Meson Cloud Contribution to the Masses of the Nucleon, Delta, and Roper Why is the Wavelet Analysis Useful in Physics of Resonances? Example of p’ and W” States L=l Baryon Masses in the l/Nc Expansion

678

Session on Lattice QCD and Heavy Quarks Convenors: Keh-Fei Liu and Shigemi Ohta 14:OO D. Richards

Lattice Calculation of Baryon Masses Using the Clover Fermion Action 14:25 W. Weise Nucleon Magnetic Moments, Their Quark Mass Dependence and Lattice QCD Extrapolations 14:50 W. Melnitchouk Chiral Extrapolation of Lattice Moments of Proton Quark Distributions 15:15 X. Liao Heavy Quark Spectrum from Anisotropic Lattices 1540 I. Narodetskii The Doubly Heavy Baryons in the Nonperturbative QCD Approach 16:05 F. Lee Excited Baryons and Chiral Symmetry Breaking of QCD Poster Session Group dinner at the Mariners Museum

16:30 18:30

Thursday, March 7 Plenary Session (Chair: E. Beise) 8:30 9:15 1o:oo 10:30 11:15 12:oo

R. DeVita

S. Jeschonnek T. Nakano P. Page

Spin Structure Functions in the Resonance Region Quark-Hadron Duality Break First Results from SPRING-8 Hybrid Baryons Lunch

Session on Structure Functions and Form Factors IV 14:OO A. Belitsky 14:20 L. Elouadrhiri 14:40

C. Weiss

15:OO B. Fox 15:20 R. Kaiser 15:40

B. Pasquini

Nucleon Hologram With Exclusive Leptoproduction Deeply Virtual Compton Scattering at Jefferson Lab, Results and Prospects Twist-3 Effects in Deeply Virtual Compton Scattering Made Simple Exclusive Processes Measured at HERMES Measurement of Hard Exclusive Reactions with a Recoil Detector at HERMES Dispersion Relation Formalism for Virtual Compton Scattering Off the Proton

679

Session on Baryon Structure and Spectroscopy IV Search for Resonance Contributions in Multi Pion Electroproduction with CLAS QCD Confinement and Missing Baryons Problem J. Vijande Photoproduction of the Z Hyperons J.W. Price Open Strangeness Production in CLAS G. Niculescu K+ Photoproduction at LEPS/SPRING-8 R. Zegers New Results on Spin Rotation Parameter A in the D. Svirida npelastic Scattering in the Resonance Region Kaon Photoproduction: Background Contributions S. Janssen and Missing Resonances S. Kondratyuk Dynamical Description of Nucleon Compton Scattering at Low and Intermediate Energies: From Polarisabilities to Sum Rules

14:OO F. Klein 14:15 14:30 14:45 15:OO 15:15 15:30 15:45

Session on Hadrons in the Nuclear Medium I11 16:30

J . Arrington

16:47 D. Debruyne 17:04 K. Egiyan 17:21 R. Niyazov 17:38 E. Piasetzky 17:55 18:12

F. Dohrmann J. Reinhold

Nucleon Momentum Distributions From a Modified Scaling Analysis of Inclusive Electron-Nucleus Scattering Medium Effects in A(Z, e l 3 Reactions at High Q2 Study of Nucleon Short Range Correlation in A(e,e') Reaction at X B > 1 N N Correlations Measured in 3 H e ( e ,e'p p)n Looking at Close Nucleons in Nuclei by High Momentum Transfer Reactions Electroproduction of Strangeness on Light Nuclei Hypernuclear Spectroscopy of i z B by the ( e ,e'Kf) Reaction

680

Session on Chiral Physics I - I1 Conven0rs:A.M. Bernstein, U. van-Kolck, and U.G. Meissner 14:OO A.M. Bernstein 14:24 B. Borasoy 14:48 E. Kolomeitsev 15:12

R. Suleiman

15:36 16:30 16:54

R. Miskimen J. Goity A. Gasparian

17:18

J. Stahov

17:42

A. Lehmann

Goldstone Boson Dynamics: Introduction to the Chiral Dynamics Session 77’ Electroproduction Off Nucleons A Unified Chiral Approach to Meson-Nucleon Interaction Measurement of the Weak Pion-Nucleon Coupling Constant 7H: , from Backward Pion PhotoProduction Near Threshold on the Proton Measurement of the Anomalous Amplitude y + 3n 7ro + y y t o NLO in ChPT A Precision Measurement of the Neutral Pion Lifetime at Jefferson Lab The Dependence of the ”Experimental” Pion Nucleon Sigma Term on Higher Partial Waves First Beam-Target Double-Polarization Measurements Using Polarized HD at LEGS

Friday, March 8 Plenary Session (Chair: T. Walcher) 8:30 9:15 1o:oo 10~30 11:15 12:oo 14:OO

E. Brash H. Fonvieille

M. Diehl W. Weise

Nucleon Electromagnetic Form Factors Virtual Compton Scattering Break Generalized Parton Distribution Baryons 2002: Outlook Lunch Tour of the experimental halls


Baryons, 2002

Quarks, baryons and chiral symmetry

Chiral Soliton Models for Baryons

Mesons and Baryons

Chiral Soliton Models for Baryons

Chiral Soliton Models for Baryons

Quarks, Baryons and Chiral Symmetry

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Baryons, 2002

Quarks, baryons and chiral symmetry

Chiral Soliton Models for Baryons

Mesons and Baryons

Chiral Soliton Models for Baryons

Chiral Soliton Models for Baryons

Quarks, Baryons and Chiral Symmetry

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