Proceedings of the International Symposium Electrophotoproduction of Strangeness on Nucleons and Nuclei: Sendai, Japan 16-18 June 2003

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Proceedings o f the International Symposium

Electrophotoproduction

sfangeness o n Nucleons and N u c l e i

This page intentionally left blank

K MAEDA H TAMURA S N NAKAMURA 0 HASHIMOTO Tohoku University, Japan

16 - 18 June 2003

Sendai, Japan

Proceedings o f the International Symposium

Electrophotoproduction

Sfangeness o n Nucleons and N u c l e i

Y N E W JERSEY

LONDON

SINGAPORE

World Scientific *

BElJlNG

SHANGHAI

*

HONG KONG

. TAIPEI

*

CHENNAI

Published by World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore 596224

USA ofice: Suite 202, 1060 Main Street, River Edge, NJ 07661 UK ofice: 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

ELECTROPHOTOPRODUCTIONOF STRANGENESS ON NUCLEONS AND NUCLEI SENDAI03 Copyright 0 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof; may not be reproduced in any form or by any means, electronic or mechanical, includingphotocopying, 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 981-238-752-8

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

Chairperson Osamu Hashimoto

Symposium Organization International advisory committee P.D. Barnes(Los Alamos) C. Bennhold(G. Washington) T. Bressani(Torino) L. Cardman(Jlab) I.T. Cheon(Yonsei) Ed. Hungerford(Houston) K. Imai(Kyoto) J. Kasagi(LNS, Tohoku) T. Kishimoto(0saka)

T. Motoba(0saka E.C.) M. Oka(Tokyo Inst. Tech.) E. Oset(Va1encia) 6. Saghai(Sac1ay) C. Schaerf(Rome) B. Schoch(Bonn ) M. Sotona(Praha) H. Toki(RCNP, Osaka) T. Walcher(Mainz)

Local organizing committee Y. Fujii(Tohoku) 0. Hashimoto(Tohoku, Chair) H. Kanda(Tohoku) K. Maeda(Tohoku) S .N. Nakamura(Tohoku)

H. Shimizu(LNS, Tohoku) T. Takahashi(Tohoku) T. Tamae(LNS, Tohoku) H. Ta mura(Tohoku) H. Yamazaki(LNS, Tohoku)

Supported by Sendai Convention Bureau by the specially promoted program “Investigation of A hypernuclei by electromagnetic probes” (Grant in aid of MEXT, Japan) V


Preface The International Symposium on Electrophoto-Production of Strangeness on Nucleons and Nuclei(SENDAIO3) was held at the Sendai International Center, Sendai, Japan from 16 June through 18 June, 2003. The symposium was motivated by recent progresses of the research on electrophoto-production of strangeness at GeV electron-beam facilities as well as extensive theoretical investigation in the field. The symposium focused the discussions on the strangeness production processes by the electromagnetic interaction both on nucleons and nuclei, and strangeness physics. It was planned as a small-sized international symposium with an intention to serve an opportunity for intensive discussions in an informal atmosphere. Both experimentalists and theorists active in the field gathered, exchanged information on recent activities and discussed future prospects of the field. Symposium started with overview talks on electromagnetic strangeness production, and then went on to the presentation on recent theoretical and experimental progresses of strangeness production. In particular, strangeness production through electromagnetic interaction on nucleons ((7, K + ) ,(y,Ko),(e,e’K+) reactions) and production of mesons such as eta, phi mesons and exotics such as Q+ were presented. Hypernuclear physics with electromagnetic probes, as (e,e!K+) and y ray hypernuclear spectroscopy were also intensively discussed. Most updated ongoing programs and future plans at the accelerator facilities, ELSA, JLAB(HALL A,B,C), Spring-8, GRAAL, LNS(TOHOKU), DAaNE, MAMI-C, were also reported, which, we believe, manifested sound and promising future of the field. A one-day workshop was also organized at the physics department as a pre-symposium on 15 June on the Aoba-yama campus of Tohoku university. In the pre-symposium, empahsis was laid on the recent progress of hypernuclear physics with not only electron beams but also with hadronic beams. Introductory talks on recent status of hypernuclear physics were given, followed by presentations of young scientists. This proceedings also include the manuscripts of the talks presented in the pre-symposium. In addition, an informal discussion sessions were held at Sakunami hot spring, located in the suburbs of the Sendai city, in the evening of 18 June after the formal session was closed. The editors are tempted to mention that it would be a fun to find words “Hot” and ”Spring” in some of the texts of this proceedings. It was proposed at Sakunami hot spring that we vii

...

Vlll

try to include the words "Hot" and "Spring" in some combination in the manuscripts as a memory of the "Hot spring discussion". More than 100 participants joined the symposium, including 30 from abroad covering 11 countries. The editors are thankful to those who gave talks in the symposium and presymposium as well as all the participants, who made this symposium scientificallyfruitful. We hope that the proceedings well describe the current status and can serve enlightening its future direction. The symposium was supported by Sendai Convention Bureau. It was also carried out as a part of the Specially Promoted Research of Grant-inAid Scientific Research of MEXT( Ministry of Education, Culture, Sports, Science and Technology), Japan. The organizer also thanks to these funding organizations. Editors of the SENDAIO3 symposium K. Maeda T. Tamura S.N. Nakamura 0. Hashimoto

Contents Symposium Organization

V

Preface

vii

Opening Address 0. Hashirnoto

xv

1. Overview of Electromagnetic Strangeness Production Strangeness Photoproduction on Nucleons and Nuclei C. Bennhold

3

Strangeness Production Experiments at Jefferson Lab R. Schurnacher

15

Hyperon Production in Photonuclear Reactions on Protons and Deuterons: The KOC" Channel H. Liihner et al.

31

Recent Results from LEPS at Spring-8 7: Nakanofor the LEPS Collaboration

42

2. Theoretical Aspects of Strangeness Production Strangeness Production via Electromagnetic Probes: 40 Years Later B. Saghai

53

Missing Resonances in Kaon Photoproduction on the Nucleon 7: Mart, A. Sulaksono and C. Bennhold

65

The Properties of the A( 1405) in Electromagnetic Reactions A. Rarnos, J. C. Nuchel; E. Oset, T.-S. H. Lee, J. A. Oller and H. Toki

75

Analyses of the Kaon Photo- and Electro-Production in the Isobar Model 7: K. Choi, M. K. Cheoun, K. S. Kim and B. G. Yu

85

ix

X

Exotic Baryons and Multibaryons in Chiral Soliton Models K Kopeliovich

96

&,o,and 27cExchanges in p Meson Photoproduction I: Oh and T . 4 H. Lee

112

Chiral Symmetry and Surface Pion Condensation in Nuclei and Hypernuclei H. Toki, I.: Ogawa, S. Tarnenaga, K. lkeda and S. Sugirnoto

119

3. Experimental Aspects of Strangeness Production on Nucleons and Nuclei Lambda Polarization in Exclusive Electro- and Photoproduction at CLAS M. D. Mestayer for the CLAS Collaboration

137

Electroproduction of Strangeness on Light Nuclei E Dohrmann et al.

146

Kaon Electroproduction at Large Four-Momentum Transfer Z? Markowitz

152

Photoproduction of Neutral Mesons with the Crystal-Barrel Detector at ELSA K Crede

158

Kaon Photoproduction at SAPHIR for Photon Energies up to 2.6 GeV K.-H. Glander Representing the SAPHIR Collaboration

168

K+h and K+CoPhotoproduction at SPring-8lLEPS M. Surnihamafor the LEPS Collaboration

178

@ Meson Photoproduction with Linearly Polarized Photons at Spring-8

184

7: Mibe for the LEPS Collaboration Photoproduction of Mesons on Nuclei at LNS H. Yamazaki et al.

191

xi

Photoproduction of Neutral Kaons at LNS 7: Takahashi

198

Kaon Nucleus Interaction Studied by the In-Flight (K-, N ) Reaction 7: Kishimoto et al.

208

4. Spectroscopy of Hypernuclei Prospect of Photoproduction of Medium-Heavy Hypernuclei 7: Motoba, P Byd?ovskj, M. Sotona, K. Itonuga, K. Oguwu and 0. Hashimoto

22 1

High Resolution Hypernuclear Spectroscopy: (e, e’K+) Reaction M. Sotona et al.

233

First Spectroscopic Study of Hypernuclei by the (e, e’K+) Reaction 7:Miyoshi

242

Recent Progress in y-Ray Spectroscopy of Hypernuclei H. Tamura et ul.

25 1

Three- and Four-Body Structure of Light Hypernuclei E. Hiyama, M. Kamimura, 7: Motoba, 7: Yamada and I: Yamamoto

26 1

5. New Facilities A New Hypernuclear Experiment with the High Resolution Kaon Spectrometer (HKS) AT JLAB Hall C S. N . Nukarnura for JLAB EOl-011 Collaboration

273

FINUDA: Ready to Start Physics S. Marcello

283

Time Projection Chamber for Photo-Production of Hyperons K . Imai

293

xii

New yBeam Line at LNS Sendai H, Shimizu

301

6. Summary A Symposium Perspective E. K Hungerford

315

Theoretical Perspective B. E Gibson

324

Pre-symposium Recent Progress of Hypernuclear Physics 1. Y-N Interactions BRBBInteraction in the SU, Quark Model and Its Applications to Few-Body Systems I: Fujiwara

343

C+PScattering Experiments with a Scintillating Fiber Active Target H. Kanda

355

Study of Spin-Dependent Interaction between Hyperon and Nucleon M. Kurosawa, J. As&, K. Nakai, M. Ieiri for the KEK PS E289 Collaboration

360

2. Hypernuclear Spectroscopy Why Interesting to Study Structure of Light Hypernuclei? E. Hiyama, M. Kamimura, 7: Motoba, T. Yamada and I: Yamamoto

367

High-Resolution y-Ray Spectroscopy of P-Shell Hypernuclei (BNL E930) M. Ukaifor the E930-I Collaboration

377

High-Resolution y-Ray Spectroscopy of Hyperfragments Produced by Stopped K- Reactions K. Miwa et al.

382

...

Xlll

Hypernuclear Spectroscopy with the (e, e’K+)Reaction K Fujii

387

3. Hypernuclear Weak Decay Nonmesonic Decay Rates and Asymmetry Parameters of Light A-Hypernuclei K. Itonaga, 7: Motoba and 7: Ueda

397

The Mesonic and Nonmesonic Weak Decay Widths of Medium-Heavy A Hypernuclei !I Sat0 and E307 Collaboration

403

Weak Decay of Light S-Shell Hypernuclei iH, ;He and :He H. Outa for KEK-PS El67/E462 Collaboration

410

Neutron Energy Spectra from Non-Mesonic Weak Decay of :He and 12 ACHypernuclei

417

S.Okada et al. The n + p and n + n Coincidence Measurement of the Non-Mesonic Weak Decay of :He B. H. Kang for KEK-PS E462 Collaboration

42 1

Asymmetry in Non-Mesonic Weak Decay of Light Hypernuclei T Maruta for KEK-PS E462/E508 Collaboration

426

Measurement of the n- Decay Width of ;He S. Kameoka for KEK-PS E462/E508 Collaboration

430

Measurement of n? Mesonic Decay Widths (r,o)of A Hypernuclei, :He and ?C H. Yimfor KEK-PS E462/E508 Collaboration

434

Program

439

List of Participants

445


OPENING ADDRESS

OSAMU HASHIMOTO CHAIRPERSON OF SENDAI03 Department of physics, Tohoku University Sendai 980-8578, Japan E-mail hashimotOlambda.phys.tohoku.ac.jp

Ladies and gentlemen, On behalf of the organizing committee, I extend our hearty welcome to all the participants to SENDAIOS. Particularly to those from abroad, we are thankful for their participation after long long trips from home to Sendai, some of them even overcoming last-minuite troubles encountered on the way to Sendai. The subject of this symposium is "strangeness production by the electromagnetic interaction". In the past years, we saw significant progresses of the field both in experiment and in theory. ELSA has been the source of excellent data for strangeness production by real photons, Spring8 and GRAAL now yield beautiful results from their laser Compton beam facilities. Jefferson Lab has been in full operation and is now steadily producing high quality and exciting new data. And, DA@NEis about to start taking data. All these experimental acitivities as well as related theoretical efforts are to be reported in the symposium. Seeing many of the active scientists here, we believe the field is expanding under the healthy condition and can expect further progress in the near future. Tohoku group has been working on strangeness nuclear physics, in particular, on the spectroscopy of hypernuclei using pion and kaon beams available at KEK and BNL. Recently, we have extended our research activity to hypernuclear investigation with electromagnetic interaction. In this conxv

XVI

text, in January 1998, we organized a workshop on ”the spectroscopy of hypernuclei, SENDAI98”, soon after we formed a new experimental group in strangeness nuclear physics at Tohoku university. Two years later in December 1999, a workshop on ”Hypernuclear physics with electromagnetic beams, HYPJLAB99” was held at Hampton University under the support from Jlab, Hampton University and Tohoku University. This workshop, SENDAI03, is, in a sense, the third of a series of these workshops.

I would also like to mention that Tohoku University, here in the city of Sendai, has a tradition of nuclear physics with electron beams. It currently operates a 200 MeV electron linear accelerator, which was constructed some 30 years ago, at Laboratory of Nuclear Science(LNS) on the Mikamine campus. It was, at that time, a powerful accelerator facility for giant resonance studies. Recently, the facility newly added a booster ring which can accelerate the beam up to 1.2 GeV, by which ”strangeness” can be produced in the threshold region. The internal tagging facility of the booster ring now provides photon beams upt to 1.1 GeV. At this facility, we are now carrying out investigation on the photo-strangeness production process in the neutral kaon channel, which has close connection with electroproduction of hypernuclei. All these activity prompted us to organize this symposium. We wish the symposium play a role of a road crossing among those investigating strangeness related physics in nucleons and in nuclei or hypernuclei with electromagnetic interactions. With many of the participants leading the field both in theory and experiment, we wish the symposium offers an opportunity to stimulate communication not only during the symposium period but also in the future. In addtion, we hope you enjoy exploring city of Sendai and the area around as well as scientific discussions. Thank you very much.

1. Overview of Electromagnetic Strangeness Production


STRANGENESS PHOTOPRODUCTION ON NUCLEONS AND NUCLEI

C . BENNHOLD Center for N,idear Studies, Department of Physics, The George Washington University, Washington, D. C. 2OOe52,USA I review the current status of kaon electromagnetic production from nucleons and nuclei. With the new data from SAPHIR and Jlab, the elementary production processes, -y+ N -+ K + A ( C ) , provide critical input to resolving the missing resonance problem. In contrast to other hypernuclear excitation mechanisms, hypernuclear photoproduction allows mapping out the A momentum distribution in the hypernuclew, thus providing dynamical information in addition to our knowledge derived from excitation spectra.

1. Introduction

Since its discovery more than five decades ago, the quark flavor Strangeness has played a special role in nuclear and particle physics. More recently, the strange quark has found itself between two theoretical domains: on the one hand is the realm of chiral symmetry with the almost massless up and down quarks, while on the other side the physics can be described in terms of the heavy quark efFective theory of the charm and bottom quarks. While the strange quark mass may be too large to ensure convergence in SU(3) Heavy Baryon Chiral Perturbation Theory, it.turns out t o be too small to be safely included in heavy-quark descriptions. Among the successes of heavy-quark physics is the description of excitation spectra of mesons and baryons that contain charm and bottom quarks. The excitation spectrum of nucleon and hyperon resonances, on the other hand, is still not well understood, despite 40 years of efforts in meson-baryon scattering and electromagnetic production processes. For this purpose, a number of laboratories like MAMI, ELSA, BATES, GRAAL and TJNAF have begun to address the issue of N * physics, delivering new experimental data with unprecedented accuracy1i2. On the theoretical side, progress is being made in the understanding of N * and Y* properties from first principles calculations, such as lattice QCD. Due to the improved actions 3

4

of the last few years, coupled with advances in algorithms and computing power, the field is quickly moving towards providing new results in hadron phenomenology. In order to provide a link between the new and improved data on one side and the results from lattice QCD and quark models on the other side, dynamical descriptions using hadronic degrees of freedom are required that can analyze the data in the various asymptotic reaction channels (like yN, r N , r r N , Q N ,K A , KC and others). 2. The Elementary Process

Since we are st ill a long way from actually calculating intermediate-energy reactions involving mesons and baryons directly from QCD, effective fieldtheoretical descriptions in terms of purely hadronic degrees of freedom are usually employed, where QCD is assumed to provide the justification for the parameters or cutoff functions used in the various approaches. In most of these approaches a potential or driving term is defined that includes standard nonresonant s-,t-, and u-channel poles along with resonances in each of these channels as bare fields which are then dressed through final-state interaction. Only the dressed s-channel poles above threshold are identified with physical resonances, the nonpolar part is considered background for the particular process (even though it may contain bare nucleon and hyperon resonances in the u-channel).

2.1. Dunamical coupled-channels models with effective Lagmngians There is general agreement that all hadronic scattering and production processes at relativistic energies are described by the Bethe-Salpeter equation which, depending on the nature of the driving term, may involve solving a four-dimensional nonlinear integral equation. Generally, a threedimensional reduction is chosen that amounts to making an assumption of the intermediate two-particle propagator which then makes the calculations more tractable. The situation is different for calculations perfornied in the so-called unitary xPT approach, here the driving terms are given by a series of contact terms whose structures are suggested by chiral symmetry. No bare resonances are included, rat her the resonances are generated dynamically through final-state i n t e r a ~ t i o n ~While ? ~ . dynamical models involving various approximations for the Bethe-Salpeter equation are becoming increasingly successful in the description of pion photoproduction, the hadronic

5

final state interaction in kaon photoproduction has usually been neglected. Without rescattering contributions the T-matrix is simply approximated by the driving term alone which is assumed to be given by a series of tree-level diagrams5. Clearly, neglecting the final meson-baryon interaction in the full meson photoproduction T-matrix automatically leads to violation of unitarity since flux that can "leak out" into inelastic channels has not been properly accounted for. Enforcing unitarity dynamically requires solving a system of coupled channels with all possible final states6??. Including unita,rity properly also raises the question of crossing symmetry which is straightforward to impose at the tree level but more involved in a coupled-channels framework. This becomes apparent when one compares the intermediate hadronic states of p ( 7 ,K + ) A with those of p ( K - , y ) A . While these two processes are related via crossing at t,he tree level, the photoproduction process proceeds trough intermediate states with zero strangeness while the radiative capture reaction requires S = -1, thus including A* and C* resonances. Since crossing symmetry is not a dynamical constraint in that, it, imposes relationships with different reactions, rather than constrain the same reaction, preserving unitarity is usually seen as more important within a coupled-channels dynaniical framework.

2.2. Background Amplitudes

Most isobar models for kaon photoproduction over the last 30 years left the leading KYN couplings as open parameters to be determined by the data. Constraining these values to within the SU(3) range gave results which were overpredicting the data by up to a factor of 10. Therefore, when left as free parameters the couplings came out to be significant,ly below their SU(3) range. On the other side, most extractions based on hadronic reactions yielded couplings constants well within the SU(3) limits. Furthermore, most isobaric models show a divergence at higher energies, suggesting that an important piece of physics has been left out: the extended structure of the hadrons, parametrized in t.erms of a hadronic form factor. The use of point-like part,icles with bare vertices disregards the composite nature of t.he baryons and mesons, thus losing the full complexity of a strongly interacting hadronic system. However, it is well-known that the sum of and the first three photoproduction diagrams-i.e., the sum of the s-,u-, t-channel diagrams-is gauge-invariant only for bare hadronic vertices with pure pseudoscalar coupling. In all other instances, one needs additional contact-type currents to ensure gauge invariance and thus current conser-

6

vation. For bare hadronic vertices with pseudovector coupling, this extra current is the well-known Kroll-Ruderman contact term. Field theory clearly mandates that a correct description of vertex dressing effects must be done in terms of individual hadronic form factors for each of the three kinematic situations given by the s-, u-, and t-channel diagrams. In a complete implementation of a field theory, the gauge invariance of the total amplitude is ensured by the self-consistency of these dressing effects, by additional interaction currents and by the effects of hadronic scattering processes in the final state *. Schematically, the interaction currents and the final-state contributions can always be written in the form of an additional contact diagram. If one now seeks to describe the dressing of vertices on a more accessible, somewhat less rigorous, level, one introduces phenomenological form factors for the individual s-, u-, and t-channel vertices. Then, to ensure gauge invariance and to remain close to the topological structure of the full underlying field theory, the simplest option is to add contact-type currents which mock up the effects of the interaction currents and final-state scattering processes. One method to handle the inclusion of such phenomenological form factors has been proposed by Ohta g . By making use of minimal substitution Ohta has derived an additional current. However, while Ohta’s method does indeed restore gauge invariance, its effect on the amplitude is the removal of any vertex dressing from the dominant electric contributions which-at least, partially-undoes some of the desirable effects of why dressed vertices needed to be introduced in the first place. Haberzettl has shown * that Ohta’s method is too restrictive and that one may retain the dressing effects suppressed by Ohta’s approach by making use of the fact that the longitudinal pieces of the gauge-invariance-preserving additional currents are only determined up to an arbitrary function. In general, the results available so far indicate that Haberzettl’s method allows fixing the KYN couplings to the (approximate) SU(3) values and produces superior results compared to Ohta’s approach. It has been used in all modern studies on kaon photoproduction 6**,10,11 in an effective Lagrangian framework.

2.3. Resonances: missing a n d otherwise

Most of the information obtained on the excitation spectrum of the nucleon over the past thirty years comes from pion scattering on nucleons. While this has proved to be useful for resonances which primarily decay into the nN channel, resonances at higher energies tend to decay into other chan-

7

nels, thus, little is known of these st,at.es. This is especially true for the so-called “missing resonances” predicted by various quark models but not seen in T N scattering. Furthermore, these data access only the hadronic excitation channels and do not address the electromagnetic excitation of the nucleon. With the commissioning of TJNAF, the data on the electroand photoproduction of N * states are expected to be of unprecedented quality. However, excellent data alone clearly do not assure an unarnbiguous extraction of resonance properties. While high quality data will permit the decomposition into multipoles with definite spin and isospin quantum numbers the separation of background and resonance contributions still requires a theoretical framework that should niininize model dependencies. This situation is similar to the one nuclear physics faced over the past 50 years where the extraction of reliable and detailed information on nuclear resonances required distinguishing between the structure part and the reaction mechanism. One of the most contentious issues in the phenomenological description of kaon photoproduction on the nucleon has been the choice of baryon resonances in the product,ion amplitude 5 . Many studies have selected resonances that contribute to the kaon photoproduction process by their relative contribution to the overall x2 of the fit. This is usually done in tree-level calculations where connections with other reaction channels are difficult to establish and no additional constraints on the couplings are included. As a consequence, some studies find large couplings of the K A channel to spin 5/2 resonances, even though neither coupled-channels analyses6v7nor older partial-wave analyses for pionic K A production give any indication that that inform such states are important. It is these multichannel analyses us of the most important resonances decaying into K A and KC final states with a significant branching ratio. In the low-energy regime t,he dominant resonances for the K A channel have been identified as the S11(1650), the p11(1?’10), and the P13(1720) states. For the KC channel, the S11(1650) lies below threshold and the dominant states are p-wave: the p11(1?’10)and the &(1720) resonances. The SAPHIR data from 1998 in the p ( y , K + ) A channel revealed for the first time a structure around W = 1900 MeV that could not be resolved before due to the low quality of the old data. According to the Particle Data Book, only the 2-star 013(2080) has been identified in older p(n-, K o ) A analyses ? as having a noticeable branching ratio into the K A channel. On the theoretical side, the constituent quark model by Capstick and Roberts l4 predicts many new states around 1900 MeV, however, only a few them

8

have been calculated to have a significant K h decay width and only one, the [D13]3(1960), is also predicted to have significant photocouplings. Fits performed in an isobar model13 lead to remarkable agreement, up to the sign, between the quark model prediction and the extracted results for the &(1960). The recent release of the new SAPHIR' and Jlab2 data allows performing new fits and more comprehensive searches for missing resonance states for the first time". Ultimately, only a multipole analysis will be able to unambiguously identify the resonances contributing to kaon photoproduction. Due to the number of double polarization observables accessible because of the selfanalyzing nature of the final hyperons a complete experiment for this reaction may be within reach.

2.4. On to higher energies

...

A large set of pion and kaon photoproduction data exit for photon energies above 4 GeV, all the way up to 16 GeV, at low momentum transfer. Clearly, individual nucleon resonances cannot be resolved any more at these energies so isobar models are not applicable any more. One finds that at energies around W = 2.2-2.5 GeV amplitudes calculated within dynamical isobar models are beginning to diverge, mostly due to the t-channel exchange terms. This is the energy region which has been ruled by Regge theory which starts from a description of t-channel Regge trajectory exchanges at forward angles. These trajectories represent the exchange of a family of particles with the same internal quantum numbers and allow a natural description of the smo0t.henergy and angular dependence observed in the data. Ref.15 has recently applied this approach to high-energy pion and kaon photoproduction by replacing the usual pole-like Feynman propagator of a single particle exchanged in the t-channel by the so-called Regge propagator while keeping the vertex structure given by the effective Lagrangian for the ground state meson of the trajectory. While the Regge model of ref.15 provides a satisfactory phenomenological description at high s and low t discrepancies appear as one approaches the high PT region of large -t and large -ti. Here one approaches the hard scattering region where the cross section becomes independent of t and displays scaling behavior as s - ~which can be interpreted as scattering off partons16. In principle, this region is accessible to pQCD; however, calculating meson photoproduction directly in terms of quarks and gluons involves thousands of Feynman diagrams at. leading order. A first step in

9

this direction was taken in ref. l7 where pQCD was supplemented by the assumption that baryons can be treated as quark-diquark systems, accounting for some nonperturbative effects. 3. Hypernuclear excitation through kaon photoproduction

With the successful completion of the Jlab Hall C experiment 89-00919 which produced discrete hypernuclear states with electrons for the first time, the exploration of hypernuclear structure through electromagnetic probes is becoming a reality. In contrast to the hadronic reactions ( K - , .-) and (+ ., K + ) , the (y, K + ) process uses, besides the photon, the rather weakly interacting K+ with its mean free path of 5-7 fm in the nuclear medium, allowing the process to occur deep in the nuclear interior. In comparison, the K - and the rf are both strongly absorbed, thereby confining the reaction to the nuclear periphery. Due to the mass difference in the incoming kaon and outgoing pion, the ( K - , .-) reaction allows for recoilless A production in the nucleus, leading to high counting rates. Kaon photoproduction, on the other hand, involves high momentum transfers due to the large production of the rest mass which will therefore project out high momentum components of the nuclear wave functions. The subject of exciting discrete hypernuclear states through kaon photoproduction was studied extensively about 10-15 years ago but has been mostly dormant for the last several years, awaiting data taking. Therefore, the number of planned and approved experiments to take place within the next few years is expected to revive interest in this field. Details of such calculations are reported elsewhere in the proceedings of t.his workshop20,I will only point out a few examples here. Given the extensive work done with the hadronic probes, what else could possibly be learnt with the photoproduction reaction that has not already been explored? In my opinion, there are at least four arenas: 3.1. High-spin unnatural parity states

The ( K - , .-) reaction predominantly excites natural parity states with low angular momentum, such as tfhe ground state ( ~ Y / ~ , ~ s l / 2 ) 1or- the substitutional state (p$2,~p3/2)O+.Reduced by about a factor of 50 in cross K + ) reaction still excites natural parity levels, but selectsection, the,+TI.( ing the ones with large angular momentum, such as the (p;/2,ap3/2)2: and (P;/~,A p1/2)2,f states, reflecting the larger momentum transfer of the process. Finally, due t,o the nature of the photon, the (y, K + ) reaction excites

10

primarily the unnatural parity, high angular momentum states, such as the ground state ( P ; / ~ , A s1/2)2- or the substitutional state (P;/~,A p3/2)3+, albeit with a strength reduced by another two orders of magnitude, as one would expect for the electromagnetic interaction. This comparison demonstrates that full spectroscopic information can only be obtained with a combination of all three techniques. 3.2. M i m r hypernuclei

The (I2W .

150 ,a100

W 0.0

0.6

1.0

1.6

a.0

2.5 I

“.” 0.0

0.5

1.0

1.5

2.0

I 2.5

Figure 5 . Results from Mohring et al. l2 for Rosenbluth separation of U L (a), UT (b), and their ratio (c). The data are compared to calculations of Refs. l 3 and 4 . Results for the A are at left and Co at right.

22

The calculations shown for comparison exhibit, at best, only fair agreement with the data. The work of Williams, Ji, and Cotanch l 3 is perhaps the better of the two, at least for the ratio of ub,/uT for the A. The authors of the paper l 2 surmise that the baryon resonance content of the models, as well as the modeling of the hadronic form factors must be improved in order to successfully reproduce these results. This is the same conclusion that can be reached from examination of the CLAS data shown above. Generally, all of these new high-precision data for photo- and electro-production of strangeness on the proton call out for a renewed effort at understanding baryon and meson exchange structure of these reactions. It would be very interesting to measure the charge form factor of the K+ meson in order to compare it with the form factor of the T+. The same Hall C data set used in the analysis of the Mohring et al. result discussed above has been used by the E93-018 Collaboration l4 to extrapolate the t-dependence of U Z to the kaon pole (the Chew-Low method). A single unpublished form factor value Q2 = 1.0 GeV2 has been obtained. Further analysis of data for values at Q2 = 0.5 and 2.0 GeV2, taken in Halls C and A, is in progress in order to determine the trend of this form factor. The decay of the electroproduced excited hyperon A(1520) -+ K - p was studied at CLAS 15. The angular distribution in the t-channel helicity frame gives information about whether the t-channel exchange particle had spin J = 0 (such as the K - ) or had J greater than 0 (such as the K-*). This is interesting because in photoproduction, at Q2 = 0, there is a clear preference for A(1520) formation via KO* exchange. At Q2 > 0.9 GeV2, the CLAS experiment showed that J = 0 exchange provides about 60% of the formation channel. These results are striking, but have not yet lead to renewed theoretical activity on this reaction mechanism.

3. Production from Nuclei The Jefferson Lab data on hyperon electroproduction on the deuteron and heavier nuclei have recently started to appear in archival journals. Other results have been shown at conferences only. Below we give an overview of the most interesting new results. They come from Hall C work, but there is also program getting underway in Hall A.

3.1. The Y N Interaction Quasi-free kaon production on the deuteron, d(e,e ' K + ) Y N , has been measured by the E91-016 Collaboration in Hall C 16. The significance of this

23

work is two-fold: it gives unique access to one of the elementary production reactions, n ( e , e ’ K + ) C - , and secondly, on one side of the quasi-free peak there is a kinematic regime where the hyperon and the nucleon have nearly the same momentum, and therefore interact via the low energy Y N interaction as a final state interaction (FSI).

missing mass (GeV) Figure 6. Reconstructed missing mass from d ( e , e ’ K + ) from Ref 16. The curves are Monte Carlo simulations which do not have Y N final state interactions turned on. FSI effects are seen as excess counts near the Ad threshold.

Figure 6 shows the reaction at Q2 = 0.38 GeV2 and a beam energy of 3.2 GeV. The curves are Monte Carlo calculations which do not include FSI. The contribution from the neutron to C- production is substantial. On the left-hand edge one sees the deficit in the prediction of the quasi-free Monte Carlo model which must be filled in by FSI. Several Y N models have been used to compute the final state interaction in the simulations (not shown here), each with a characteristic S-wave scattering length and effective range; some sensitivity has been shown, favoring the “Verma” and “Jiilich A” potentials and not favoring “Jiilich B” .

3.2. Hypemuclear Electmpmdvction A remarkable achievement of the Jefferson Lab program has been the observation of electromagnetically produced hypernuclear states in light nuclei. Experiments using two different approaches have each succeeded in finding evidence for such states.

24

Using the standard Hall C spectrometers, the E91-016 Collaboration l7 measured the reactions A(e, e'K+)YX for 1H,2H,3 He,4 H e , C,and A2 targets, at Q2 = 0.35 GeV2 and for the lab angle between the virtual photon and the kaon at O 0 , 6 O , and 1 2 O . The most compelling result was for the 4 H e target, shown in Fig. 7 which showed clear bound state peaks at the end of the quasi-free production spectrum for all three scattering angles. These peaks correspond to the formation of the well-known hypernucleus i H . The cross section was estimated to be about 20 nb/sr. The data in the figure shows no evidence of C hypernuclear production (dashed lines high in quasi-free spectrum).

"

3.9

3.925 3.95 3.975

4

4.025 4.05 4.075

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MM (GeV)

c:4M)

0

200

0 3.9

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M M (GeV)

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3.925 3.95 3.975

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4.025 4.05 4.075

4.1

MM (GeV)

Figure 7. Missing mass distributions for H e ( e ,e'K+) showing quasi-free Lambda production and the formation of the bound state A H , from Dohrrnann et al.

The limitation of the experimental technique used to produce this result is that the missing-mass resolution is insufficient to extend these measurements to heavier hypernuclei where many excited states are present.

25

Another method which achieves resolution of under 1 MeV would be required to make electromagnetic hypernuclear production truly interesting as a research tool for hypernuclear spectroscopy. This other method was pioneered by the E89-009 collaboration 18. They used the Hall C SOS spectrometer to detect kaons, but used a dedicated dipole "Enge splitpole" spectrometer for the electrons. In addition, a beamsplitter magnet was used to allow the electron angle to be pushed all the way to zero degrees, thus decreasing Q2 and maximizing the rate of good events. Also, great care was taken to minimize straggling effects in materials. The result was obtained l8 for the reaction '2C(e,e'K+)i2B, seen in Fig. 8, which showed peaks corresponding to bound A's in the S and in the P shells.

80 70

40

30 2

0

2 I

10

6

4 ,

,

,

,

l

5

1 0 1 2 1 4 1 6 Ex Energy (MeV)

8 ,

I

I

I

I

0

I

I

,

I

I

5 BA(MeV)

Figure 8. Missing mass distributions for ' * C ( e ,e'K+)A'B showing peaks corresponding to the ground state (A in the S shell), and P-shell excited state (A in the P shell). The curve shows predictions for some core-excited states in which the host B nucleus is not in its ground slate. From Ref

''

The experiment achieved a missing mass resolution of 0.9 MeV FWHM, which can be compared with about 1.5 MeV as the best value achieved using

26

the ( T + , K f ) reaction for hypernuclear spectroscopy. The experiment was limited by statistics and resolution, so that little additional quantitative information has emerged. The experiment demonstrated that spectroscopic resolution is achievable, but to turn the method into a research tool a better instrument is needed. A new kaon spectrometer has been built that should achieve 0.4 MeV resolution and permit count rates of over several 100 per day for the A2B ground state. It will be installed at Jefferson Lab in mid-2004. In Hall A at Jefferson Lab the E94-107 Collaboration 2o is also planning to start hypernuclear spectroscopy in late 2003. They will use the existing HRS spectrometers, augmented by a septum-magnet arrangement which will allow the electron spectrometer to reach 6’ in the lab and by a RICH detector for more effective K / x separation.

4. The @+ state

In the naive quark model, baryons come only in colorless 3-quark flavor combinations. However, no fundamental rule forbids combinations of more quarks as long as they are also colorless. Hence, for decades there have been searches for other multi-quark structures that would, if they exist, be important ingredients of hadronic physics. No such unusual states had been convincingly identified however, so the Fall 2002 announcement by the LEPS group at Spring-8 21 in Japan of a narrow pentaquark state near 1540 MeV that decays into K+n caused renewed excitement. This state is manifestly “exotic” since the K + contains an anti-s quark, which cannot be an ingredient in an ordinary baryon. A large number of theoretical papers have appeared in recent months, as well as at least 4 experimental confirmations showing that this topic has become very hot. Spring-8’s LEPS group was inspired by the theoretical prediction of Diakonov, Petrov, and Polyakov 25 who predicted a narrow uuddii pentaquark state within the framework of a chiral soliton model, in which it appears as one member of an anti-decuplet of 5-quark states. The observation of a state with some of the predicted features is not yet final proof, of course, that this model is the optimal explanation. The CLAS Collaboration at Jefferson Lab has recently reported 23 results from the exclusive reaction yd + K+K-pn in which the neutron is reconstructed via the missing mass off the three detected charged particles. Two of many possible diagrams through which the O+ might be formed are shown in Fig. 9. The “two-step” nature of the production mechanism 21122123124,

27

has the experimental benefit that the K-’s that are typically very forward peaked rescatter to larger lab angles, and therefore are more inside the CLAS acceptance.

b)

a)

Figure 9. Diagrams leading to the production and decay of a 8+ from exclusive reactions on the deuteron.

The O+ signal was sought in the invariant mass of the K’n decay channel, and the final result is shown in Fig. 10. The signal is deduced to have about “5 sigma” significance, using a smooth (polynomial) background. Various background shapes have been tested, with similar significances. Production of excited hyperons is present in the same final state, and forms background under the peak in the final spectrum; the A( 1520) events were removed explicitly, however, with a cut on the K-p mass distribution. Full Monte Carlo modeling of the background has not been completed, although preliminary tests have suggested that the background has a large contribution from non-resonant K K production off the bound nucleon. Immediately one wonders whether the O+ state could also be reached in photoproduction off the proton directly. At CLAS there is a search at this time for the reaction y p -+ O+ -+ w+7r-Kfn. A positive result has been reported recently from SAPHIR 24, in the same channel. Interestingly, CLAS does have evidence for the Of in the reaction y p --+ K - 7r+ Of --+ K - 7r+ K+ n. (The result was shown in the oral presentation but is not included here since the data are still in flux.) In conclusion, the study of this new exotic baryonic state is very intense at this time, with positive sighting of a narrow 0’ by at least 4 experimental groups, and with a plethora of theoretical interpretation underway.

+

+ +

+ +

+

+

+

28

Figure 10. Invariant mass of the K + n system, which has strangeness S = +1, showing a sharp peak at the mass of 1.548 (GeV/c)2. The fit (solid line) to the peak on top of the smooth background (dashed line) gives a statistical significance of about 5 0 . The dashed histogram shows events removed by the hyperon cut, and the dotted histogram shows the scaled background from non-pKK events.

5. Other Works in Progress Additional work in progress on strangeness production at Jefferson Lab has not been mentioned so far due to time and space constraints. In the future we hope to present results on the following topics: (i) the radiative decay of the C(1385), which tests quark-model wave-functions 26, (ii) cross sections 27 for y p + KOC+ (iii) the beam-recoil double polarization observables Ci and Ci in p ( y , K + ) A 9 , (iv) cross sections for K+ photoproduction off the deuteron 2 8 , (v) results for the “fifth” structure function in electroproduction 29, (vi) photoproduction cross sections for the excited hyperons 3 0 , (vii) line-shape analysis for photoproduction of the A(1405) decaying to different C n charge states, as a test of its structure 3 1 ; (viii) states 32. photoproduction of S = -2 Cascade (F) 6. Summary

The disparate experimental results presented here make it difficult to summarize this report in a few words or a single central new concept. The main

29

observations are that (a) interesting new baryon resonance structure has been seen in both photo- and electro-production of strangeness on the nucleon; (b) electroproduction off the deuteron has shown that it is possible to test models of the Y N final state interaction; (c) hypernuclear production from 3 H e and 4He and from 12C shows the feasibility of using electromagnetic probes to study production and structure of hypernuclei; and (d) an exotic new baryon, the @+, has been confirmed to exist at Jefferson Lab, a discovery which is engendering a great deal of new theoretical and experimental work. Acknowledgments The author wishes to thank numerous colleagues who made their results available for this talk and paper. They include K. Baker, S. Barrow, E. Beise, D. Carman, F. Dohrmann, K. Hicks, J. Melone, R. Feuerbach, V. Koubarovski, K. Livingston, P. Markowitz, J. McNabb, M. Mestayer, G. Niculescu, J. Price, J. Reinhold, S. Stepanyan, and L. Tang. They and other colleagues offered advice and suggestions which are gratefully acknowledged. This work is supported by DOE contract DE-FG02-87ER40315. References 1. B. Mecking et al., Nucl. Instrum. and Methods A503,513 (2003), and references therein. 2. J.W.C. NcNabb et a6 nucE-ez/0305028;submitted to Phys. Rev. Lett.; W. J. C . McNabb Ph.D. Thesis, Carnegie Mellon University (2002) (unpublished). 3. T. Mart, C. Bennhold, H. Haberzettl, and L. Tiator, “KaonMAID 2000” at www .kph.uni-mainz. de/M AID/kaon/kaonmaid. html. 4. T. Mart and C. Bennhold, Phys. Rev. C61,012201 (2000); C. Bennhold, H. Haberzettl, and T. Mart, nucl-th/9909022 and Proceedings. of the 2nd Int’l Conf. on Perspectives in Hadronic Physics, Trieste, S. Boffi, ed., World Scientific, (1999). 5 . S. Janssen, J. Ryckebusch, D. Debruyne, and T. Van Cauteren, Phys. Rev C65,015201 (2001); S. Janssen et al., Eur. Phys. J. A 11, 105 (2001);curves via private communication. 6 . M. Guidal, J.-M. Laget, and M. Vanderhaeghen, Phys Rev. C61,025204 (2000); M. Vanderhaeghen, M. Guidal, and J.-M. Laget, Phys. Rev. C57, 1454 (1998). 7. M. Q. Tran et al., Phys. Lett. B445,20 (1998); M. Bockhorst et al., Z.Phys. C63,37 (1994). 8. CLAS Experiment 98-109, P. Cole, spokesperson, and K. Livingston and J. Melone, (private communication). 9. CLAS Experiment 89-004, R. Bradford, PhD thesis.

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10. R. Feuerbach et al., to be published. Ph.D. Thesis, Carnegie Mellon University (2002) (unpublished). 11. D. S. Carman et al., Phys. Rev. Lett. 90,131804 (2003); M. Mestayer, these proceedings. 12. R. M. Mohring et al., Phys. Rev. C67,055205 (2003). See also the earlier paper for the same experiment: G. Niculescu et al., Phys. Rev. Lett. 81,1805 (1998). 13. R.A.Williams, C.-R. Ji, and S. R. Cotanch Phys. Rev. C46,1617 (1992). 14. 0. K . Baker for the E93-018 collaboration (private communication). 15. S. P. Barrow et al., Phys. Rev. C64,044601 (2001). 16. J. Reinhold for the E91-016 collaboration, Proceedings of Baryons 2002, C. Carlson and B. Mecking, Eds., World Scientific, 589, (2002), and private communication. 17. F. Dohrmann for the E91-016 collaboration, Proceedings of Baryons 2002, C. Carlson and B. Mecking, Eds., World Scientific, 585, (2002), and private communication. 18. T. Miyoshi et al., Phys. Rev. Lett. 90,232502 (2003). 19. Y. Fujii et al., Nucl. Phys. A721,1079c (2003). 20. P. Markowitz for the E94-107 collaboration (private communication). 21. T. Nakano et al., Phgls. Rev. Lett. 91,092001 (2003). 22. V. V. Barmin et al., hep-ex/0304040, (2003); accepted by Yad. Phys. 23. S. Stepanyan et al., hep-ex/0307018, (2003); submitted to Phys. Rev. Lett. 24. J. Barth et al., hep-ex/0307083, (2003). 25. D. Diakonov, V. Petrov, and M. Polyakov, 2. Phys. A359,305 (1997). 26. CLAS Experiment 89-024, G. Mutchler, spokesman. 27. CLAS Experiment 89-004, B. Carnahan, Ph.D. Thesis, Catholic Univ. of America. 28. CLAS Experiment 89-045, B. Mecking, spokesman, I. Niculescu, contactperson. 29. CLAS Experiment 99-006, D. Carman and B. Raue, spokesmen. 30. CLAS Experiment 89-004, H. Juengst, contactperson. 31. CLAS Experiment 89-004, R. Schumacher, spokesman. 32. CLAS Approved Analysis, J. Price, spokesman.

HYPERON PRODUCTION IN PHOTONUCLEAR REACTIONS ON PROTONS AND DEUTERONS: THE K o X + CHANNEL*

H. LOHNER, J. BACELAR, R. CASTELIJNS, J. MESSCHENDORP, s. SHENDE KVI Groningen, Zernikelaan 25, 9'747 A A Groningen, The Netherlands EoehnerOkvi.nl FOR THE CB-ELSA / TAPS COLLABORATION Univ. Basel, Switzerland, Univ. Bochum, Germany, Univ. Bonn, Germany, Unav. Dresden, Germany, Univ. Erlangen, Germany, Petersburg NPI Gatchana, Russia, Univ. Giessen, Germany, K V I Groningen, The Netherlands

With the combined setup of the Crystal Barrel and TAPS photonspectrometers at ELSA in Bonn we have studied photonuclear reactions on protons and deuterons. From the series of experiments on single and multiple neutral meson emission we concentrate here on the hyperon production off protons and deuterons, and in particular on the K°C+ decay channel. The reaction is characterized by the final state of 6 photons and a forward emitted proton. We report on results of simulations to demonstrate the feasibility of the experiment. First results on the identification of kaons and hyperons are presented.

1. Introduction The spectrum of baryon excitations is not yet well described on basis of QCD. Theoretical studies of baryon resonances take into account. the internal degrees of freedom of the flavor triplet of light u, d and s quarks. Models differ, however, in the treatment of the spatial dynamics which provides different modes of excitation. A stringent test of hadron models requires a systematic study of baryon excitations and their respective decay modes into the mass region of 1 GeV above the nucleon mass and beyond. Recent predictions in a quark-pair creation model or a collective string-like

'

'presented a t the international symposium on electrophoto-production of strangeness on nucleons and nuclei - sendai03, sendai, japan, june 16 -18, 2003

31

32

three-quark model revealed substantial decay branches into KA and KC final states. Kaon production experiments will be an important tool to establish or disprove ”missing” resonances and thus to determine the relevant degrees of freedom of quark models. The observed q decay branches of S11 baryon resonances seem to find an explanation in mixing with other exotic resonances of pentaquark nature or with quasi-bound S11 states near the Kh or KC threshold. The precise threshold behaviour of the K°C+ decay, accessible via the multiphoton-proton decay channel, in photoexcitation of the proton may provide a signature of an additional S11 resonance.

2. Photoproduction of q-mesons

The photoproduction of q-mesons in the second resonance region is completely dominated by the excitation of the Sll(1535) nucleon resonance which so far is the only known nucleon resonance with a strong branching into the Nq-channel. The structure of the S11(1535) in terms of the quark model is still poorly understood. Alternatively, the Sll(1535) resonance was treated as a quasi-bound KC-state which may explain the large qN branching, or as a quasi-bound N q (penta-quark) state ’. Of particular interest is the Q2-dependence of the electromagnetic helicity coupling For an extended, molecular-like object one expects a much faster drop of the coupling with the momentum transfer than for a conventional three-quark resonance. The experimental values show a flat Q2-dependence which is consistent with a three-quark nature. Therefore, if a quasibound KC-state exists, it should be strongly mixed with the threequark configuration in order to explain the peculiar branching ratio. This requires a 3rd Sll resonance near the two S11 resonances predicted by the quark model and near the K C threshold. Although such a resonance has not been firmly established, there is strong evidence for an additional S11 resonance from recent measurements on 77 photoproduction ’. These data could only be explained in quark-model calculations with the inclusion of an extra S11 resonance with a mass of 1780 MeV 8 . The existence of such a resonance near the K C threshold would support speculations about a possible KC molecular state. The verification of this conjecture necessitates a high-quality excitation function, angular distributions and polarization measurements near the KC threshold. Systematic data in the threshold region are needed in order to establish such a resonance and can be achieved with the combination of Crystal Barrel and TAPS at ELSA g. In the future studies of the threshold behaviour

33

may also become possible with the upgraded MAMI and the combination of Crystal Ball and TAPS l o .

3. KoE+ photoproduction The reaction yp + K°C+ was measured with the SAPHIR detector at ELSA. A total of 405 events was accumulated in the photon energy range from threshold up to 1.55 GeV, which corresponds to ca. 200 MeV in center-of-mass energy (W) above threshold. In SAPHIR the decay modes K," + T+T- and Cf + nT+ and C+ + pn0 were studied. Events were completely reconstructed from the incident photon energy and the three charged particles in the final state. The data are shown in the lower left part of Fig. 1 (from ref. l1 and 12) and are a good basis for the eventrate estimate. This experiment improved considerably the quality of older data l 3 which are indicated in the figure by the open circles. Fig. 1 also

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Figure 1. Total cross section for K C photoproduction (with the SAPHIR data for 'yp -+ K°C+ on the lower right) it9 function of the center-of-mass energy W. The curves show results from an isobar calculation with (solid) and without (dashed) inclusion of the P13(1720) resonance. Older data l 3 are displayed by the open circles.

34

shows the data for the much better determined K+Co channel and indicates the required quality for a study of the threshold behaviour. The data are compared with a tree-level approximation 14J2 of the kaon photoproduction process. Guided by coupled channels results, a tree-level amplitude was constructed that simultaneously reproduces K + A , K+Co and K°C+ data. The model includes resonances that were found to give important contributions in coupled channels calculations. It is found that the reaction mechanism is resonance dominated in all isospin channels. The curves in Fig. 1 show the calculations with (solid) and without (dashed) inclusion of the PIs(1720) resonance. However, for a precise determination of the resonance contribution in the K°C+ channel, e.g., to indicate a strong S-wave contribution by a steep rise at threshold, the data are not precise enough. For this purpose an excitation function is required with center-of-mass energy bins W w 20 MeV and error bars below 5%, and corresponding angular distributions. This is the goal of the proposed experiment exploiting neutral decay modes. The K," decays with a BR of 31.4% into roroand the C+ decays with a BR of 51.6% into TOP. The reaction is thus characterized by the final state of 6 photons and a forward emitted proton with a total branching ratio of 15.6%.

Figure 2. Side view of Crystal Barrel and TAPS setup at ELSA. The Crystal Barrel is modified to leave on opening cone of 30" for the forward region to be covered by TAPS consisting out of 528 BaFz crystals in a wall at a distance of 1.2 m from the target center.

35 800

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Q 400: 0

:

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0 Time Of FligM (ns)

Figure 3. The calibrated proton energy versus tirne-of-flight. The proton energies above 400 MeV have been calibrated using the missing proton energy in the well-identified 9 meson channel.

4. Crystal Barrel and TAPS setup at ELSA

The combination of the Crystal Barrel detector (CB), consisting of 1290 CsI2 crystals, and the TAPS photon spectrometer, consisting of 528 BaF2 crystals, offers almost 4n acceptance (see Fig. 2) and excellent energy and position resolution for the final-state photons in the proposed reaction. TAPS was be placed in a wall configuration with hexagonal boundaries at forward angles covering the polar angle region from 5" to 30" at a distance of 1.2 m from the target center. The Crystal Barrel acceptance ranges from 30" to 170". The target, a 5 cm long liquid hydrogen cell, is surrounded by the SCIntillating FIbre inner detector (SCIFI), covering the solid angle of the CB. The SCIFI allows to correlate the measured position of charged particles with the corresponding cluster of detectors in the CB and it acts as veto counter for neutral particles. TAPS can identify charged particles online by the thin plastic CPV counters in front of each crystal and in addition offline by the pulse-shape analysis of the BaF2 signals and the time of flight. Protons with kinetic energy above 400 MeV will cause significant leakage of shower energy. With a time resolution of 0.2 ns ( 0 ) the kinetic energy above 400 MeV can be recovered from the TOF information (Fig. 3) using the missing proton energy in the well-identified q meson channel. The direction of protons was determined from the measured position in TAPS or the CB.

36

0

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1.9

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W (GeV) Figure 4. Excitation function for K C photoproduction with the SAPHIR data (open circles 11) for yp + K°C+ as function of W. The filled squares indicate the results of this simulation with the expected accuracy.

5. Results from simulations

For various reactions data sets of lOOk events were generated and analyzed according to the experimental conditions. Since both TAPS and the CB have been used extensively in previous experiments, their response is well known and incorporated accordingly. 5.1. Detection eficiency

The reaction y p + K°C+ has been simulated for fixed photon energies of 1.2, 2.0 and 2.5 GeV. For the final state population the phase space distribution was assumed which appears to be the most appropriate assumption near threshold and expecting an S or P wave contribution. The energy and angle distribution for photons and protons show that the high energy photons are mostly found in TAPS and that the reaction can be triggered by the appearance of a proton in TAPS. In 68% of the accepted events the proton and at least one photon are detected in TAPS. From the 6 photon four-momenta and the proton four-momentum as detected by TAPS and CB the final-state particles were subsequently reconstructed by analysing the invariant mass spectra for yy,noro, and p r o combinations. After subtracting the residual smooth combinatorial background we recover 36%of all simulated reactions. This number is composed

37

out of a geometrical acceptance of 91% per particle and a survival probability of 64% for the subsequent cuts.

0

Figure 5. The 37r0 invariant mass distribution showing the prominent 71 peak contribution.

5.2. Background

The final state signature of the desired reaction can be produced by various competing reaction channels which might thus contribute to the combinatorial background below the Kf and Cf mass peak. We have investigated the following channels which are expected to give the strongest contribution 0

(a) yp + q p + nOnonop+ 67 p with a cross section of ca. 2 pb at 2 GeV and a branching ratio of 32.1% (b) TP + rl’P + n0.rovp+ P with a cross section of ca. 1.2 pb at 2 GeV and a bra.nching ratio of 8% ( c ) y p + 7rononop3 6y p with a cross section below 1 pb at 1 GeV and a branching ratio of 96%.

w

0

The latter case is a worst case scenario for sequential decays from higher lying resonances which is approximated by the phase-space distribution of 3 no in the final state

38

M,,

versus M ,

1200

1160 1100

d sat

I

Figure 6. The invariant mass distributions of the p no versus the nono combination. Projections show the combinatorial background (dark) and the KO and C+ mass contributions (grey).

From reactions (a) and (b) only a few events survive the kinematical cuts. Considering the cross sections and branching ratios we estimate a background contribution of 0.2%. The worst contribution stems from reaction (c). considering the branching ratios and that the cross section for this reaction may be at most two times larger than for the desired reaction, we are left with a signakbackground ratio of 1:2. The background due to reaction (c) decreases by a factor 2 with increasing photon energy from 1.2 to 2 GeV due to the wider phase space distribution. Thus at higher energy the signakbackground ratio approaches 1:1. The expected excitation function for KC photoproduction is shown in Fig. 4 and compared to previous SAPHIR data. With a considerable improvement on the accuracy we can expect much higher sensitivity to resonance admixtures. The energy (W) dependence of the simulated data is taken according to the calculation shown in Fig. 1 by the solid curve. 6. First results

With the maximum beam energy of 3.2 GeV electrons at ELSA tagged photon beams have been obtained with typical intensities of 107/s. At

39

Figure 7. Examples for the C+ identification at two selected energies of W = 1.71 GeV (left) and W = 1.76 GeV (right). The insets show the C+ peak after background subtraction. We obtain a mass resolution of about 2.5 %.

several electron beam energies photonuclear reactions have been measured for several hundred hours with unpolarized and polarized photons on a 5cm long liquid hydrogen or liquid deuterium target. The linearly tagged photons have been obtained by coherent bremsstrahlung in a diamond crystal. Variations of energy calibrations have been studied and corrected in day-by-day samples using the pulse-shape information in TAPS and the light-pulser information in the Crystal Barrel. For about 30% of the available data the first orienting steps of the data analysis have been made for the proton target and photon energies above the KC threshold. Requiring events with at least 6 photons and one charged particle in TAPS (i.e. at forward angles) the invariant mass of ro -+ yy and q + 3n0 mesons can be obtained with resolutions a ( M ) / M of 7% and 4%, respectively, on top of the combinatorial background. Constraints on energy and momentum conservation reduce the combinatorial background considerably. Fig. 5 shows the example of the 3r0 invariant mass distribution with the prominent q peak contribution above a small residual background. Fig. 6 shows the attempts to identify the neutral kaon and Cf final state from kinematical selections at the center-of-mass energy W=1.71

40

GeV which is 20 MeV above the threshold. The two-dimensional graph shows the invariant mass of the p no versus the r o r ocombination. The grey parts of the projections are obtained by requiring 2a wide regions around the KO mass peak for the C+ and around the C+ mass peak for the KO projection, respectively. The dark background regions are obtained by selecting side-bands outside the peak regions for the KO and the C+ mass region, respectively. The projections clearly show the KO and the C+ peak contributions above the combinatorial background with a peak to background ratio of about 1:2. This is consistent with the expectations from simulations. Fig. 7 shows examples for the C+ identifica,tionat two selected energies of W = 1.71 GeV and W = 1.76 GeV. It is obvious that the combinatorial background shifts to higher energies with increasing photon beam energy, while the E+peak remains at the stable position. After background subtraction we obtain a satisafctory mass resolution of about 2.5 %. With the amount of presently analyzed data it is premature to obtain differential cross sections. However the angular distributions at various energies near threshold have been inspected showing a slight forward peaking. By applying an angle-integrated detector acceptance a first attempt has been made to obtain integrated cross sections. These appear to be close to but slightly lower in value than the previously obtained SAPHIR data. A more detailed analysis of differential cross sections is in progress. In particular the method of kinematical selections will be replaced by the well established kinematical fitting method which is able to reduce the combinatorial background and improve the mass resolutions considerably. However, the presently obtained data will be quite important for checking and controlling parameters of the kinematical fitting procedure.

7. Deuterium target Having determined the KC production near threshold on the proton, the quasifree production on the proton in the deuteron will allow to analyse the C - neutron final state interaction. The cross sections will have to be studied as function of the relative C - neutron momentum. To this end we have taken extensive datasets with both unpolarii~dand polarized photons on the deuterium target. Data taking has only recently been finished. For the analysis of r o and 77 mesons we have obtained similar mass resolutions as for the proton.

41

8. Conclusions With the combined setup of the Crystal Barrel and TAPS at ELSA a number of neutral decay modes of nucleon resonances can be studied with high detection efficiency. The analysis of the excitation function, differential cross sections and the hyperon polarisation of the K°Ct channel will provide valuable data for a coupled channels analysis of nucleon resonances above the KC threshold. This investigation may lead to a better understanding of the properties of the s11(1535) resonance. First results on the detection of neutral decay modes of the K°C+ channel have been obtained. The signal/background ratio and first estimates of the cross section are according to expectations. The support of the ELSA accelerator crew in providing high quality beam is gratefully acknowledged. One of us (H.L.) wishes to thank the organizers of the Sendai Symposium for the kind invitation to this very stimulating workshop and the hot-springs discussion.

References 1. S. Capstick and W. Roberts, Phys. Rev. D58,074011 (1998). R. Bijker, F. Iachello, and A. Leviatan, Phys. Rev. D55,2862 (1997). B. Krusche et al., Phys. Rev. Lett. 74, 3736 (1995). N. Kaiser, P.B. Siege1 and W. Weise, Phys. Lett. B362,23 (1995). P. Stoler, Plays. Rev. Lett. 66,1003 (1991). Z. Li and R. Workman, Phys. Rev. C53,R549 (1996).

2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14.

F. Renard et al., Phys. Lett. B 528 (2002) 215 B. Saghai, Z. Li, Eur. Phys. J. A 11 (2001) 217; B. Saghai, Z. Li, nucl-th/0305004 H. Lohner et al., accepted proposal ELSA/3-2001, 2001; H. Lohner et al., accepted proposal ELSA/l-2002, 2002. R. Beck, H3-Treffen, Mainz, March 2000. S. Goers et al., Phys. Lett. B464,331 (1999). T. Mart, Phys. Rev. C62, 038201 (2000). ABBHHM Collaboration, Phys. Rev. 188,2060 (1969). C. Bennhold et al., nucl-th/9901066.

RECENT RESULTS FROM LEPS AT SPRING-8 *

T. NAKANO FOR THE LEPS COLLABORATION RCNP, Osaka Univerrity 10-1 Mihogaoka, Ibamki, Osaka, 567-0047, Japan E-mail: nakano Orcnp. Osaka-u.ac.jp

The polarized photon beam at Spring-8 is produced by backward-Compton scattering of laser photons from 8 GeV electrons. The maximum energy of the photon beam is 2.4 GeV which is above the s.? production threshold. We report the status of the facility and new results obtained by experiments with this high quality beam.

1. Laser-Electron Photon beam facility at Spring-8 (LEPS)

The Spring-8 facility is the most powerful third-generation synchrotron radiation facility in the world. The energy of the electrons in the storage ring is 8 GeV and the beam current is 100 mA. The laser-electron photon (LEP) beam at the Spring-8 is generated by Backward-Compton scattering of laser photons with the &GeV electrons. The maximum energy of the beam is currently 2.4 GeV for a 351-nm (3.5 ev) Ar laser, which is well above the threshold for SS productions. The polarization of the LEP beam is about 95 % at the the maximum energy when laser lights are linearly polarized. The polarization drops as the photon energy decreases and crosses zero at the half of the maximum energy. An energy of laser photons can be changed so that the polarization remains reasonably high in the energy region of interest. The LEP energy is determined by measuring the energy of a recoil electron with a tagging counter which measures the deviation of the recoil electron from the 8-GeV electron beam orbit. Since the tagging counter does not cover the region near the beam orbit, a photon with an energy *This work is supported by the Ministry of Education, Science, Sports and Culture of Japan, by the National Science Council of Republic of China (Taiwan), and by KOSEF of Republic of Korea. 42

43

below 1.5 GeV cannot be tagged. The energy resolution of the tagged photon is 15 MeV ( 0 ) mainly determined by the energy spread of the electron beam and an uncertainty of a photon-electron interaction point in the 7.8-m straight section. The operation of the laser-electron photon beam at Spring-8 started in July, 1999. The intensity of the beam is about 2.5 x lo6 photons/sec for a 5 W laser-output, and a typical tagger rate is 8 x 105/sec. Figure 1 shows a schematic drawing of the LEPS detector. For the tracking of the charged particles, a silicon-strip vertex detector (SSD) and 3 drift chambers are used. The SSD consists of single-sided silicon-strip detectors (vertical and horizontal planes) with the strip pitch of 120 pm. The first drift chamber located before a 0.7-T magnet consists of 6 wire planes (3 vertical planes, 2 planes at +45", and 1 plane at -45"), and the other two drift chambers after the magnet consist of 5 planes (2 vertical planes, 2 planes at +30", and 1 plane at -30"). A time-of-flight (TOF) scintillator array is positioned 3 m behind the dipole magnet.

target Cherenkov counter

\ Silicon Vertex Detectors

Figure 1. The LEPS detector setup.

Electron-positron pairs produced before the target are rejected online

44

by a plastic counter, and the pairs produced at the target are rejected by an aerogel Cerenkov counter (AC) with the index of 1.03. The electron and positorons which escape the online trigger rejections are blocked by lead bars which were set horizontally along the median plane inside the magnet gap. Pions with a momentum higher than 0.6 GeV f c are vetoed online by the aerogel Cerenkov counter (AC). A 0.5-cm thick plastic scintillator (SC) located 9.5 cm downstream from the 5-cm thick liquid-hydrogen (LH2) target ensures at least one charged particle produced in the LH2 target. The events from the SC is turned out to be very useful to study events generated from neutrons in carbon nuclei at the SC The angular coverage of the spectrometer is about f0.4 rad and f0.2 rad in the horizontal and vertical directions, respectively. The momentum resolution (0) for l-GeV/c particles is 6 MeV/c. The timing resolution (u) of the TOF is 150 psec for a typical flight length of 4 m from the target to the TOF. The momentum-dependent mass resolution is about 30 MeVf c2 for a l-GeV/c kaon.

-

2. First physics run and results

The physics run with a 5-an long liquid H2 target wad carried out during December, 2000 to June, 2001. The trigger required a tagging counter hit, no charged particle before the target, charged particles after the target, no signal in the aerogel Cerenkov counter, at least one hit on the TOF wall. A typical trigger rate was about 20 counts per second.

2.1. K+ photo-production Recent measurements for K + h photo-production at SAPHIR indicated a structure around W = 1.9 GeV in the total cross-section '. It attracted theorist's interest to study missing nucleon resonances in this process. Mart and Bennhold showed that the SAPHIR data can be reproduced by inclusion of a new 0 1 3 resonance which have large couplings both to the photo and the K h channels according to the quark model calculation '. Although it is difficult to draw a strong conclusion on the existence of 0 1 3 resonance from the cross-section measurements, the photon polarization asymmetry is very sensitive to the missing nucleon resonance. The LEPS collaboration measure the asymmetry in the photon-beam energy region of 1.5-2.4 GeV, while the measurement below 1.5 GeV has been carried out at GRAAL '. Fig. 2 shows the photon polarization asymmetry distributions for A and C productions. All kinematical variables except for the K+ polar angle were

45

integrated in our acceptance regions. Most of the acceptance effects were canceled by taking a ratio of ( H - V ) / ( H V), where H and V are number of events in each angle bin for horizontal and vertical polarizations, respectively. The detailed results and discussions are reported by M. Sumihama in this conference.

+

-

2' -0.2 -0.4 -0.6 -0.8

0

50

100

150

200

250

300

35

0 (deg. -

'z

1 0.8

% 0.6

z 0.4

3 0.2 T o

g -0.2

-0.4

-0.6 -0.8 1

Figure 2. Photon polarization asymmetry distributions for A and C productions.

2.2.

4 photo-production

A q5 meson is almost pure sI state. Therefore, diffractive photo-production of a q5 meson off a proton in a wide energy range is well described as a pomeron-exchange (multi gluon-exchange) process However, at low energies other contributions arising from meson (T,q)-exchange 8 , a scaler (O++ glueball)-exchange 9 , and sS knock-out lo are possible. These contributions fall off rapidly as the incident y-ray energy increases, and can be studied only in the low energy region near the production threshold. The experimental separation of these contributions are difficult if one measure only differential cross-sections because they have similar photon-energy and momentum transfer dependences. Linearly polarized photons are an ideal probe to decompose these contributions. For natural-parity exchange such as pomeron and 0++ glueball exchanges, the decay plane of K + K 63778.

46

is concentrated in the direction of the photon polarization vector. For unnatural-parity exchange processes like 7r and 77 exchange processes, it is perpendicular to the polarization vector. Pichowsky and Lee predicts that the meson exchange processes dominate in the low photon energy region around 2.3 GeV. However, a preliminary analysis of the KK decay asymmetry in the forward angles showed the natural-parity exchange contributions were still dominant in the region. The detailed results and discussions were given by T. Mibe l 1 in this conference.

2.3. Observation of a S = + l

Baryon Resonance

We searched for baryon resonances with strangeness quantum number S=+l in the K- missing mass spectrum for the y n + K+ K- n reaction 12. The search was motivated in part by a recent paper by Diakonov, Petrov and Polyakov l 3 where masses and widths of an antidecuplet baryons were predicted from the chiral soliton model. The lightest member of the anti-decuplet is the O+ which is an exotic 5-quark state with a quark configuration of uudd3 that subsequently decays into a K+ and a neutron. The model predicts the mass of the O+ to be 1530 MeV/c2 with a narrow width of 5 15 MeV/$. For the present analysis, we selected K+K- pair events produced in the SC, which accounted for about half of the K+K--pair events. The missing mass M M y K + ~ -of the N(y, K+K-)X reaction was calculated by assuming that the target nucleon (proton or neutron) has the mean nucleon mass of 0.9389 GeV/c2 ( M N )and zero momentum. Subsequently, events with 0.90 < MM./K+K- < 0.98 GeV/$ were selected. The main physics background events due to the photo-production of the (b meson were eliminated by removing the events with the invariant K+K- mass from 1.00 GeV/c2 to 1.04 GeV/c2. In order to eliminate photo-nuclear reactions of ~p + K+K-p on protons in 12C and ‘H at the SC, the recoiled protons were detected by the SSD. The direction and momentum of the nucleon in the final state was calculated from the K+ and K- momenta. And we rejected such events in which the recoiled nucleon was out of the SSD acceptance or the recoiled proton hit was found in the SSD. A total of 109 events satisfied all the selection criteria (“signal sample”). In case of reactions on nucleons in nuclei, the Fermi motion has to be taken into account to obtain appropriate missing-mass spectra. The missing

+

+

-

+

47

mass corrected for the Fermi motion, MM;K*, is deduced as

+

MM,CK* = MM?K* - M M - / K + K - M N .

(1)

The validity of the correction was checked with the y n + K+C- + K+.rr-n sequential process, where the K+ and 7r- were detected as shown in Fig. reffig:sigma.

'1

z-

A

n

35

1.051.075 1.1 1.1251.151.1751.21.2251.251.2751.3

M

q (GeV/c2)

Figure 3. The missing mass, M M y C K + spectra , for the K + s - events from the SC (solid histogram) and for Monte Carlo events for the -p + K+C- channel (clotted curve) calculated via Eq. 1. The dashed histogram shows the missing mass spectrum without the Fermi-motion correction.

The corrected K+ missing-mass distribution for the events that satisfy all the selection conditions is compared with that for the events for which a coincident proton hit was detected in the SSD. In the latter case, a clear peak due to the y p + K+A(1520) + K+K-p reaction is observed while the A(1520) peak does not exist in the signal sample. This indicates

+

48 that the signal sample is dominated by events produced by reactions on neutrons. Fig. 4 shows the corrected K - missing mass distribution of the signal sample. A prominent peak at 1.54 GeV/c2 is found. The broad background centered at 1.6 GeV/c2 is most likely due to non-resonant K+K- production and the background shape in the region above 1.59 GeV/c? has been fitted by a distribution of events from the LH2. The estimated number of the events above the background level is 19.0 f 2.8, which corresponds to a Gaussian significance of 4.6 0 .

-

15 cu(3

cu

8 5

10 -

C

Q)

&

5-

MMk- (GeV/c2)

Figure 4. The M M ; K - spectrum for the signal sample (solid histogram) and for events from the LH2 (dotted histogram) normalized by a fit in the region above 1.59 GeV/c2.

After subtracting the background from the signal sample, the spectrum in the region of 1.47 5 MM;,< 1.61 GeV/c2 was compared with Monte Carlo simulations assuming a Breit-Wigner function for a resonance distribution. The best fit to the spectrum gives the mass of the resonance to be

49

1.54 f 0.01 GeV/c2. And the upper limit for the width was determined to be 25 MeV/c2 with a 90 % C.L.. This narrow peak strongly indicates the existence of an S = +1 resonance which may be attributed to the exotic 5-quark baryon proposed as the O+. was announced by the LEPS Soon after a preliminary result collaboration at the international conference PANIC in October 2002, the CLAS collaboration at Jefferson Lab re-analyzed photo-reaction data which were collected in 1999 by using a liquid deuterium target. They found a 5.3 (T peak at 1542 MeV in the nK+ invariant mass spectrum of the reaction yd + K+K-pn, where all charged particles in the final state were detected 14. Since the momentum of the final neutron was fully determined by using total momentum conservation law, their result was not affected by a Fermi motion of the initial neutron. The CLAS collaboration also announced an evidence for the @+ by analyzing the reaction yp + K+K-&n in a different data set 15. Prior to the CLAS reports, the DIANA collaboration at the Institute of Theoretical and Experimental Physics (ITEP) in Russia reexamined lowenergy K+ Xe collision events in the Xennon bubble chamber, which were taken in 1986. They found a 4.4 peak at 1539 MeV with a very narrow width of < 9 MeV in the invariant pKo invariant mass spectrum of the charge-exchange reaction K+Xe' + KOpXe' 16. Most recently, the SAPHIR collaboration at ELSA in Germany reanalyzed old data and found a O+ peak at 1540 MeV with a width less than 25 MeV in the reaction yp + KoK+n 17. They found no evidence for a O++ in the reaction and concluded that the should be isoscaler. All experiments are very consistent with each other: The peak position of the O+ is about 1540 MeV and the width is very narrow. However, further experimental studies are needed in order to establish the O+. The determination of the spin and parity seems to be crucial to understand the nature of the state.

+

3. Acknowledgments

The authors gratefully acknowledge the dedicated efforts of the staff of the SPring-8 for providing a good quality beam.

References 1. M.Q. Tran et al., Phys. Lett. B445,20 (1998). 2. T. Mart and C. Bennhold, Phys. Rev. C61, (R)012201 (2000); T. Mart, in these proceedings.

50 S. Capstick and W. Roberts, Phys. Rev. D58,074011 (1998). A. d’dngelo, a talk in Baryons 2002 conference. M. Sumihama, in these proceedings. T.H. Bauer et al., Rev. Mod. Phys. 50, 261 (1978). A. Donnachie and P.V. Landshoff, Nucl. Phys. B267,690 (1986). M.A. Pichowsky and T.-S. H. Lee, Phys. Rev. D56,1644 (1997). T. Nakano and H. Toki, in Proc. of Intern. Workshop on Exciting Physics with New Accelerator Facilities, Spring-8, Hyogo, 1997, World Scientific Publishing Co. Pte. Ltd., 1998, p.48. 10. A.I. Titov, Y. Oh, and S.N. Yang, Phys. Rev. Lett. 79, 1634 (1997); A.I. Titov, Y. Oh, and S.N. Yang, Phys. Rev. C58,2429 (1998). 11. T. Mibe, in these proceedings. 12. T. Nakano et al. (LEPS collaboration), Phys. Rev. Lett. 91,012002 (2003). 13. D. Diakonov, V. Petrov, and M. Polyakov, Z. Phys. A359, 305 (1997). 14. S. Stepanyan et al. (CLAS Collaboration), arXiv:hep-ex/0307018; R. Schumacher, in these proceedings. 15. V. Kubarovsky et al. (CLAS Collaboration), arXiv:hep-ex/0307088. 16. V.V. Barmin et al. (DIANA Collaboration), Phys. At. Nucl. 66,1715 (2003). 17. J. Barth et al. (SAPHIR Collaboration), arXiv:hep-ex/0307083.

3. 4. 5. 6. 7. 8. 9.

2. Theoretical Aspects of Strangeness Production


STRANGENESS PRODUCTION VIA ELECTROMAGNETIC PROBES: 40 YEARS LATER

B. SAGHAI

Dipartement d'Astrophysique, de Physique des Particules, d e Physique Nucliaire et d e l'lnstumentation Associie, CEA/Saclay, 91 191 Gif-sur-Yvette, France E-mail: [email protected] A brief review of the associated strangeness electromagnetic production is presented. Very recent K f A photoproduction data on the proton from threshold up to EFb = 2.6 GeV are interpreted within a chiral constituent quark formalism, which embodies all known nucleonic and hyperonic resonances. The preliminary results of this work are reported here.

1. Introduction

This conference witnessed the advent of thousands of data points from JLab/CLAS1 and ELSA/SAPHIR2 on the K + A and K+C" photoproduction on the proton. Moreover, the recent data with polarized photon beam from Spring-8/LEPS3 and with electrons from JLab4 announce the start of a new era in this field, ringing the moment of the truth for phenomenologists! Actually, this journey started some 40 years ago (see e.g. Ref.5), with the pionner and significant work performed by Thorn6. The data which are now becoming available, were anticipated some 20 years ago and gave a new momentum to the phenomenological investigation^^?^. Those studies, based on the Feynman diagrammatic technique, included s-,u-, and t-channel contributions, and produced models differing mainly in their content of baryon resonances. Later, more sophistications were i n t r o d u ~ e d lo ~ > ~ t 13, the most significant ones being: z) Introduction of spin- 312 and 512 n u c l e ~ n i cand ~ ~spin-312 ~~ hyperonic resonances". This latter would not have been possible without the incorporation" of the so-called off-shell effects inherent to the fermions with spin 2 312, which of course also applies to the relevant nucleon resonances. zz) Introduction of hadronic form factors at strong vertices and preserv53

54

ing the gauge invariance of the amplitudes14. The well known main difficulty in the kaon production, compared to the n and 77 cases, is that the reaction mechanism here is not dominated by a small number of resonances. This fact implies that we need to embody in the model contributions from a large number of resonances, the known ones being shown in Table I. Given that, according to the spin of the resonances, one needs 1 to 5 free parameters per resonance; it is obvious that a meaningful study of the resonance content of the underlying reaction mechanism is excluded within such approaches. Table I. Baryon resonances15 with mass MN* 5 2.5 GeV. Notations are La1 ~ J ( ~ U S and S ) LI mass) for N * and Y * ,respectively. Baryon

N*

A*

c*

However, isobaric models provide us with useful tools, if other more appropriate formalisms allow us to single out the most relevant resonances in the reaction mechanism and determine their couplings in order to significantly reduce the number of free parameters. Such an opportunity is offered to us by a chiral constituent quark approach, as discussed in the next Section. Nevertheless, this latter being a non-relativistic formalism,

55

can not be applied t o the electroproduction processes, other than at low Q2 kinematic region. So, a possible scenario could be t o pin down the reaction mechanism in the photoproduction using the constituent quark formalism, then pick up the most relevant resonances and their couplings extracted via the quark model and embody them in the Feynman diagrammatic approach t o study the electroproduction reactions. The capability of Feynman diagrammatic technique to provide the elementary operators and be used as input into the strangeness production on nuclei has already been proven16. Finally, the advent of realistic elementary operators in line with the above procedure implies coupled-channel treatment^'^?'^. In the following Sections, we will focus on the very recent yp -+ K + h and study them via a chiral constituent quark approach based on the broken SU ( 6) @ O(3) symmetry. 2. Theoretical Frame

The starting point of the meson photoproduction in the chiral quark model is the low energy QCD Lagrangianlg

L = $ [yp(i8’

+ V’ + y5A’)

- m] 1c, + . . .

(1)

+

where $ is the quark field in the S U ( 3 ) symmetry, V p = ( [ t a p [ [8,[t)/2 and A” = i(Et8,[-[8,[t)/2 are the vector and axial currents, respectively, with [ = e m f . f is a decay constant and the field II is a 3 8 3 matrix,

in which the pseudoscalar mesons, 7 r , K , and q, are treated as Goldstone bosons so that the Lagrangian in Eq. (1) is invariant under the chiral transformation. Therefore, there are four components for the photoproduction of pseudoscalar mesons based on the QCD Lagrangian,

where N i ( N f )is the initial (final) state of the nucleon, and w(wm) represents the energy of incoming (outgoing) photons (mesons).

56

The pseudovector and electromagnetic couplings at the tree level are given respectively by the following standard expressions:

j

The first term in Eq. ( 3 ) is a seagull term. The second and third terms correspond to the s- and u-channels, respectively. The last term is the tchannel contribution and is excluded here due to the duality hypothesis20. The contributions from the s-channel resonances to the transition matrix elements can be written as

with k = Ikl and q = (qI the momenta of the incoming photon and the outgoing meson respectively, & the total energy of the system, e - ( k 2 + q 2 ) / 6 a E o a form factor in the harmonic oscillator basis with the parameter ato related to the harmonic oscillator strength in the wave-function, and M N . and r(q)the mass and the total width of the resonance, respectively. The amplitudes d N * are divided into two parts21: the contribution from each resonance below 2 GeV, the transition amplitudes of which have been translated into the standard CGLN amplitudes in the harmonic oscillator basis, and the contributions from the resonances above 2 GeV treated as degenerate, since little experimental information is available on those resonances. The contributions from each resonance is determined by introducing20i22 a new set of parameters C N * ,and the following substitution rule for the amplitudes d N * : cN*dN*,

(7)

MFI, = C&M&T,

(8)

dN*

+

so that

where MF? is the experimental value of the observable, and MgT is calculated in the quark mode121. The SU(S)@O(S)symmetry predicts CN*= 0.0 for S11(1650), D13(1700), and 015(1675) resonances, and CN* = 1.0 for other resonances in Table 11. Thus, the coefficients CN*measure the discrepancies between the theoretical results and the experimental data and show the extent to which the S U ( 6 ) @ O ( 3 ) symmetry is broken in the process investigated here.

57

Table 11. Resonances discussed in Figs. 1 t o 4, with their assignments in SU(6) 18O(3) configurations, masses, and widths. SU(6) @ O(3)

Mass

Width

(GeV)

(GeV)

1.650

0.150

1.520

0.130

1.700

0.150

1.675

0.150

1.720

0.150

1.680

0.130

1.440

0.150

1.710

0.100

1.900

0.500

2.000

0.490

One of the main reasons that the SU(6) @ O(3) symmetry is broken is due to the configuration mixings caused by the one-gluon exchange23. Here, the most relevant configuration mixings are those of the two 5'11 and the two Dl3 states around 1.5 to 1.7 GeV. The configuration mixings can be expressed in terms of the mixing angle between the two S U ( 6 ) @ O ( 3 ) states I N ( 2 P ~ > ) and "('PM) >, with the total quark spin 1/2 and 3/2. To show how the coefficients CN* are related t o the mixing angles, we express the amplitudes AN* in terms of the product of the photo and meson transition amplitudes

AN* CC< NIH,IN*

>< N*IHeIN >,

(9)

where H , and He are the meson and photon transition operators, respectively. For example, for the resonance s11(1535) Eq. (9) leads to

AS,, IX - s i n 0 ~ 1 N ( ~ P ~>)) ~ -

< N ( 2 P ~ ) lI -- sin8s < N('PM);-)IH~~N > . (10)

Then, the configuration mixing coefficients can be related to the configura-

58

tion mixing angles

3. Results and Discussion The above formalism has been used t o investigate the recent data on the differential cross sections'>2,as well as recoil' A and beam3 asymmetries. The adjustable parameters in this approach are the K Y N coupling constants and one strength ( C p in Eq. 7) per resonance (Table 11).Other resonances in Table I are included in a compact form and bear no free parameters. Figures 1 t o 4 show the results for three excitation functions at B E M = 31.79', 56.63', and 123.37' as a function of total center-of-mass energy ( W ) . The choice of the angles is due t o the data released by the CLAS collaboration'. The full model contains the following terms: z) Background (Bg): composed of the seagull, nucleon and hyperons Born terms, as well as contributions from the excited u-channel hyperon resonances; ii) High Mass Resonances (HMR):contributions from the excited resonances with masses higher than 2 GeV, handled in a compact form as mentioned earlier; iii) Resonances: contributions from the excited nucleon resonances (Table 11).

This model is depicted as full curves in the Figures. Fig. 1 shows the full model and the two set of data from CLAS', SAPHIR2 a t the same angles. Those differential cross section data are compatible at the most backward angle, but show significant discrepencies at other two angles. However, the fitting procedure is driven by the CLAS data, which bear smaller uncertainties. Given the discrepencies between the two data set, the model reproduces in a reasonable way the experimental results. In figures 1 t o 4, the full model curves are depicted, while in each figure contributions from individual resonances (Table 11) are singled out. An account of those contributions is given below.

59

a) S-wave resonances In Fig.1 the dashed curves (A) show the sum of contributions from the background terms (Bg), High Mass Resonances (HMR), and the s11(1535) resonance. A peak appears at all three angles close to threshold. The other two terms (specially HMR) have large contributions at forward angles and higher energies. The second 5'11 resonance, which comes in, due to the configuration mixing, suppresses the effect of the first resonance and affects

0.4 0.3 0.2 c JLab ; 0 =32"

0.1

0.0

-

0.3

L, m

3

3 0.2 F D 0.1

c:

=

t

JLab ; 0 4 7 "

0.0 t

0.2

JLab ; 0 =123"

Saphir Full model --- A Bg + HMR + S1 l(1535) 0

= B=A

+ S1 l(1650)

0.1

0.0

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

W Figure 1. Differential cross section for the process ~p -+ KfA as a function of total center-of-mass energy (W) in GeV. The full curves are from the model embodying all known resonances. Contributions from the background terms, higher mass resonances d u s S1I 11,535) and STI (1650) a r c qhnwn hv dashed a n d dnsh-dnttwl r i i n r c = c reqnc=rtivolv The JLab (stars) and SAPHIR (circles) data are from Refs. [l] and [2], respectively.

60

0.4 0.3 0.2 * JLab ; 0 =32"

0.1

0.0 n Fli l+

0.3

3

s 0.2

c:

z! 13

w

0.1

* JLab ; 0 =57" I-

0.0

* JLab ; 0 =123" o

0.2

Saphir

- Full model C=B+P11(1440)+P11(1710) D = C + P13(1720) E = D + P13(1900)

0.1

0.0 1.6

Figure 2.

1.7

1.8

1.9

2.0

w

2.1

2.2

2.3

2.4

Same as Fig. 1, but with contributions from P-wave resonances shown.

very slightly higher energy region (curves B).

b) P-wave resonances The Roper resonance, being far below threshold and in spite of its large width, has no significant contribution. The p11(1710) introduces a tiny structure at forward angles around W M 1.7 GeV (curves C). The first PIS enhances that structure (curves D). The most dramatic effect is due to the P13(1900). At most forward angle, the curve E gives almost the same result as the full calculation, especially above W ~ 1 . GeV. 8 At the two other angles, roughly half of the cross section is obtained in the 1.7 < W < 2.1 GeV

61

region. Below W M 1.8 GeV, we witness strong interference phenomena, while the effects around W M 1.9 GeV correspond to the (almost) on-shell contributions. c) Spin-3/2 D-wave resonances The &(1520) and D13(1700) affect slightly the extreme angles results. The first one (curves F) enhances the cross sections corresponding to the curves E, while the second one suppresses them with comparable strength. The final curves G are almost identical to the curves E. Here, &(1700) contributes again due to the configuration mixing mechanism. 0.4

0.3 0.2 * JLab ; 0 =32"

0.1

0.0

-

0.3

rn 4

3

s 0.2

2

0 =

0.1

* JLab ; 0 =57'

0.0

* JLab ; 0 =123 o Saphir

-Full model

0.2

F = E + D13(1520) G = F + D13(1-700)

0.1

0.0

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

W Figure 3.

Same as Fig. 1, but with contributions from Dl3-resonances shown.

2.4

62

d) Spin-5/2 D- & F-wave resonances The 015(1675) shows a noticeable contribution only at the most forward angle (curves H). In the contrary, the effects of the F15(1680)appear at two other angles (curves I), and become very important at the most backward angle above W M 1.8 GeV. Here also we are in the presence of strong interference mechanisms. Finally, the addition of the F15(2000)leads to the full curves, allowing us to reproduce data around W M 1.9 GeV, as well as the high energy part of the data at the most backward angle.

0.4

0.3 0.2 0.1

0.0

-

0.3

l+

1 UY

e

s 0.2

2J 0

W

0.1

* JLab ; 0 =57"

0.0

-o Saphir Full model

0.2

H = G + D15(1675) I = H + F15(1680)

0.1

-----___ 0.0 1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

W Figure 4. Same as Fig. 1, but with contributions from 0 1 5 - & F15-resonances depicted.

63

4. Summary and Concluding remarks In this contribution, the preliminary results of a chiral constituent quark model have been compared with the most recent excitation functions measurements at 3 angles from CLAS' and SAPHIR2. The discrepencies between the two data set do not allow t o reach strong conclusions on the underlying reaction mechanism. However, the role played by higher spin and higher mass resonances, such as P11(1900), F15(1680), and F15(2000) is established. The obtained model reproduces the single polarization asymmetries from CLAS and LEPS. Those results, shown during the Conference, could not be reproduced here because of lack of space. To go further, several directions deserve attention and effort. From experimental side, single and double polarization data, e.g. being analyzed by the GRAAL collaboration, will very likely shed a valuable light on the reaction mechanism issues. From theoretical point of view, the following points need to be studied24: i) The same formalism should be used t o interpret the data on the K+C" channel. The forthcoming data from LNS25 on the K" will also put more constraints on the models. ii) The effect of the third ,911 resonance, in line with the q p final state investigations2', has t o be studied for the strangeness channels. If this latter resonance has a molecular structurez6,it should show up very clearly in the strangeness production processes. iii) Given that the SAPHIR data go beyond the resonance region, t o explain highest energy data, one needs very likely t o introduce the t-channel contributions. For the same reason, explicit investigation of resonances with spin 2 7/2 might be relevant. Once such improvements t o the quark models are ensured, then the coupled channel effects18 have t o be considered. The couplings extracted within the coupled-channel formalisms can then be embodied in the isobaric approaches, including a reasonable number of resonances, t o produce the needed elementary operators and study the electroproduction on both proton and nuclei.

Acknowledgments It is a pleasure for me t o thank the organizers for their kind invitation t o this very stimulating conference. I am indebted to K.H. Glander and R. Schumacher for having provided me with the SAPHIR and CLAS data, respectively, prior t o publication. I am grateful t o my collaborators Z. Li and T. Ye.

64

References 1. J.W.C. McNabb et al. (The CLAS Collaboration), nucl-ex/0305028. 2. K.H. Glander et al. (The SAPHIR Collaboration), nucl-ex/0308025, t o appear in Eur. Phys. J. A. 3. R.G.T. Zegers et al. (The LEPS Collaboration), Phys. Rev. Lett. 91, 092001 (2003). 4. R.M. Mohring et al. (The E93018 Collaboration), Phys. Rev. C 67, 055205 (2003); D.S. Carman et al. (The CLAS Collaboration), Phys. Rev. Lett. 90, 131804 (2003). 5. R.A. Adelseck and B. Saghai, Phys. Rev. C 42, 108 (1990). 6. H. Thom et al., Phys. Rev. Lett. 11, 434 (1963); H. Thom, Phys. Rev. 151, 1322 (1966). 7. S.S. Hsiao and S.R. Cotanch, Phys. Rev. C 28, 1668 (1983); R.A. Adelseck, C. Bennhold, L.E. Wright, Phys. Rev. C 32, 1681 (1985). 8. R.A. Williams, C.R. Ji, S.R. Cotanch, Phys. Rev. C 46, 1617 (1992). 9. J.C. David, C. Fayard, G.H. Lamot, B. Saghai, Phys. Rev. C 53, 2613 (1996). 10. T. Mizutani, C. Fayard, G.H. Lamot, B. Saghai, Phys. Rev. C 58, 75 (1998). 11. T. Mart and C. Bennhold, Phys. Rev. C 61, 012201 (2000). 12. B.S. Han, M.K. Cheoun, K.S. Kim, I-T. Cheon, Nucl. Phys. A691, 713 (2001). 13. S. Janssen, D.G. Ireland, J . Ryckebusch, Phys. Lett. B562, 51 (2003); S. Janssen, J . Ryckebusch, T. Van Cauteren, Phys. Rev. C 67, 052201 (2003). 14. R.M. Davidson and R. Workman, Phys. Rev. C 67, 058201 (2001). 15. K. Hagiwara et al., Particle Data Group, Phys. Rev. D 66, 010001 (2002). 16. T.S.H. Lee, V.G.J. Stoks, B. Saghai, C. Fayard, Nucl. Phys. A639, 247 (1998); T.S.H. Lee, Zhong-Yu Ma, H. Toki, B. Saghai, Phys. Rev. C 58, 1551 (1998); L.J. Abu-Raddad, J . Piekarewicz, Phys. Rev. C 61, 014604 (2000); F.X. Lee, T. Mart, C. Bennhold, L.E. Wright, Nucl. Phys. A695, 237 (2001); P. Bydzovsky et al. nucl-th/0305039; M. Sotona, these Proceedings; T. Motoba, these Proceedings. 17. J . Car0 Ramon, N. Kaiser, S. Wetzel, W. Weise, Nucl. Phys. A672, 249 (2000); J.A. Oller, E. Oset, A. Ramos, Prog. Part. Nucl. Phys. 45 157, (2000); G. Penner and U. Mosel, Phys. Rev. C 66, 055212 (2002). 18. W.-T Chiang, F. Tabakin, T.S.H. Lee, B. Saghai, Phys. Lett. B517, 101 (2001). 19. A. Manohar and H. Georgi, Nucl. Phys. B234, 189 (1984). 20. B. Saghai and Z. Li, Eur. Phys. J. A l l , 217 (2001). 21. Z. Li, H. Ye, M. Lu, Phys. Rev. C 56, 1099 (1997). 22. Z. Li and B. Saghai, Nucl. Phys. A 644, 345 (1998). 23. N. Isgur and G. Karl, Phys. Lett. B72, 109 (1977); N. Isgur, G. Karl, R. Koniuk, Phys. Rev. Lett. 41, 1269 (1978); J. Chimza and G. Karl, Phys. Rev. D 68 054007 (2003). 24. Z. Li, B. Saghai, T. Ye, in progress. 25. T. Takahashi et al. (The NKS Collaboration), these Proceedings. 26. Z. Li and R. Workman, Phys. Rev. C 53, R549 (1996).

MISSING RESONANCES IN KAON PHOTOPRODUCTION ON THE NUCLEON

T. MART, A. SULAKSONO Departemen Fisika, FMIPA, Universitas Indonesia, Depok 16424, Indonesia

C . BENNHOLD Center for Nuclear Studies, Department of Physics, The George Washington University, Washington, D. C. 20052, USA

+

+

New kaon photoproduction data on a proton, y p + K + A, are analyzed using a multipole approach. The background terms are given in terms of gauge invariant, crossing symmetric, Born diagrams with hadronic form factors while the resonances are parametrized using Breit-Wigner forms. Preliminary results suggest a number of new resonances, as predicted by many quark model studies. A comparison between the extracted multipoles and those obtained from KAONMAID is presented.

1. Introduction

Considerable theoretical and experimental efforts to understand the structure of the nucleon have been devoted for more than fifty years. A consequence of this substructure is the nucleon resonance spectra found in the region between 1 - 3 GeV. This region is accessible neither through perturbative QCD at high energies nor through chiral perturbation theory at low energies. There is hope that lattice QCD will provide answers through numerical techniques. Meanwhile, our knowledge of resonance physics comes mostly from phenomenology. This paper presents a new investigation of the nucleon spectrum through the photoproduction of a kaon on a proton. To this end, we will make use of a multipole approach to describe the resonant states. Such studies has been reported by previous authors albeit using a limited data base. We report preliminary results using the new data that have become available this year from SAPHIR3 and JLAB4. 'i2,

65

66

2 . Formalism 2.1. Background Amplitudes

The basic background amplitudes are obtained from a series of tree-level Feynman diagrams, shown in previous work1>5f+12. They contain the standard s, u , and t-channel Born terms along with the K*(892) and Kl(1270) t-channel poles. Apart from the Kl(1270) exchange, these background terms are similar to the ones used by Thorn'. The importance of the Kl(1270) intermediate state has been pointed out in Ref.7. To account for the hadronic structures of interacting baryons and mesons we include the appropriate hadronic form factors in the hadronic vertices by utilizing Haberzettl's method" in order to maintain gauge invariance of the amplitudes. Furthermore, to comply with the crossing symmetry requirement we use a special form factor in the gauge terns, as has been proposed by Davidson and Workmanll. Thus, compared to the previous pioneering work1, the major advancement in the background sector is the use of hadronic form factors to control its contribution in a gauge-invariant and the crossing-symmetric fashion.

2.2. Resonance Amplitudes

The resonant electric and magnetic multipoles for a state with the mass M R , width I', and angular momentum 1 are assumed to have the Breit-Wigner form

where s represents the square of the total c.m. energy, kR and qR are the photon and kaon momenta evaluated at the resonance's pole (s = M i ) , 8 is the phase angle, j , = 1 f1for El& and j , = 1 for Mi&. The factors r , E ( M ) and r K represent the branching ratios of the resonance into y p and K'A, respectively. The 211 (qR) denote Blatt-Weisskopf barrier penetration factors which accounts for the dependency of partial decay widths on the momentum and

67

(b)

(a)

(4

(C)

Figure 1. Contribution of the s-, u-, and t-channel to the background amplitudes for kaon photoproduction on the nucleon y p + K+ A. The contact diagram (d) is required to restore gauge invariance after introducing hadronic form facton.

+

+

are given by15 uob) = 1 , Ol(Z)

=2/(1+

+

2),

+

.2(.) = 24/(9 3 2 .4) , ~ 3 ( 2= ) x6/(225 + 452' + 6x4 x 6 ) , 214(5) = x8/(11025 1 5 7 5+ ~~ 1 3 5 +~ lox6 ~ +z ' )

(2)

+

+

,

Following Thom' , in this calculation the interaction radius R has been fixed at about one Fermi (1/R = 200 MeV). All observables can be calculated from the CGLN amplitudes16

F = iu . € P I +d . iju . (L x

€)

F2

+ iu . k q . €F3+ iu .Q q .€F4 ,

(3)

where the amplitudes Fi are related to the electric and magnetic multipoles given in Eq. (1)for up to I = 4 by

+

+

+

Fi = Eo+ - $(E2+ 2M2+) EZ- 3Mz+$(E4+ 4M4+) - +(E4- 5M4-) +~(EI++MI+-$(E~++~M~+)+E~-+ cos8 ~M~-}

+

+

+ 9 {Ez+ + 2M2+ - $(E4++ 4&+) + E4- + 5M4-} cos2 8 + F(E~+ + 3 ~ 3 + ) 8 -t- ? ( E ~ ++ 4 ~ ~ C +O S )~8 , (4) F2 = 2M1+ + M I - - :(4M3+ + 3M3-) +3 {3Mz+ + 2M2- - $(5M4+ + 4M4-)} cos8 + $ ( 4 ~ ~ ++ 3 ~ C O S~~8 + Y(5iw4+ 4 + 4hi4-) 8 , (5) F 3 = 3 { El+ - Mi- - g(E3+ - M 3+) + E3- + M3-} + 15 { E2+ - Mz+ f E 4 - + M4- - g(E4+ - M4+)} cos8 COS~

COS~

+ 1"5(E3+ 2 - M3+) cos2 8 + y ( E 4 + - M4+) c0s38 ,

(6)

68

F4

= 3 { M2+ - E2+ - M2- - E2- - g(M4+ - Ed+ - M4- - E4-)}

+15(M3+ - E3+- M3- - E3-) cos8 -M4- -Ed-) cos2 8 .

+ Y ( M 4 + - E4+ (7)

These amplitudes are combined with the CGLN amplitudes obtained from the background terms1>12and substituted into Eq. (3).

3. Results and Discussion In Ref.2 Tanabe et al. put forward a model which contains the resonances in the partial waves Sll, P ~ IP13, , 0 1 3 , and GI7 resonances to fit the old K + A photoproduction data. It is well known that the KfA threshold region is dominated by the states S11(1650), PI1(1710), and P13(1720). For our analysis, we allow states up to spin 712 to contribute. Sample preliminary results are shown in Table 1, where we explored the sensitivity of the data to two separate resonant states at different energies in the same partial wave, as predicted in some quark modelsl8. In the fitting procedure, we constrain the mass of all resonances to vary between 1600 and 2200 MeV. For certain partial waves, such as D15 and F17, the fit generates spurious states in close proximity to each other (Model I). Yet, fits with only one state in each of these partial waves lead the states with masses quite different from what is found before (Model II), indicating that the results presented here cannot be yet be interpreted as signaling new resonances in these partial waves. We summarize the results as follows: 0

0

0

S11 states In the two models the mass of the first S11 does not significantly change, this first ,911 is clearly related to the four-star ,911 in the PDG table. A second 5'11 state appears above 2 GeV but its position does not remain fixed. PI, states The fit prefers two states in this partial wave, one at lower energy around 1700 MeV and one in the 1850-1900 MeV mass region. The width of the lower state turns out to be surprisingly narrow with 100 MeV, casting doubt on the interpretation that this state is the 9 1 (1710) resonance that is usually found with a much broader width of 300 - 400 MeV. P 1 3 states This situation is similar to the PI1 case. Two states are preferred by the fit, the lower with a mass below 1700 MeV, possibly cor-

69 Table 1. Resonance states and their parameters extracted from fit to models I and model 11. The units for M , I?, and 8 are given in MeV, MeV, MeV, and deg., respectively.

m,

- -Model I r A4 8 1610 2043 1728 1893 1654 1909 2200 1741 1780 1774 1921 1900 1723 2082

-

b

365 283 100 312 184

3.38 7.76 6.17 12.28 5.79 -3.29 240 -3.68 -1.33 4.45 183 -1.11 315 1.50 4.49 151 11.59 0.53 105 9.30 3.05 343 -11.36 -6.01 315 11.64 5.69 100 0.05 0.41 133 0.52 - -1.19 1.85

13.8 -76.5 -180.0 87.7 -42.6

- -Model I1 r M 1610 2200 1707 1836 1688

354 400 100 100 121

140.3

1850

400

-94.2

1912

148

1750

252

2179

400

1715

90.4 -21.4

4.12 -4.94 5.00 1.92 5.45 -2.97 3.67 -2.61 -5.72 1.64 -0.62 -4.15 -4.07 1.83

13.5 91.2 152.3 -180.0 -8.26

100

-0.69 0.94

128.7

1730

100

180.0

2011

400

0.25 0.14 1.59 1.37 1.91

-41.1 156.7 -66.9 179.9

148.8 180.0 171.7 116.6 -180.0

-

-10.1

responding to the p13(1720) and a state at higher energy with a broader width of 250 - 400 MeV. 0 1 3 stat8es Using quark model predictions as guidance, a previous analysis8 suggested that a new resonance in this partial wave, the 013(1900), provides an explanation for the new structure found in the old SAPHIR data around 1900 MeV. Our new results with the new data point a more confusing and still incomplete picture, the fits find a lower state around 1750 MeV, while the mass of the higher state appears to be ill determined. 0 1 5 and FITstates In both partial waves, the fit clearly rejects two separate states,

70

P ( Y, K t ) A

. d 'D

-1.0

-0.5

0.0

0.5

1.0

-0.5

0.0

0.5

1.0

.0.5

0.0

0.5

1.0

cos 8 Figure 2. The p ( y ,K + ) A differential cross sections as a function of kaon angle. Dashed and solid lines refer to the Model I and I1 of Table 1 , respectively. Data are taken from Ref. 3113.

71

0.10

0.05 0.00

0.15 0.10

0.05 0.00 0.25 0.20 0.15 0.10

0.05 0.00 0.25 0.20 n 0.15 3. 0.10 v 0.05 0.00 0.25 0.20 b 0.15 0.10 'D 0.05 0.00

. % . 5:

1.6

1.7 1.8 1.9 2.0 2.1 2.2 2.3 1.6 1.7 1.8 1.9 2 0 2.1 2.2 2.3 2.4

W (GeV) Figure 3.

Same as in Fig. 2, but for W distribution.

yet when combined into one resonance, the mass turns out to be unstable. It is not clear yet if resonances are really needed in these partial waves or if these phenomena are mocking up missing

72

P(Y . K + ) A 1.0

1.660 GeV

1.898 Gev

1.770 GeV

cos e

-1.0 -1.0

-0.5

0.0

0.5

1.0

4.5

0.0

0.5

1.0

cos e Figure 4. The A recoil polarization for the p ( y , K + ) A reaction. Notations are as in Fig2.

10 0.5

0.0 -0.5

I .o 0.5

w

0.0

4.5 1.0

05

0.0 -0,s

'

-1.0 0.5

0.6

0.7

0.8

0.9

1.0

0.6

0.7

0.8

COS

0.9

1.0

0.6 0.7

0.8

0.9

1 1.0

e

Figure 5 . Photon asymmetry for the p ( y , K + ) A reaction. Notations are as in Fig 2.

background physics. GI7 states The only well-known state in this partial wave is around 2100 MeV, a new state with a mass as low as 1750, as suggested by our fit, would be surprising. Further studies will have to verify if this state is in fact required to fit the data.

73

I .o

4.4 -0.6

3.0 0.5

-1.5 0.4

-0.6 -0.8

-0.4

j

0.2

\.

-0.6

-0.4

0.1

-0.15

-0.1

-0.05

-0.2 0.05

0.05 0.05

-0.05 -0.1 -0.15 -0.1 1.6

1.8

2.0

2.2

-0.2 2.4 1.6

-0.05 1.8

2.0

2.2

2.4

-0.1 1.6

1.8

2.0

2.2

2.4

-0.1 1.6

1.8

2.0

2.2

2.4

W (GeV) Figure 6. Electric and magnetic multipoles for the p ( y , K + ) A reaction. Dashed and solid lines represent Model I and Model I1 of Table 1. Dash-dotted lines display the multipoles obtained from the KAON-MAID ~ o l u t i o n ' ~where , only resonances with 1 5 2 are included.

These sample results display the difficulty in identifying a unique set of resonances required to fit the data. Clearly, minimization of the x2 cannot be the only criterion for establishing a new resonance but one must achieve consistency with other reactions through a genuine multichannel analysis. Figures 2-5 compare the model fits with the available differential cross section and polarization data. As expected from the two x2 the models are virtually indistinguishable in these observables, yet can lead to very differ-

74

ent multipoles, as shown in Figure 6. Clearly, more polarization data are needed that should permit a more model-independent multipole analysis.

Acknowledgment This work was supported in part by the QUE project (TM and AS) and the U.S. Department of Energy contract no. DE-FG02-95ER-40907 (CB).

References H. Thom, Phys. Rev. 151,1322 (1966). H. Tanabe, M. Kohno and C. Bennhold, Phys. Rev. C39, 741 (1989). K.-H. Glander et al, nucJ-ex/0308025. J. W. C. McNabb et al, nucJ-ex/0305028. F. X . Lee, T. Mart, C. Bennhold, H. Haberzettl and L. E. Wright, Nucl. Phys. A695,237 (2001). 6. R. A. Adelseck and B. Saghai, Phys. Rev. C42,108 (1990). 7. R. A. Adelseck and L. E. Wright, Phys. Rev. C38,1965 (1988). 8. T. Mart and C. Bennhold, Phys. Rev. C61, 012201 (2000). 9. R. A. Arndt, I. I. Strakovsky, R. L. Workman and M. M. Pavan, Phys. Rev. C52,2120 (1995). 10. H. Haberzettl, C. Bennhold, T. Mart and T. Feuster, Phys. Rev. C58, 40

1. 2. 3. 4. 5.

(1998). 11. R. M. Davidson and R. Workman, Phys. Rev. C63,025210 (2001). 12. J. C. David, C. Fayard, G. H. Lamot and B. Saghai, Phys. Rev. C53,2613 (1996). 13. M. Q. Tran et al., Phys. Lett. B445,20 (1998). 14. K. Hagiwara et al., Phys. Rev. D66,010001 (2002). 15. J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (John Wiley & Sons, New York, 1952). 16. G. Knochlein, D. Drechsel and L. Tiator, Z. Phys. A352, 327 (1995). 17. See: http://www.kph.uni-mainz.de/MAID/kaon/kaonmaid.html 18. S. Capstick and W. Roberts, Phys. Rev. D 58,074011 (1998).

THE PROPERTIES OF THE A(1405) IN ELECTROMAGNETIC REACTIONS

A. RAMOS

Departament d’Estructum i Constituents de la Matkria, Universitat de Barcelona, E-08028 Barcelona, Spain

J. C. NACHER AND E. OSET Departamento de Fisica Teo’rica and IFIC, Centro Mixto Universidad de Valencia- CSIC, Apartado 22085, E-46071 Valencia, Spain T.-S. H. LEE Physics Division, Argonne National Laboratory, Argonne, IL 6043.9, USA J. A. OLLER Departamento de Fisica, Universidad de Murcia, 30071 Murcia, Spain H. TOKI RCNP, Osaka University, Ibaraki, Osaka 567-0047, Japan The properties of the h(1405), obtained from various electromagnetic reactions, are studied within the framework of a coupled-channel chiral unitary scheme. We present cross sections for the reaction yp + K+h(1405), recently measured at SPringS/LEPS, and for the radiative production K - p -+ yh(1405). The latter reaction gives rise to a narrower h(1405), slightly displaced towards higher energies. If confirmed by experiment, this would be a clear evidence of the recently claimed two-pole nature of the A(1405).

1. Introduction

One of the primary goals in the field of hadronic physics is to understand the nature of baryon resonances, ie. whether they behave as genuine three quark states or can be dynamically generated through the iteration of a p propriate non-polar terms of the meson-baryon interaction. In the last decade, chiral perturbation theory (xPT) has emerged as a powerful scheme to describe low-energy meson-meson and meson-baryon dynamics, but it is 75

76

limited to low energies and cannot describe the physics close to resonances (poles in the T-matrix). These two shortcomings have been recently circumvented by combining chiral dynamics with non-perturbatrive unitarization techniques (UxPT) [l-121. The h(1405) is one particular example of these so-called dynamical resonances. Recently, the interest in studying its properties has been revived by the observation that the nominal h(1405) is in fact built up from two poles of the T-matrix in the complex plane, having different widths and coupling differently to xC a.nd K N states [13], as also found later in Ref. [14]. In the present contribution we discuss how the h(1405) can be observed in several electromagnetic reactions, using a chiral unitary approa.ch that generates the resonance from the interaction of K-p with its coupled channels. After describing briefly the essentials of our K-p scattering model, we move to the electromagnetic reactions. To test the scheme, we first revisit the radiative production of the ground-state J p = 1/2+ hyperons, yA, yCo, and show that the consideration of through the reactions K-p the complete meson-baryon basis in the unitary coupled-channel scheme is crucial to reproduce some measured threshold branching ratios [15]. Next, we present a study of the reaction ~p -+ K+A(1405), recently measured at, SPring8/LEPS [16], both on free protons and in the medium [17]. Finally, we present results for the reaction K - p + yA(1405), which produces a narrower A( 1405), slightly displaced towards larger energies [18]. From the study of Ref. [13], we now understand that, since in this reaction the photon has to ra.diate energy before the A(1405) can be produced, the resonance is in fact initiated by a K-p state, thereby selecting the dynamical pole contribution that couples more st,ronglyto K N , which is located at a higher energy and also has a smaller width. -+

2. Meson-baryon scattering model

The search for dynamically generated resonances proceeds by first constructing the meson-baryon coupled states from the octets of ground state positive-parity baryons ( B )and pseudoscalar mesons (a) for a given strangeness channel. Next, from the lowest order lagrangian

we derive the driving kernel in s-wave

77

with which we solve the coupled-channel Bethe-Salpeter equation

+

Ta3. .= Va3 . K z G z9 ~ ~

(3)

where z , j , l axe channel indices and the &l and Tlj amplitudes are taken on-shell. This is a particular case of the N/D unitarization method when the unphysical cuts are ignored [4, 51. Under these conditions the diagonal matrix GIis simply built from the convolution of a meson and a baryon propagator and can be regularized either by a cut-off (qkax),as in Ref. [3], or alternatively by dimensional regularization depending on a subtraction constant (a!)coming from a subtracted dispersion relation [6, 71. In the case of K - p scattering, we consider the complete basis of mesonbaryon states, namely K - p , Kon, nA,qA, qCo, r + C - , n-C+,n°Co,K+E:and KoEo, thus preserving SU(3) symmetry in the limit of equal baryon and meson masses. Taking a cut-off of 630 MeV, the scattering observables, threshold branching ratios and properties of the A( 1405) resonance were well reproduced [3], as shown in Table 1 and Fig. 1. Table 1. Branching ratios at K - p threshold. Experimental values taken from Re&. [19, 201.

I Ratio

I

Exp.

1

Model

h

m

2

a

$ v

z

CI

a2

B rn

a

z

1350

1400

1450

C.M. Energy (MeV)

Figure 1. The x C invariant ma88 distribution around the A(1405) resonance. Results in particle basis (solid line), isospin basis (short-dashed line) or omitting the I ~ A 7Co , channels. Experimental histogram taken from Ref. [21].

78

This and similar models have generated s-wave resonances in all strangeness sectors [3,6-121, giving rise to a singlet and two octets of dynamical baryon resonances with J" = 1/2- [13, 141. As a consequence, the nominal A(1405) is in fact represented by two poles of the T-matrix, having different widths and coupling differently to TC and K N states. In the chiral model of R.efs. [3, 71, these poles appear at ZR = 1390 - i66 and zfi = 1426 - i16, so that the first (second) pole couples more strongly to the TC ( Z N ) states. 3. Radiative production of ground state hyperons: K - p --f yA,yEo

It was first demonstrated by Siege1 and Saghai [22] that the K - capture rates in K - p + yA, yCo reactions were very much affected by initial K - p interactions. However, about 30 - 50% deviation of the coupling constants from the SU(3) values was needed in that work to obtain an accurate description of the data. We studied these reactions [15] incorporating the unitary K - p scattering chiral model of Ref. [3], in order to elucidate whether the data can also be well described with the parameters fixed by the SU(3) chiral symmetry, hence providing us with additional support to the interpretation of the A(1405) as a quasi-bound meson-baryon state with S = -1. The amplitude for t,he K - p + y Y reaction is represented schematically in Fig. 2, where the photoproduction mechanisms, contained in the blob labelled A, are depicted in Fig. 3. Only the meson-exchange term (3c) and the contact term (3d) survive, due to the s-wave nature of the meson-baryon interaction and the fact that the reaction is studied at threshold [15].

P

Figure 2.

Y

Schematic representation of the K - p

B 4

yY amplitude.

The resulting branching ratios at threshold are summarized in Table 2. The Born term alone gives a very poor description of the branching ratios, especially for Co photoproduction, while the inclusion of initial state interaction through the chiral coupled channels model improves the situation substantially, especially for R, the ratio of branching ratios, which is reduced by a factor 14 . It is interesting to note that, when the qA,11C0

79

k--P

t

I

P

+

P

(d

(dJ

Figure 3. Photoproduction mechanisms

channels are omitted, the A branching ratio cannot be reproduced. This is in line with the pioneering work of Ref. [22], which omitted the q channels and had to assume a fictitious breaking of SU(3) in the coupling constants to restore agreement with the data. Finally, we present results including a form factor of A, = 1 GeV at the meson-baryon-baryon vertices accounting for the composite nature of hadrons. Our results agree with the data within experimental errors, indicating that there is no need for a substantial breaking of SU(3) to understand the dynamics of these reactions. Table 2. Branching ratios (in units of 10-3) for the reactions, compared with the data [23. B K - P+-,A

A (Born)

+

A TGA (full) no 7) channels full

+ cut-off EXP

BK - p - + - , c ~

1.12

0.073

R 16.4

1.58

1.33

1.19

2.47

1.27

1.94

1.10

1.05

1.04

0.86 f 0.16

1.44 f0.31

0.4 - 0.9

4. Photoproduction of the A(1405): -yp -+ K+A(1405) The A( 1405) can be produced from the reaction (7, K+)on protons, recently implemented at LEPS of SPring8/RCNP [16]. When performed on nuclei, this reaction may also be used as a means to learn about modifications of the A(1405) in the medium, as was already suggested in Ref. [24]. The mechanisms that would initiate the reaction y p -+ K + M B , where M B is any of the 10 states that couple to the A(1405), are depicted diagrammatically in Fig. 4. The A(1405) is generated dynamically by multiple scattering of the meson-baryon pair in any of the related coupled channels, as depicted in Fig. 5. Choosing a photon energy around EyLab = 1.7 GeV,

80

the particles are produced with low energy. In this case the contribution of the meson pole terms (diagrams a, b, of Fig. 4) is negligible and, in addition, terms that would involve pwave type couplings or the excitation of pwave resonances like the C(1385) are also suppressed. Explicit details of the formulation can be found in R.ef. [17].

1

Figure 4.

b)

1

Feynman diagrams used in the model for the y p

K+A(1405) reaction.

Figure 5. Diagrammatic representation of the meson-baryon final state interaction in the yp -+ K+A(1405) process.

The invariant mass distribution of the final meson-baryon state is depicted in Fig. 6. The r°Co cross section (dot-short-dashed line) follows very closely the real shape of the A(1405) resonance (solid line), since the r°Co state is built up from I = 0 and I = 2 components and the I = 2 contribution to the reaction is small. Due to the particular isospin decomposition of the r C states, the r - C and r f C - cross sections differ in the sign of the interference between I = 0 and I = 1 amplitudes (omitting the negligible I = 2 contribution). This difference has been observed in the experiment performed at SPring8/RCNP [16] and provides some information on the I = 1 amplitude. When all channels are summed, including r A , the interference terms cancel and the cross section is given by I = 0 and I = 1 contributions, the latter being a smooth background over the resonant shape of the former. Although this seems to imply that detecting the K+ could be sufficient to determine the shape and strength of the A(1405), one should also consider the possible contamination of the pwave C(1385) resonance in this region.

81

6.6

4.6

n-d

7 P ..

--> f

YB

E, = 1.7 OeV

a ,

'

1.6

0.6

Figure 6. Mass distribution for the different channels. The C+n-, C-n+ and Cono distributions are shown in the figure with the dashed lines. The solid line with the resonance shape is the sum of the three C n channels divided by three. In addition the distributions for noA and K - p production are also shown.

When this reaction is performed on nuclei, one finds that the Fermi motion of the proton produces, for a given experimental set up of photon and K+ momenta, a large spreading of invariant masses due to the high momentum of the incident photon [17]. Any trace of the original resonance is lost in nuclei and, in order to see genuine dynamical medium effects, one would have to measure explicitly the TC states, including appropriate final state interaction corrections. 5. Radiative production of the A(1405): K - p + yA(1405) The energy lost by the photon radiated in the K-p yA(1405) reaction allows us to inspect the region below the K - p threshold, where bhe A( 1405) appears. The resonance is generated by multiple scattering of meson-baryon pairs in coupled channels, depicted schematically in Fig. 7. By coupling t,he external photon, one generates the rest of diagrams shown in the figure. For the low energy K - involved in this reaction, it has been shown [18]that the contact term contributions are negligible and the reaction is dominated by diagrams of rows 3,4,5,6plus the magnetic part in row 8. This is opposite to what happens in the photoproduction reaction, where the dominant terms are the contact ones and the Bremsstrahlung contributions can be neglected. Results for the cross sections in the K - p + r-C+y, .rr+C-y, T ~ C O ~ , n0Ay, K - m channels are shown in Fig. 8. The cross section for K - p -+

-+

82

Figure 7. Feynman diagrams used in the model for the K - p

-+

A ( l 4 0 5 ) ~reaction.

K'ny is very small and is not plotted. The A( 1405) peak appears clearly in the TC spectrum (dotted line) and, as before, the sum of all channels or, equivalently, the detection of the photon alone seems at first sight sufficient to obtain the shape of the resonance. However, this measurement would be contaminated by the excitation of the C(1385), a p-wave resonance that can be easily excited in this reaction, and the detection of the final meson and baryon, in coincidence with the phot,on, would be required. In any case, the small branching ratio (12%) of the C(1385) into the TC channel makes it easy to extract the A(1405) contribution, which decays only into that channel. Note that t,he invariant mass distribution appears displaced to higher energies ( w 1420 MeV) and it is narrower (35 MeV) than what one obtains from the photoproduction reaction. This is an evidence of the existence of two poles representing the nominal A(1405), having different widths and coupling differently to TC and K N st,ates [13]. In the present, reaction, the photon has to be radiated from the initial K-p state so that the subthreshold resonance is generated. This ensures that the A( 1405) is initiated from K-p states, hence selecting the pole that couples more strongly to K N which is narrower and appears at a higher energy. When this reaction is performed on nuclei, Fermi motion effects are

83

1.5-

1.35

1.40

u, (dcv) 1.45

1.50

Figure 8. Mass distribution for the different channels BS a function of the invariant mass M I of the final meson baryon system. The solid line with the resonance shape is the sum of cross sections for all channels. Dotted line: pure 1 = 0 contribution from the C.rr channels. The effects of the Fermi motion with ( p = po/4) is shown with solid line.

moderate, due essentially to the small momenta of the incident K - and emitted y. The resonant shape obtained in nuclear mat,ter at, p0/4, where PO is normal nuclear matter density, is only slightly wider, so that genuine medium modifications could in principle be visible on top of Ferini motion broadening. However, on would have to measure TC states in coincidence to avoid t,he contribution of the pwave C(1385) resonance. 6. Summary and Conclusions

In this contribution we have shown, in the framework of a chiral unitary scheme, that the properties of the A(1405) can be obtained from various electromagnetic reactions. We have first tested our chiral model for the meson-baryon interaction on the radiative production of ground state hyperons, showing that a good agreement with the data can be obtained with interaction couplings fixed by the SU(3) symmetry of the chiral lagrangian. The photoproduction reaction, yp K+h(1405), produces different shapes when detecting T+C- or T-C+ cross sections, due to the interference between I = 0 and I = 1 amplitudes, as seen recently in SPring8/RCNP. This reaction is not suited to study medium modifications of the h(1405) because of the large Fermi motion broadening induced by the large momentum of the incoming photon. Finally, we have shown that the radiative production reaction K - p -+ -+

84

7A( 1405) produces a narrower resonance, slightly displaced towards higher energies. We have argued that this reaction selects one of the two poles that represent the nominal A(1405), t he one coupling more strongly t o K N states, which has a smaller width and is located at a higher energy. Acknowledgments This work is supported by DGICYT (Spain) projects BFM2000-1326, BFM2002-01868 and FPA2002-03265, t he EU network EURIDICE contract HPRN-CT-2002-00311, and the Generalitat ed Catalunya project 2001SGR00064.

References N. Kaiser, P. B. Siegel and W. Weise, Nucl. Phys. A594,325 (1995). N. Kaiser, T. Waas and W. Weise, Nucl. Phys. A612,297 (1997). E. Oset and A. Ramos, Nucl. Phys. A635,99 (1998). J. A. Oller and E. Oset, Phys. Rev. D60,074023 (1999). J. A. Oller and U.G. Meissner, Nucl. Phys. A673,311 (2000). J. A. Oller and U. G. Meissner, Phys. Lett. B500,263 (2001) 7. E. Oset, A. Ramos and C. Bennhold, Phys. Lett. B527,99 (2002). 8. A. Ramos, E. Oset and C. Bennhold, Phys. Rev. Lett. 89, 252001 (2002). 9. J. C. Nacher, A. Parrefio, E. Oset, A. Ramos, A. Hosaka and M. Oka, Nucl. Phys. A678,187 (2000). 10. T. Inoue, E. Oset and M. J. Vicente-Vacas, Phys. Rev. C65,035204 (2002). 11. M. F. M. Lutz and E. E. Kolomeitsev, Nucl. Phys. A700,193 (2002). 12. C. Garcia-Recio, J. Nieves, E. Ruiz-Arriola and M. J. Vicente-Vacas, Phys. Rev. D67,076009 (2003). 13. D. Jido, J. A. Oller, E. Oset, A. Ramos and U. G. Meissner, Nucl. Phys. A725,181 (2003). 14. C. Garcia-Recio, M. F. M. Lutz and J. Nieves, nucl-th/0305100. 15. T. S. Lee,3. A. Oller, E. Oset and A. Ramos, Nucl. Phys. A643,402 (1998). 16. J. K. Ahn, for the LEPS collaboration, Nucl. Phys. A721,715r (2003). 17. J. C. Nacher, E. Oset, H. Toki and A. Ramos, Phys. Lett. B455,55 (1999). 18. J. C. Nacher, E. Oset, H. Toki and A. Ramos, Phys. Lett. B461,299 (1999). 19. D. N. Tovee et al., Nucl. Phys. B33,493 (1971). 20. R. J. Nowak et al., Nucl. Phys. B139,61 (1978). 21. R. J. Hemingway, Nucl. Phys. B253,742 (1985). 22. P. B. Siegel and B. Saghai, Phys. Rev. C52,392 (1995). 23. D. A. Whitehouse et al., Phys. Rev. Lett. 63,1352 (1998). 24. V. Koch, Phys. Lett. B337,7 (1994).

1. 2. 3. 4. 5. 6.

ANALYSES OF THE KAON PHOTO- AND ELECTRO-PRODUCTION IN THE ISOBAR MODEL

T. K. CHOI Department of Physics, Yonsei University, Wonju 220- 710, Korea E-mail: [email protected]. ac.kr

MYUNG KI CHEOUN AND K. S. KIM BK21 Physics Research Division and Institute of Basic Science, Sungkyunkwan University, Suwon 440- 746, Korea E-mail: [email protected] B. G. YU Hankuk Auiation University, Koyang 200-1, Korea E-mail: [email protected]. kr The SAPHIR cross section data of K + A and K + C o reactions are analyzed with new SPring-8(LEPS) data on the beam polarization asymmetry, which are taken into account as new constraints on the Isobar model. The simultaneous fit of model parameters to these data yields the consistent description of both data at the price of worse x2 value and rather large K’ contribution. The role of resonance &(1895) is obvious in the energy region E, 1: 1.45 GeV and the resonance F15(1650) improves the x2 fit of cross sections with beam polarization data to a good degree. Analysis of kaon electro-production p ( e , e’K+)h is also presented by including the contribution of the longitudinal virtual photon. Various electro-magnetic form factors for K, K1 and K* resonances are adopted to compare dependence of the electro-production cross section on these form factors. Our recent progress in this field is also presented.

1. Introduction

Recently there has been a renewed interest in kaon photo-production process, motivated partly by the ”missing resonance” problem and much efforts were made to investigate the nucleon resonances in the reaction on and experiment both sides of the theory Mart et.al. proposed that the secondary resonance peak visible in the SAPHIR data of K + A photo-production should be responsible for the nu516.

29334

85

86

cleon resonance with mass around 1.9 GeV. They indicated that, it is the 0 1 3 resonance state, which is hidden in other liadronic processes, thus called "missing". Saghai and, later advocated by Penner et.aE. ', showed that such a secondary peak can be also reproduced by the variation of model parameters without 0 1 3 state. In fact, since the Isobar model has many model parameters adjustable within the x2 limit as discussed in the work of Janssen 4 1 it may be premature to determine the existence of a particular resonance state in a specific energy region by simply looking into the total cross section alone. To conkm the conjecture of the new resonance, it is necessary to examine the consistency of the conjecture with other observables, such as the polarization observables. Furthermore, new data on the beam polarization asymmetry have been measured at the LEPS experiment, which shows not,able deviations from the existing model calculations '. We are motivated by this point and our purpose here is to show that the SAPHIR cross sections data with the conjecture of 013(1895) are consistent with the LEPS photon beam polarization daba. On the other hand, the recent data from JLAB using the polarized electron beam are expected to give more significant constraints not only on the coupling constants of the relevant resonances, but also on the related electro-magnetic form factors. Both polarized photon and polarized electron beam facilities complement each other. In this talk our first step endeavor to combine both data is introduced with some discussions on the electro-magnetic form factors peculiar to the kaon electro-production process. 2. Photo-production

The transition amplitude for reactions, p ( y , K+)A and p ( y , K+)& is given as a sum of two separate terms

M

= MBackground

4-MResonance ,

(1)

where the background amplitude is composed of the pseudovector(PV) coupling Born terms of direct and cross channels together with t-channel kaon pole t,erm. In addition, including the contact interaction term of PV coupling and the gauge correction terms given by the Haberzettle prescription lo, the background t,erm reads,

The resonance amplitude MResonance in our model includes nucleon resonance N * and hyperon Y*resonances on the basis of the following options;

87

(i) Resonances with the appreciable strong decay ratio relevant to the process in the PDG are considered. (ii) For K+A photo-production, N * resonances, such as s11(1650), p11(1710) and p13(1720) in s-channel are dominant ones for the steep rise of the cross section near threshold, while as A* resonances, &1(1900) and p31(1910) give rise to the dominant resonant peak for K+Co photoproduct ion. (iii) The u-channel hyperon resonances, Pol( 1810) and P11(188O), which usually contribute backward angle kaon production, are expected to play roles in the differential cross sections. But the contributions would be small. (iv) The resonance parameters are subject to respect the empirical data on the radiative kaon capture by crossing symmetry and cut-off mass A in strong form factors plays a significant role on adjusting the Born term to data points.

2.1. K + A Photo-production Given that the resonances with their parameters are constrained by those options mentioned above, we write a basic set for the K+A photoproduction as follows, Basic set = Background

+ K* + K1 + Sll(1650) + p11(1710) + p13(1720),

(3)

and take the transition amplitude of our present work as,

< I(+AOlTlV = Basic

set

>ours

+ &3(1895) + 8’15(1680)+ A*So1(18OO)+ h*~01(1810).(4)

With coupling constants, g K p A / & = 3.74, gxpc/& = 1.09 fixed to the broken SU(3) value and cut-off A taken as 0.8 GeV/c, we obtained a good fit of the SAPHIR cross sections of K + A photo-production, as shown in figure 1. It is found that the resonance 0 1 3 plays a role of raising the peak near E,=1.45 GeV, while the inclusion of resonance F15(1680) improves remarkably x2 value within our model. Therefore, our result favors the confirmation of &(1895). It is worth remarking that the simultaneous fit of the SAPHIR cross section with the LEPS polarization leads to the large increase of the coupling constant of K* . Based on the basic set in eq.(3), Mart et. al. included only Ol3(1895)

88 y + p --> K++ A

0

our madel

1.5

2

Figure 1. Total cross section of p(y, K + ) A reactions.

without Y * resonances exchanges in the transition amplitude ',

< K'C'ITlyp

>MB=

Basic set

+h(1895).

(5)

They also obtained the successful description of cross sections with the cut0.5 GeV2/c2, rather soft. However, the model (MAID2000) fails off A' to reproduce the LEPS polarization observable 9. 2.2. K + X o Photo-production

In a similar way, with a basic set for the K+Co photo-production given as Basic set = Background

+ K* + &1(1650) + Pll(1710) + A*S31(1900)

+A*PSI( 19lo),

(6)

we take the transition amplitude as follows,

< K+C'Iqyp

>ours

+ K1 + P13(1720) + P33(1920) + Fla(2000) +A*P01(18lO) + C*P11(188O). = Basic

set

(7)

In figure 2, we show the result of X+& cross section with the transition amplitude given in eq.(7). The data points are taken from SAPHIR

89 y + p -->K+ + zo 3,

1

I

Figure 2. Total cross section of p ( y , K+)Co reactions.

experiment5. For this reaction, Mart et. al. took only K1 axial vector meson exchange in the t-channel and without Y*resonances exchanges in the u-channel

< K+CoJTJyp> M B =

Basic set

+ KI .

(8)

Note that in model calculations of Mart and Bennholdl, the neglect of uchannel hyperon resonances yields a mandatory use of rather soft cut-off parameters in order to fit the data. Janssen et. al. indicated this point and included hyperon resonances in their calculation with a hard cut-off for form factors.

< I(+xoITIyp >Janssen = Basic set

+ &(1720) + A*Po1(1810) 4- C*P11(1880).

(9)

They found that delta resonances are insensitive to the beam polarization data of LEPS and yield poor predictions for the data, although they obtained a successful reproduction of cross sections. In figure 3 we display our results for the beam polarizations of K + A and K+Co, which are fitted with model parameters chosen to reproduce the total cross sections, figure 1 and figure 2 respectively. Our model predictions for the observables are in good agreement with the experiments, while as the models of Mart and Janssen were reported to predict a tendency opposite to the LEPS beam polarization datag.

90

Figure 3. Photon polarizations asymmetry for thep(y, K + ) h (left) and p(y, K + ) C o (right) reactions as a function of cosm+O; for each different photon-energy bins upto 2.0GeV. The fitting curves from our model are shown with the experimental data

3. Electro-production

In this section we applied our previous model 3 , which was constructed for Orsay kaon photo-production data, to the electro-production. Since the coupling constants of the relevant resonances necessary to describe the reaction are determined in the photo-production data, we do not use the fitting scheme, but simply exploit the results of the previous one, i.e., the coupling constants of each participating particle, for the case of electroproduction 14. However, similar to the hadronic form factors attached to account for the hadron structure in a tree-diagram approach, one needs indispensably to introduce electro-magnetic (EM) form factors. It, gives rise to two sort of ambiguities, which should be stated clearly before continuing

91

present discussions. One is the possibility of the violation of gauge invariance. Many ways to restore the gauge invariance for the hadronic form factors are suggested already but the recipe for the EM form factors is still not clear, in specific, if we take both form factors into account. We exploit the GrossRiska method l 5 which turned out to effectively maintain the gauge invariance in case of pion electro-production 16. The other is concerned with the shape of the EM form factors. Many types of them calculated from theoretical models l7 were applied to the reaction with some cut-off parameters, whose values were fitted to the data l82I9. But these parameters were determined simultaneously with other coupling constants. Since the EM form factors do not appear in the photo-production, we do not fit them to the electro-production data, but investigate the consequences of various type of form factors extracted from the other papers in the electro-production. 11712113,

3.1. Basic Formula The general cross section for the electro-production is given as,

da

(G

)= dau ~ + ELdaL ~ + ~dapsin~Ocos2$ + ~ ~ d a ~ s i n O c ,o s $ -1

(10)

E = [l - 2 kZ ~ t a n ~ ( : ) ] is the transverse polarization, and E L = kZ - F f means the longitudinal polarization. Detailed descriptions for each

where

term can be found elsewhere18. In this talk we limit our discussion to the unpolarized cross section, which is a sum of first two terms in the above equation. We do not show the result for the polarized cross section because we want to grasp a general dependence of the cross section on the model spaces and the EM form factors. More detailed calculations for the polarized beams at JLAB will appear near future time. 3.2. Electrw-Magnetic Form Factors

We adopt, as for the nucleon's EM form factors, the results of ref. l7 and exploit them for the baryon resonances. For y N * R form factors, F", = F2P and F," = 0 are taken, and for yY*A, we use FF' = FT and FT* = 0. But, for y h h , F 2 = FF, F 1 = F,'", and for y h C , F2 = FT and F 1 = 0 are used, respectively. For h n form factor we compare two different types

92

which is typical to the Vector Meson Dominance (VMD) model. The Constituent Quark Model (CQM) gives FK’

(&’)

=

a 1-a 1 + Q2/A5 + 1 + Q2/Ai with a = 0.398 ,A1 = 0.642,

A2 =

1.386 .

(12) In the sense that both form factors can describe the experimental results, both types are available for the electro-production. But kaon resonances K* and K1 do not have any experimental results, so that the following two form factors inspired by the VMD modeIs are compared

which is termed as an extended VMD (EVMD) l9 because it allows a direct coupling to the hadron, and simplified VMD (SVMD) l8

F K * , K ~ (=Q1/(1+ ~ ) Q2/A2) with A x + = 0.95 , A K ~= 0.55 .

(14)

We exploit the same form factor for both K” and K1 mesons. The dependence of the cross section on the kaon form factors was studied firstly, but both form factors do not give any discernible differences, expectedly. But kaon resonances show drastic changes, which result is shown at Figure 4. The lowermost (dashed) line is the case of the SVMD, the dotted curve is the case of EVMD. Both results can not reproduce the data, but the difference is unexpectedly large. It is because of totally different modelslsJ9. Actually Q2 dependence of both form factors are quite different. It means that for unanimous result regarding kaon resonances’ form factors one needs more careful calculations. The uppermost result is the case of soft EM form factors of J = 5/2 resonance, which resonance is peculiar to our model. It just shows that the s-channel contribution is quite sensitive on that of tchannel. So called duality can be inferred from this result. Therefore it would be a hard task to obtain information of each resonance form factors at this stage unless one agrees with explicit role of each resonance. 4. Conclusion and discussion

The cross sections and beam polarization data on kaon photo-productions K+A and K+Co are reproduced with cut-off A and coupling constants taken to yield a reasonable x2 value in a simultaneous fit of SAPHIR and LEPS dat,a. In practice, the inclusion of LEPS data makes the x2 value worse in the fitting procedure of SAPHIR cross sections. In this work, in order to remedy this situation, we considered the resonance with spin 5/2 and mass

93 2

0.5

I

I

I

I 0.4

-

0.2

I

Q2(Ge$/cz)

+

Figure 4. Differential cross section d o r r ~= dou d a as ~ a function of momentum transfer Q 2for the reactions e p + e’K+h. The curves is the calculation of our model.

around 1.9 GeV and tested. In the case of K + A photo-product,ion, the resonance with spin 5/2 state F15(1680) plays a significant role to reduce the x2 value and, besides delta resonance P33( l92O), the nucleon resonarice F15 (2000) gives a considerable contributions to the K+Co photo-production in the present calculation. These findings respect the fact that the nucleon resonances with spin 5/2 give the nontrivial contributions, when applied to fit to the LEPS data with the same parameters for the SAPHIR. data. It is also noticeable that the contribution of K* in the t-channel becomes dominant, with the increase of its coupling constant in the same fitting procedure to the LEPS polarization data points. By the dualit,y of s-channel and t-channel, this, in turn: implies that there would be more s-channel resonances contributing to the energy region Ey = 1.5 GeV of both reactions. Although we do not present here the results of the differential cross sections with respect to the produced kaon angle in each energy bins, we could remark that the backward suppression of kaon angle implies minor role of hyperon resonances. However, since its role is to adjust the range of cut-off parameters, we include the hyperon resonance, Sol(1800), Po1(1810) to obtain the moderate value of cut-off A. The contributions of hyperon resonances considered here are, nevertheless, even suppressed to reach the optimal results for the simultaneous fitting procedure. In case of electro-production, one has expected the extraction of the kaon form factor because of the t-channel pole dominance in this reaction. But interferences of other resonances would make it. quite difficult. This

94

is a contrast to the caye of pion electro-production. More steady and consistent descriptions of the reaction are necessary for this purpose. All of these shortcomings might imply some limits of the Effective Lagrangian Approach(ELA). Of course, the ELA would not be the most appropriate approach to the descriptions of kaon-production 20. It seems to have reached a stage elaborated enoughz1. It has too many parameters not only from the resonances but also from hadronic and/or electro-magnetic form factors. Moreover, models with only a few resonances can reproduce the experimental data to a good degree. Plausible substitutes for the ELA, such as coupled channel method for multi-channel processes z 2 , and quark models for more consistent recipes for the resonances have their own merits, but have also demerits still yet. Forthcoming results from JLAB would give more constraints on our ELA method, so that more refined and more physical ELA could be realized. In specific, beam polarization data would play crucial roles to separate each contributions of the relevant resonances. Such calculations are under progress. 23924125,

References 1. T. Mart and C. Bennhold, Phys. Rev.C61, (R)012201 (2000). 2. B. Saghai, nacGth/0105001, (2001). 3. Bong Soo Han, Myung Ki Cheoiin, K. S. Kim and 11-Tong Cheon, Nucl. Phys. A691, 713 (2001). 4. S. Janssen, J. Ryckebusch, W. V. Nespen, D. Debruyne and T . V. Cauteren Eur. Phys. J A l l , 105 (2001). 5. M. &. R a n , et.al., Phys. Lett. B445, 20 (1998). 6. W. J. C. McNabb, et. al., nucl-e~/0305028,(2003). 7. G. Penner and U. Mosel, Phys. Rev., C66 055212 (2002). 8. T. Mart, et. al., MAID2000 ht tp: //www. kph. mi-rnainz.de/ MAID/kaon/kaonmaid. html (2000). 9. R. G. T. Zegers, et. al., Phys. Rev. Lett. 91, 092001-1 (2003). 10. H. Haberzettle, Phys. Rev. C62, 034605 (2000). 11. H. Haberzettl, C. Bennhold, T. Mart,, and T. Feuster, Phys. Rev. C58, R40 ( 1998). 12. H. Haberzettl, Phys. Rev. C 56, 2041 (1997). 13. K. Ohta, Phys. Rev. C 40, 1335 (1989). 14. T. Azemoon, et. al, Nucl. Phys. B 95, 77(1975). 15. F. Gross and D. 0. Riska, Phys. Rev. C 36, 1928 (1987). 16. S. Nozawa and T.-S.H. Lee, Nucl. Phys. A513, 511(1990). 17. M. F. Gari and W. Kruempelmann, Z. Phys. A 322, 689(1985); Phys. Lett. B 173, lO(1986); Phys. Rev. D 45 1817(1992). 18. J . C. David, C. Fayard, G. H. Lamot, and B. Saghai, Phys. Rev. C 53,

95

2613(1996). 19. R. A. Williams, C-R. Ji, and S. R. Cotanch, Phys. Rev. c 46, 1617(1992). 20. Proceedings of ”Electrophoto-production of Strangness on Nucleons and Nuclei (SENDAIOS)”, (2003). 21. Bijan Saghai, Proceedings of ”Electrophoto-production of Strangness on Nucleons and Nuclei (SENDAI03)”, (2003). 22. Wen-Tai Chiang, F. Tabakin, T.-S. H. Lee, B. Sahgai, Phys. Lett., B517, 101,(2001). 23. Zhenping Li and Ron Workman, Phys. Rev., C53, R549, (1996). 24. Zhenping Li and Bijan Saghai, Nucl. Phys., A644, 345, (1998). 25. Bijan Saghai and Zhenping Li, Euro. Phys. Jou. A l l , 217, (2001).

EXOTIC BARYONS AND MULTIBARYONS IN CHIRAL SOLITON MODELS

V. KOPELIOVICH Institute for Nuclear Research of RAS, Moscow 117312, Russia

Recently observed baryonic resonance with positive strangeness is discussed. Mass and width of this resonance are in agreement with chiral soliton model predictions. A number of other exotic states are predicted within this approach, some of them are probably observed in experiments. Existence of exotic multibaryons is expected as well.

1. Introduction In recent experiments the baryonic resonance has been discovered with positive strangeness and rather small width, r < 24 MeV, and subsequent experiment has confirmed this discovery a. This resonance is observed independently in different reactions on different experimental setups in Japan, Russia, USA and FRG, therefore only few doubts remain now that it really exists. This baryon, predicted theoretically in originally called P 8and later O', together with the well known resonances h(1520) and z(1530) has one of the smallest widths among available baryon resonances. It has necessarily one quark-antiquark pair in its wave function since baryons made of 3 valence quarks only can have negative strangeness, S < 0. Besides this, some hints have been obtained on detector CLAS in reaction of n+n- electroproduction on protons for existence of new resonance with zero strangeness, positive parity, strong coupling to the An channel and weak to the N p g. This resonance could belong to one of the multiplets of exotic baryons considered in lo. Review of experimental situation, methods of detection of exotic and so called cryptoexotic states (states with hidden exotics) before discovery of @+ can be found, for example, in . 'l2i3

63778

aThese data, as well as where resonance was observed in analysis of neutrino/antinutrino interactions with nuclei, became available after the workshop.

96

97

2. Multiplets of exotic baryons

Exotic, in specific meaning of this word, are baryonic states which cannot be made of 3B valence quarks ( B is the baryon number) and should contain one or more quark-antiquark pairs. Obviously, any state with positive strangeness is exotic one, as well as states with large enough negative strangeness, S < -3B. Besides, for any value of hypercharge Y or strangeness S < 0 there are exotic states with large enough isospin, I > (3B S ) / 2 . It is due to the fact tha.t nonzero isospin have only nonstrange quarks u,d, and the number of nonstrange valence quarks equals to 3B S. The new-found hyperon with positive strangeness and at least one quark-antiquark pair in the wave funct,ionis called also the pentaquark state. It is well known that baryons (hadrons, more generally) contain the so-called sea quarks and gluons which carry large fraction of their momenta. But in the O-pentaquark the qg-pair has definite quantum number, antistrangeness, therefore it is in fact valence quark-antiquark pair. From theoreticai point of view the existence of such states was not unexpected. Such possibility was pointed out by a number of people within the quark models 12, as well as in the chiral soliton approach I 3 7 l 4 . Analysis of peculiarities of exotic baryons spectra, for arbitrary B-numbers, and estimates of energies for exotic SU(3) multiplets was made in 15. First numerical estimates of the masses of the antidecuplet components were made in Relatively small mass of the components of antidecuplet, in particular O+, was predicted in a number of papers and strictlyspeaking, it was not enough grounds for this in 6 , 1 4 , because the mass splitting in the octet and decuplet of baryons was not described in these papers. In the paper an assumption was important to provide the prediction Me+ = 1530 MeV, that the nucleon resonance N*(1.71) is the nonstrange component of the antidecuplet. The small width re = 15 MeV was obtained in only. Topological soliton models are very economical and effective in predicting the spectra of baryons and baryonic systems with various quantum numbers. The relativistic many-body problem to find the bound states in a system of three, five, etc. quarks and antiquarks is not solved in this way, of course. However, many unresolved questions of principle are circumvented so that calculations of spectra of baryonic states become possible without detalization of their internal structure. In such models baryons or baryonic systems (nuclei) appear as quantized classical (chiral) fields configurations obtained in the procedure of classical energy or mass minimization. Here

+

+

6314,7.

6914,7,8,16,

98

important role plays the quantization condition

l7

YR = NcB/3

(1)

where YR is the ”right” hypercharge, or hypercharge of the state in the body-fixed system, Nc - the number of colors of underlying QCD, B is baryon number coinciding with topological number characterizing the classical field configuration. For each SU(3) multiplet ( p , q) the maximal hypercharge or triality Ym,, = ( p 2q)/3, and relation should be fulfilled evidently Y,,, 2 YR,or

+

p+2q

NCB

2- 3 ’

(2)

which means that p+2q = 3(B+m)

(3)

at NC = 3, with m being positive integer. This quantization condition has simple physical interpretation: we start from originally nonstrange configuration which remains nonstrange in the body fixed system. All other components of the ( p , q ) SU(3) multiplet in the laboratory frame appear as a result of rotation of this configuration in SU(3) configuration space, are described by Wigner final SU(3)-rotations functions, and each multiplet should contain original nonstrange state. It is natural to call the multiplets with m = 0 the minimal multiplets 15, for B = 1the minimal multiplets are well known octet and decuplet, multiplets with smaller dimension are forbidden due to Guadagnini quantization condition l7 (recall that the number of components of the multiplet N(p, q) = ( p l ) ( q 1)(p q 2)/2). The states with m = 1 contain at least one additional quark-antiquark pair. Indeed, the maximal hypercharge ITmu, = 2 in this case, or strangeness S = $1 for the upper components of such multiplets, i.e. the pair q S should be present in the wave function, q = u or d. Due to SU(3) invariance of strong interactions all other components of such multiplet should contain additional quark-antiquark pair 1 5 . One more restriction appears from the consideration of the isospin, really the components with maximal isospin. It (27) and (35)-multiplets are the pentaquark is easily to check, that states, but the multiplet with maximal p , (28)-plet with ( p , q ) = (6,O) contains already 2 qQ pairs, i.e. it is septuquark. This follows from the fact that this multiplet contains the state with S = - 5 and the state with S = 1, isospin I = 3. All baryonic multiplets with B = m = 1 are shown in Fig.1.

+

(m),

+

+ +

99

{m}J = 1 / 2

(27) J = 3/2; 1/2

yt 0

( 3 5 ) J = 5 / 2 ;3 / 2

.

-

(28) J = 5/2

Figure 1. The 1 3 - Y diagrams for the baryon multiplets with B = 1, m = 1. Large full circles show the exotic states, smaller - the cryptoexotic states which can mix with nonexotic states from octet and decuplet.

+

The minimal value of hypercharge is Ymin= -(2p q ) / 3 , the maximal isospin I,,, = ( p + q ) / 2 at Y = ( p - q ) / 3 . Such multiplets as { 2 7 } , ( 3 5 ) for m = 1 and all multiplets for m = 2, except the last one with (p,q) = (9,O) in their internal points contain 2 or more states with different values of spin J (shown by double or triple circles in Fig.1).

3. The mass formula In the collective coordinates quantization procedure one introduces the angular velocities of rotation of skyrmion in the S U ( 3 ) configuration space, x k being Gell-Mann matriW k , k = 1, ...8: At(t)A(t) = -iWk&/2, ces, the collective coordinates matrix A ( t ) is written usually in the form

100

A = ASUZezp(ivX4)A;,, ezp(ipX8/A.The corresponding contribution to the lagrangian is quadratic form in these angular velocities, with momenta of inertia, isotopical (pionic) 0,and flavor, or kaonic OK as coefficients 17: 1 2 Lrot = -0,(w, 2

1 NCB + w,2 + w,") + -OK@: + ... + w;) - 2 2 & i wg*

(4)

The expressions for these moments of inertia as functions of skyrmion profile are presented below. The quantization condition ( 1 ) discussed above follows from the presence of linear in angular velocity wg term in (4)originated from the Wess-Zumino-Witten term in the action of the model The hamiltonian of the model can be obtained from (4) by means of canonical quantization procedure 17:

'*.

1 H = Mcl + -g2 20,

+ 20K

where the second order Casimir operator for the SU(3) group, Cz(SU3) = C:=,Ri, with eigenvalues for the (p,q) multiplets C2(SU3)p,q= (p2+ p q + q 2 ) / 3 p q, for the S U ( 2 ) group, C z ( S U 2 ) = = R f R; Ri = J ( J 1) = I R ( I R 1). The operators R, = d L / a w , satisfy definite commutation relations which are generalization of the angular momentum commutation relations to the SU(3) case 17. Evidently, the linear in w terms in lagrangian (4) are cancelled in hamiltonian (5). The equality of angular momentum (spin) J and the so called right or body fixed isospin IR used in (5) takes place only for configurations of the "hedgehog" type when usual space and isospace rotations are equivalent. This equality is absent for configurations which provide the minimum of classical energy for greater baryon numbers, B 2 2. For minimal multiplets (m = 0) the right isospin IR = p / 2 , and it is ~ (5) equals to easy to check that coefficient of 1 / 2 0 in

+ + +

z2

+

K = C2(SU3) - 2'

-N6B2/12

= NcB/2,

+ +

(6)

for arbitrary N c b. So, K is the same for all multiplets with m = 0 15, see Table 1, the property known long ago for the B = 1 case 17. For nonminima1 multiplets there are additional contributions to the energy proportional to m / 0 and ~ m 2 / 0 ~according , to (5)15. It means that in the framework should be kept in mind that for N c different from 3 the minimal multiplets for baryons differ from octet and decuplet. They have ( p , q ) = (1,(Nc - 1)/2), (3,(Nc 31/21,...( N G ,0).

101

of chiral soliton approach the ”weight” of quark- antiquark pair is defined by parameter 1 / @ K 7 and this property of such models deserves better understanding. N(p7q) (8)

(lo}

(a} (27) (35) (28)

(35) (64) (81) (80) (55)

m 0 0 1 1 1 1 2 2 2 2 2

cZ(Su3) 3 6 6 8 12 18 12 15 20 27 36

J = IR 112 312 112 312; 112 512; 312 512 312; 112 512; 312; 112 7/2; 512; 312 712; 512 7/2

K(Jmaz)

312 312 3/2+3 3/2+2 3/2+1 3/2+7 3/2+6 3/2+4 3/2+2 3/2+9 3/2+18

K(Jmaz

- 1)

3/2+5 3/2+6 3/2+9 3/2+9 3/2+9 3/2+16

Table.l. The values of N ( p , q ) , Casimir operator C2(SU3), spinJ = ZR, coefficient K

for first two values of J for minimal ( m = 0) and nonminimd (m = 1 , 2) niultiplets of baryons.

It follows from Table 1 that for each nonzero m the coefficient K ( J m a z ) decreases with increasing N(p7q), e.g. K ~ / ~ ( 3 5 1 , see also next Section. Rotation time can beestimated easily, Trot x / w with w d-/@~. It is more difficult to estimate T d e f o T m , one can state onlythat it is greater than the time needed for light to cross the skyrmion, rtTavel ~ R H So, . the rigid rotator approximation is valid if T @ K R* (27,-2,1,3/2 > X (35,1,5/2,5/2 > 135, -3,1/2,5/2 > 128,2,3,5/2 > 128, -4,0,5/2 >

In, Im, =**[m,

< sz >o -

0.60 0.73 0.80 0.58 0.67 0.75 0.83 0.50 0.58 0.67 0.75 0.57 0.82 0.44 0.85 0.61 0.78

A 6.175 2.924 1.369 155 263 371 289 418 544 665 580 694 792 814 707 989 784 1269 1938 2221

-

B C Data 5.556 5.61 2.641 2.84 1.244 1.45 139 164 176 243 277 254 335 393 379 319 314 293 433 446 452 545 591 586 648 715 733 625 601 600 725 771? 722 810 830? 825 ? 842 847 758 750 1011 1048 878 853 1312 1367 2136 2043 2379 2345

Table.2. Values of masses of the octet, decuplet, antidecuplet and some components of higher multiplets (with nucleon mass subtracted). A: e = 3.96;B: e = 4.12; C: fit with

two parameters Q K and rsB

lo.

As it can be seen from Table 2 the agreement with data for pure Skyrme

105

model with one parameter is not so good, but the observed mass of O+ is reproduced with some reservation. To get more reliable predictions for masses of other exotic states the more phenomenological approach was used in lo where the observed value MQ = 1.54 GeV was included into the fit, and O K , FsB were the variated parameters (variant C in Table 2 and Fig.2). The position of some components of {27}, (35) and (28) plets is shown as well.

{lo) J=3/2

(31J=1/2

(27) J=3/2

(35) J=Y2

Figure 2. Lowest rotational states in the S U ( 3 ) soliton model for fits C and D. The experimental masses of the (8) and (10) baryons are depicted for comparison. Not all states of the (35) are shown. This figure is taken from

lo.

The variant D shown in Fig.2 takes into account the term in H S B which appears from the p - w mixing in effective lagrangian 7110:

The best description of the octet and decuplet masses was obtained at A = 0.4. Such contribution was included also in where the linear in hypercharge term HgB = BY with ,L? N -156 MeV plays an important role. Such term is absent in approach 7110.

106

It looks astonishing at first sight that the state O+ containing strange antiquark is lighter than nonstrange component of antidecuplet, N * ( I = 1/2). But it is easy to understand if we recall that all antidecuplet components contain qQ pair: O+ contains 4 light quarks and 3, N* contains 3 light quarks and sB pair with some weight, C* E {fO} contains u,d , s quarks and s3, etc. The mass splitting inside of decuplet is influenced essentially by its mixing with (27) plet components lo, see Fig.1, which increases this splitting considerably - the effect ignored in The mixing of antidecuplet with the octet of baryons has some effect on the position of N* and C * , the position of 0' and Si,2 is influenced by mixing with higher multiplets lo. The component of (35)-plet with zero strangeness and I = J = 5/2 is of special interest because it has the smallest strangeness content (or s z ) smaller than nucleon and A. As a consequence of isospin conservation by strong interactions it can decay into An, but not to N n or Np. According to the results presented in Table 2, the components of {28}plet containing 2 qQ pairs, have the mass considerably greater than that of other multiplets on Fig.1. All baryonic states considered here are obtained by means of quantization of soliton rotations in SU(3) configuration space, and have therefore positive parity. A qualitative discussion of the influence of other (nonzero) modes - vibration, breathing - as well as references to corresponding papers can be found in 'OJ6. The realistic situation can be more complicated than somewhat simplified picture presented here, since each rotation state can have vibrational excitations with characteristic energy of hundreds of MeV. If t,he matrix element of the decay 0+ -+ K N is written in a form

MQ+ K N = 90 K N 'ii N 75%

4~t

(18)

with U N and u0 - bispinors of final and initial baryons, then the decay width equals to

where AM = M - m N , M is the mass of decaying ba.ryon, pkm - the kaon momentum in the c.m. frame. For the decay constant we obtain then g 0 K N N 4.4 if we take the value r Q + K N = 10 MeV as suggested by experimental data 1-5. This should be compared with g n N N N 13.5. So, some suppression of the decay 0 + K N takes place, but not large and understandable, according to

107

5 . Exotic multibaryons

There is no difference of principle, within the chiral soliton approach, between baryons and multibaryons, as it was demonstrated in previous sections. The latter are quantized configurations of chiral fields which correspond to the minima of classical energy for arbitrary baryon number. The equality between body-fixed isospin and spin of the quantized state, specific for hedgehog-type configuration, does not hold anymore. It is easy to understand that minimal (nonexotic) multiplets for B = 2 coincide with m = 1 multiplets for B = 1, i.e. they are antidecuplet, including the deuteron - isosinglet state, (27)-plet, including the isotriplet NN-state (so called singlet deuteron), (35) and (28)- plets. Similarly, the minimal multiplets for B = 3 are those for B = 1 and m = 2, see Table 1. Here we show two examples of lowest exotic multiplets with m = 1: the {%)-plet for B = 2 and (28)-plet for B = 3, Fig.3. There is isodoublet of positive strangeness dibaryons, 2D& 2 H e z + ' with minimal quark contents (332144, ( 8 4 ~ 3 4which , have the energy about 600 MeV above 2N-threshold, according to calculation performed in 2o in the slow rotator approximation. The spectrum of all minimal dibaryons was calculated in 2o as well. For B = 3 there is positive strangeness tribaryon (isosinglet) 3 H e g f ,its quark content is (352154. The position of the components of this multiplet is not calculated yet. One can state, however, that the difference of the masses of positive strangeness isosinglet and ground state of 3 H e

M H -~M ~H = ~ OS,B=3

+ 0(1/Nc)

(20)

with G . - the energy of antistrangeness excitation. The energies of flavor and antiflavor excitation for multiskyrmion were Calculated in 23 for baryon numbers up to 22, for B > 8 within rational map approximation 24, using the results obtained in comprehensive paper 25. Their characteristic feature is that they depend slightly on B-number. It is known that the difference between antiflavor and flavor excitation energies 26 aF,B

- WF,B = NCB/(4@F,B),

(20)

-

for any flavor (strangeness, charm or beauty) and baryon number. Since @F,B B roughly 23, this difference depends weakly on B-number and 1 26. Numerically scales like Ng is close to 600 MeV with small N

CThechemical symbol is ascribed according to the total charge of the baryonic state.

108

(%}B=2

{%}I?

=3

Figure 3. The 13-Y diagrams for the lowest exotic multibaryons: {%}-plet of dibaryons and {28}-plet of tribaryons with m = 1. Large full circles show the exotic states, smaller - the cryptoexotic states.

variations 23. However, the 1/Nc corrections are not negligible, and this question deserves further study. The positive strangeness dibaryons should decay into K N N , tribaryons - into K3N final states with a width of same order of magnitude as re. There are also exotic states with negative strangeness: dibaryons with S = -4, isospin I = 2, with electric charge in the interval from Q = -3 to Q = +1, and tribaryons with S = -4, I = 3 and charge from -4 up to +2, see Fig.3. As usually, it would be difficult to produce such states, but their detection could be easier: they decay mainly into =-hyperons and pions. To conclude this section, note that there are other predictions of states in chiral soliton models which are exotic in the common meaning of this word: for example, charmed or beautiful hypernuclei bound stronger than strange hypernuclei 27. The supernarrow electromagnetically decaying dibaryon with width about 1 keV below the NNT threshold 28 was observed in two experiments but not confirmed in 31 in the mass interval below 1924 MeV. Its searches certainly deserve further efforts.

-

29930,

6. Conclusions and prospects The mass and width of recently detected baryon with positive strangeness, Of are in agreement with predictions of the topological (chiral) soliton

109

model d . Possibly, another exotic baryon with zero strangeness has been observed g . To be sure that the observed 0+ belongs to antidecuplet, the measurement of its spin and parity is necessary first of all, as well as establishing its partners in SU(3) multiplet (antidecuplet). The searches for the state 0' E (27) with isospin I = 1 are of interest. The double charged state a*++could appear as a resonance in K + p system. Since this state is by (120 - 160) MeV heavier than 0+ l o , its width . The absence of such should be at least 3 - 4 times greater than that of resonance could be a serious problem for the whole chiral soliton approach. Let us note also that the mass splitting inside of antidecuplet obtained in 7,10 is considerably smaller than in where it is about 540 MeV. In addition, the deviation from equidistant law is large in 7,10,6as a consequence of configuration mixing being taken into account. As a result, the value of mass of the hyperon with isospin I = 3/2, Z:,2 obtained in lo is considerably smaller than in 8 . It is worth noting that its mass estimate made in 22 within quark-diquark-diquark model is close to our result lo. The value of the mass of C* E also is lower in lo and is more close to C*(1770) than to C*(lSSO). Many exotic resonances of interest have large values of isospin, therefore they cannot be observed in reactions of pion or kaon scattering on nucleons, but could be seen in reactions of two and more pions (kaons) production, similar to reaction studied in '. It could be attractive a possibility to identify the state of mass 1.72 GeV observed in with a component of (35)-plet with S = 0, I = 5/2. But the isospin selection rule for reaction of electroproduction with one-photon exchange makes such identification difficult. Another possibility noted already in 9, is that it is cryptoexotic component of (27)-plet with isospin 3/2 and mass about 1.76 GeV, according to lo. Of course, there is no contradiction between chiral soliton approach and the quark (or quark-diquark, etc.) picture of baryons and baryon resonances, as it is stated in some papers. Both approaches are dual, the first one describes baryons or baryonic systems from large enough distances and allows to calculate such characteristics where the details of internal structure of baryons are not essential, one of such characteristics is just the mass of baryons. The consequences of discovery of new baryon resonance are considered in several recent papers 22,32-34 and others, many of them have been reviewed 67718

N

{m)

dAs it was noted, from rigoristic point of view one could doubt in each of these predictions, therefore experimental confirmation was necessary.

110

’-‘

and analysed in 34. Hopefully, the results obtained in and open new interesting chapter in physics of baryon resonances, and its new pages can be devoted also to studies of baryonic systems with exotic properties. I am thankful to H.Walliser for numerous conversations, the present talk is based to large extent on the paper l o . I’m indebted also to L.B.Okun’, B.O.Kerbikov, A.E.Kudryavtsev for useful questions and discussions, and to O.Hashimoto, T.Nakano, R.Schumacher for discussions during this Workshop. The work has been supported by the Russian Foundation for Basic Research, grant 01-02-16615.

References 1. T. Nakano e t a1 (LEPS collaboration) Phys. Rev. Lett. 91, 012002 (2003); hep-ex/0301020 2. V. Barmin et al (DIANA collaboration) hep-ex/0304040 3. R. Schumacher (CLAS collaboration), Talk at this Workshop; S. Stepanyan et al, hep-ex/0307018 4. J. Barth et al, (SAPHIR collaboration) hep-ex/0307083 5. A.E. Asratyan, A.G. Dolgolenko and M.A. Kubantsev, hep-ex/0309042 6. M. Praszalowicz, Proc. Of Workshop Skyrmions and Anomalies Krakow, Poland, 20-24 Febr. 1987, p.112. Update version hep-ph/0308114 7. H. Walliser, Nucl. Phys. A548, 649 (1992) 8. D. Diakonov, V. Petrov, M. Polyakov, Z. Phys. A359, 305 (1997) 9. M. Ripani et al, (CLAS collaboration) hep-ex/0210054; hep-ex/0304034 10. H. Walliser, V.B. Kopeliovich, J E T P 124, 433 (2003); hep-ph/0304058 11. L.G. Landsberg, Phys. Usp. 42, 871 (1999) 12. R.L. Jaffe, SLAC-PUB-1774; D. Strottman, Phys.Rev. D20, 748 (1979) 13. M. Chemtob, NucLPhys. B256, 600 (1985) 14. L.S. Biedenharn and Y. Dothan, From SU(3) to Gravity (Ne’eman Festschrift), Cambridge University Press, Cambridge (1986) 15. V. Kopeliovich, Phys. Lett. B259, 234 (1991) 16. H. Weigel, Eur. Phys. J. A2, 391 (1998) 17. E. Guadagnini, NucLPhys. B236, 35 (1984) 18. E. Witten, Nucl. Phys. B223, 433 (1983) 19. B. Schwesinger, H. Weigel, Phys. Lett. B267, 438 (1991) 20. V. Kopeliovich, B. Schwesinger, B. Stern, Nucl. Phys. A549, 485 (1992) 21. B. Moussalam, Ann. of Phys. (N.Y.) 225, 264 (1993); F. Meier, H. Walliser, Phys. Rept. 289, 383 (1997) 22. R. Jaffe, F. Wilczek, hep-ph/0307341

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23. V.B. Kopeliovich, W.J. Zakrzewski, JETP Lett, 69, 721 (1999); Eur. Phys. J C18, 389 (2000); V.B. Kopeliovich, JETP, 93, 435 (2001) 24. C. Houghton, N. Manton, P. Suttcliffe, Nucl. Phys. B510, 507 (1998) 25. R.A. Battye, P.M. Sutcliffe, Rev. Math. Phys. 14, 29 (2002) 26. D. Kaplan, I.R. Klebanov, Nucl. Phys. B335, 45 (1990); I.R. Klebanov, K.M. Westerberg, Phys. Rev. D53, 2804 (1996) 27. V. Kopeliovich, J E T P 96, 782 (2003); Nucl. Phys. A721, 1007 (2003); nucl-th/0209040 28. V. Kopeliovich, Phys. Atom. Nucl. 58, 1237 (1995) 29. A. Khrykin et al, Phys. Rev. C64, 034002 (2001) 30. L.V. Filkov et al, Eur. Phys. J. A12, 369 (2001) 31. A. Tarnii et al, Phys. Rev. C65, 047001 (2002) 32. A. Hosaka, hep-ph/0307232 33. M. Karliner, H.J. Lipkin, hep-ph/0307243 34. B.K. Jennings, K. Maltman, hep-ph/0308286

fa,

U,

AND 2~ EXCHANGES IN p MESON PHOTOPRODUCTION

YONGSEOK OH Institute of Physics a n d Applied Physics, Yonsei University, Seoul 120-749, Korea E-mail: yohaphya. yonsei. a c . b

T.-S. H.LEE Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, E-mail: leeOtheory.phy. anl.gov

U.S.A.

The u meson exchange model for p photoproduction at low energies is re-examined and a new model is developed by considering explicit two-pion exchange and the fz tensor meson exchange. The f2 exchange model, which is motivated by the low energy proton-proton elastic scattering, is constructed by fully taking into account of the tensor structure of the f 2 meson interactions. Phenomenological informations together with tensor meson dominance and vector meson dominance assumptions are used to estimate the fz meson’s coupling constants. For 271. exchange, the loop terms including intermediate nN and w N channels are calculated using the coupling constants determined from the study of pion photoproduction. It is found that our model with f2 and Z A exchanges can successfully replace the commonly used u exchange model that suffers from the big uncertainty of the coupling constants. We found that the two models can be distinguished by examining the single and double spin asymmetries.

Recently the measurements on the electromagnetic production of vector mesons from the nucleon targets have been reported from the CLAS of TJNAF l P 3 , GRAAL of Grenoble ‘, and LEPS of Spring-8 More data with high accuracy on various physical quantities of these processes are expected to come soon. These new data replace the limited old data of low statistics and provide an opportunity to understand the production mechanism of vector mesons at low energies. They are also expected to shed light on resolving the ‘missing resonance’ problem 7-10. However, it is well-known that thorough understanding of the nonresonant background mechanisms is crucial to extract the properties of the resonances and to identify any missing resonances from the data for meson 516.

112

113

Y

N

N

V

Y

N

N

V

N

N

Figure 1. Models for p photoproduction. (a,b) t-channel Pomeron and one-meson exchanges ( M = ~ z , T , ~ , c T(c,d) ). s- and u-channel nucleon pole terms.

production processes l1,l2. As a continuation of our effort in this direction 11, we explore the nonresonant mechanisms of p photoproduction in this work. Through the analyses of vector meson photoproduction, we learned that at high energies the total cross sections are dominated by the Pomeron exchange, which is responsible to the diffractive features of the data at small t. However, at low energies, meson exchanges or Reggeon exchanges are dominant over the Pomeron exchange and responsible to the bump structure of the total cross section near threshold. In w photoproduction, it is well-known that one-pion exchange is the most dominant process. In p photoproduction, however, the situation is not so clear. There are, in general, two models for the major production mechanism of p photoproduction at low energies. One is the u meson exchange model 13, l 4 and the other is the f2 meson exchange model 15-17. The u exchange model is motivated l3 by the observation that the p + m y decay is much larger than the other radiative decays of the p meson such as p + ny. Therefore the role of 2n exchanges is expected to be important in the production mechanism of p photoproduction. It is then assumed that the nn in the nny channel can be modeled as a u meson such that the apy vertex can be defined for calculating the u exchange mechanism as illustrated in Fig. l(b). In practice, the product of the coupling constants QapyggNN of this tree-diagram is adjusted to fit the cross section data of p photoproduction at low energies. The parameters of the

114

I

I

n Il I

I I I In: I I

Figure 2. 2.rr exchange in p photoproduction. The intermediate meson state ( M ) includes 7~ and w , and the baryon (B) includes the nucleon.

u exchange model determined in this way are

131 l 4

--

The resulting u mass parameter is close to the value Mu = 0.55 0.66 GeV of Bonn potential 18. If we further take the value gzNN/4n = 8.3 10 from Bonn potential, we then find that the resulting gupy is close to the values from the QCD sum rules, gupy(QCDSR) = 3.2 f 0.6 l 9 or 2.2 f 0.4 20. However such a large value of gupy overestimates the observed p -+ nonoy decay width by two orders of magnitude 21-24. If we accept the empirically estimated but model-dependent value of the SND experiment 23, BR(p + +0.9 07) = (1.9 -0.8 f 0 . 4 ) x we get Igupy( M

0.25.

(2)

This value is smaller than that of Eq. (1)by an order of magnitude. Therefore, the u exchange model suffers from the big uncertainty of g u p y . Furthermore, there is yet no clear particle identification of the u meson and the use of u exchange in defining N N potential has been seriously questioned. Thus it is possible that the u exchange may not be the right major mechanism for p photoproduction. Therefore, we take a different approach for p photoproduction l7 in this work. Here we consider the f2 exchange and two-pion exchange mechanisms. Instead of considering the radiative decay of the p through the u , we consider the consequences of the strong po --+ &n- decay which accounts for almost the entire decay width of the p meson. With the empirical value of the p meson decay width, one can define the pnn vertex which then leads naturally to the two-pion exchange mechanism illustrated in Fig. 2 with M = T in the intermediate state. Clearly, this two-pion exchange

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mechanism is a part of the one-loop corrections discussed in Ref. 11 for w photoproduction. A more complete calculation of one-loop corrections to p photoproduction is accomplished in this work by including not only the intermediate T N state but also the intermediate w N state. The f 2 exchange model for p photoproduction was motivated by the the analyses for p p elastic scattering 2 5 . In the study of p p scattering at low energies the secondary Regge trajectory is important, which is represented by the f trajectory. The idea of Pomeron-f proportionality then had been used to model the Pomeron couplings from the f2 couplings 26-28 before the advent of the soft Pomeron model by Donnachie and Landshoff 29. By considering the important role of the f trajectory in p p scattering, it is natural to consider the f2 exchange model for vector meson photoproduction. However, the f 2 exchange model developed in Refs. 15, 16 for p photoproduction used the Pomeron-f proportionality in the reverse direction. Namely, they assume that the structure of the f2 couplings is the same as that of the soft Pomeron exchange model. Thus the f 2 tensor meson was treated as a C = +1 isoscalar photon, i.e., a vector particle. In addition, the fit to the data is achieved by introducing an additional adjustable parameter to control the strength of the f2 coupling 15. In this work, we elaborate an f2 exchange model starting from effective Lagrangians constructed by using the empirical information about the tensor properties of the f2 meson. The main objective of this work is to construct a model including this newly constructed f 2 exchange amplitude and explicit two-pion exchange amplitude discussed above. We now construct an f2 exchange model solely based on the tensor structure of the fi meson. We will use the experimental data associated with the fz meson, the tensor meson dominance, and vector meson dominance assumptions to fix the f 2 coupling constants such t,hat the strength of the resulting f2 exchange amplitude is completely fixed in this investigation. Following Refs. 32, 33, the effective Lagrangian accounting for the tensor structure of the f 2 N N interaction reads 17130131,

where f,” is the f 2 meson field and M N is the nucleon mass. The coupling constants were first estimated by using the dispersion relations in the analyses of the backward T N scattering 32 and the TT + N N partial-wave amplitudes. Here we use 34

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Figure 3. Differential cross sections of model (A) and (B) a t E, = 3.55 GeV. The dashed line is the result of model (A) and the solid line is that of model (B). Experimental data are from Ref. 2.

The most general form for the f V y vertex satisfying gauge invariance reads 30

(r(W(W-2)= M f e

6

6

f PUAfvr nXClu(w),

(5)

where E and E' axe the polarization vectors of the photon and the vector meson, respectively, and the form of AfvT can be found in Ref. 17. The tensor meson dominance together with the vector meson dominance constrain 30 the coupling constants of Afvr. The details on the f 2 interactions and tensor meson dominance are given in Ref. 17. In this work, we explore two models: model (A) includes the Pomeron, cr, T , Q exchanges, and the s- and u-channel nucleon terms, while model (B) is constructed by replacing the 0 exchange in model (A) by the f 2 and 2n exchanges. (See Figs. 1 and 2.) The full calculations of the yp + pop differential cross sections from model (A) and (B) are compared in Fig. 3. From those figures, one may argue that model (B) is slightly better in small t region. However, it would be rather fair to say that the two models are comparable in reproducing the data. We therefore explore their differences in predicting the spin asymmetries, which are defined, e.g., in Ref. 35. The results for the single and double spin asymmetries are shown in Fig. 4 for

117

4 (GeVJ

4

(GeV')

4 (GeV')

-I (GeV")

Figure 4. (left panel) Single spin asymmetries of model (A) and (B) at E-, = 3.55 GeV. : C and C:$ of Model (A) and (right panel) Double spin asymmetries C,",T, C,",, , (B) at E-, = 3.55 GeV. Notations are the same as in Fig. 3.

E7 = 3.55 GeV. Clearly the spin asymmetries would be useful to distinguish the two models and could be measured at the current experimental facilities. Of course our predictions are valid mainly in the small t region since the N* excitations, which are expected to be important at large t are not included in this calculation. Therefore, measurements of such quantities at small t region should be crucial to understand the main non-resonant production mechanisms of p photoproduction at low energies. Finally let use mention about the role of the f2 exchange in q5 photoproduction. In this case, we can consider the exchanges of the f~(1270)and f;(1525) mesons. However such exchanges are expected to be negligible zf the f 2 and f; mixing is close to the ideal mixing. This is because the ideal mixing makes the fz@y and f ; N N couplings vanish, although f2NrCTand f;&y do not. Since the amplitude of this process contains gfibrGfiNN or gflb7GfiNN: its contribution is expected to be small if the f2- f; mixing is close to the ideal mixing. Acknowledgments

Y.O. was supported by Korea Research Foundation Grant (KRF-2002-015CP0074) and T.-S.H.L. was supported by sion Contract No. W-31-109-ENG-38.

U.S. DOE Nuclear Physics Divi-

References 1. CLAS Collaboration, E. Anciant et al., Phys. Rev. Lett. 85, 4682 (2000); K. Lukashin et al., Phys. Rev. C 63,065205 (2001), 64, 059901(E) (2001).

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2. CLAS Collaboration, M. Battaglieri et al., Phys. Rev. Lett. 87, 172002 (2001). 3. CLAS Collaboration, M. Battaglieri et al., Phys. Rev. Lett. 90, 022002 (2003). 4. J. Ajaka et al., in Proceedings of 14th International Spin Physics Symposium, edited by K. Hatanaka et al., (AIP Conf. Proc. 570, 2001), p. 198. 5. T. Nakano, in Proceedings of 14th International Spin Physics Symposium, edited by K. Hatanaka et al., (AIP Conf. Proc. 570, 2001), p. 189. 6. T. Mibe, in these proceedings. 7. S. Capstick and W. Roberts, Prog. Part. Nucl. Phys. 45, S241 (2000). 8. Y. Oh, A. I. Titov, and T.-S. H. Lee, Phys. Rev. C 63, 025201 (2001). 9. Q. Zhao, 2.Li, and C. Bennhold, Phys. Rev. C 58, 2393 (1998). 10. A. Titov and T.-S. H. Lee, Phys. Rev. C 67, 065205 (2003). 11. Y. Oh and T.-S. H. Lee, Phys. Rev. C 66,045201 (2002); Nucl. Phys. A 721, 743 (2003). 12. G. Penner and U. Mosel, Phys. Rev. C 66, 055211 (2002). 13. B. Friman and M. Soyeur, Nucl. Phys. A 600, 477 (1996). 14. Y. Oh, A. I. Titov, and T.-S. H. Lee, nucl-th/0004055, in NSTAR2000 Workshop, edited by V. Burkert et al., (World Scientific, Singapore, 2000), p. 255. 15. J.-M. Laget, Phys. Lett. B 489, 313 (2000). 16. N. I. Kochelev and V. Vento, Phys. Lett. B 515, 375 (2001); 541, 281 (2002). 17. Y. Oh and T.-S. H. Lee, nucl-th/0306033. 18. R. Machleidt, K. Holinde, and C. Elster, Phys. Rep. 149, 1 (1987). 19. A. Gokalp and 0. Yilmaz, Phys. Rev. D 64, 034012 (2001). 20. T. M. Aliev, A. Ozpineci, and M. Savci, Phys. Rev. D 65, 076004 (2002). 21. A. Gokalp and 0. Yilmaz, Phys. Lett. B 508, 25 (2001). 22. A. Bramon, R. Escribano, J. L. Lucio M., and M. Napsuciale, Phys. Lett. B 517, 345 (2001). 23. SND Collaboration, M. N. Achasov et al., Phys. Lett. B 537, 201 (2002). 24. Y. Oh and H. Kim, hep-ph/0307286. 25. A. Donnachie and P. V. Landshoff, Phys. Lett. B 296, 227 (1992). 26. P. G. 0. Fkeund, Phys. Lett. 2, 136 (1962); Nouvo Cimento 5A, 9 (1971). 27. R. Carlitz, M. B. Green, and A. Zee, Phys. Rev. Lett. 26, 1515 (1971). 28. Yu. N. Kafiev and V. V. Serebryakov, Nucl. Phys. B 52, 141 (1973). 29. A. Donnachie and P. V. Landshoff, Nucl. Phys. B 244, 322 (1984). 30. B. Renner, Phys. Lett. 33B, 599 (1970); Nucl. Phys. B 30, 634 (1971). 31. K. Raman, Phys. Rev. D 3, 2900 (1971). 32. H. Goldberg, Phys. Rev. 171, 1485 (1968). 33. H. Pilkuhn et al., Nucl. Phys. B 65, 460 (1973). 34. N. Hedegaard-Jensen, Nucl. Phys. B 119, 27 (1977); E. Borie and F. Kaiser, ibid. 126, 173 (1977). 35. A. I. Titov, Y. Oh, S. N. Yang, and T. Morii, Phys. Rev. C 58, 2429 (1998).

CHIRAL SYMMETRY AND SURFACE PION CONDENSATION IN NUCLEI AND HYPERNUCLEI

H. TOK1:Y. OGAWA, S. TAMENAGA Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567-004 7, Japun K. IKEDA AND S. SUGIMOTO Institute of Chemical and Physical Research (RIKEN), Wako, Saitama 351-0198, Japan

The properties of finite nuclei and hyper nuclei are studied by using the chiral sigma model in the framework of the relativistic mean field theory. We reconstruct an extended chiral sigma model in which the omega meson mass is generated dynamically by the sigma condensation in the vacuum in the same way as the nucleon mass. We could demonstrate that the surface pion condensation is able to provide the appearance of the magic number at N = 28. We find that the energy differences between the spin-orbit partners are reproduced by the finite pion mean field which is completely a different mechanism from the standard spinorbit interaction. We discuss also that this model naturally provides very small spin-orbit splitting in hyper nuclei.

1. Introduction Chiral symmetry is known to be the most important symmetry in the hadron physics. This is because the quantum chromo-dynamics (QCD) is the underlying theory of the strong interaction, in which the up and down quarks have essentially zero masses. Chiral symmetry governs the quark dynamics. In the real world, the quarks are confined and chiral symmetry is spontaneously broken. As the Nambu-Goldstone boson of the spontaneous breaking of chiral symmetry, the pion emerges with almost zero mass.l At the hadron level, chiral symmetry is known to be essential to describe various experiments. It is then very natural to use the Lagrangian with chiral symmetry for the description of nuclei. It. is, however, common to *e-mail address: [email protected]

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describe nuclei with the Lagrangian without the pion. In this talk, we would like to discuss why we want to introduce pions in the description of nuclei and how to incorporate the pion in the mean field approximation. We shall present the status of our project on the study of the pion and the chiral symmetry in finite nuclei. 2. RMF model and the necessity of pion

We would like to start showing that the RMF model with nicely tailored parameter set is able to describe nuclei in the entire mass region. The RMF lagrangian density is given

L

= $(iypaP - M - g,a - gWyPwP- gPyprafa)+ + la a@, - 31m2g2 - 13g2 . 0 3 - zg3O4 1 2 P a - + Q ~ , , W+~im:wPwp + +g4(w@w~)~

Rap” + Lm2 a ap - a1RaPV 2 PPPP - I F FP” -e$yPFAP$, 4

(1)

P“

where the field tensors of the vector mesons and of the electromagnetic field take the following form:

{

QP” =

apw”

- a,w,

RE” = a,P: - 8.P;

- 29,E

abc b c

PpP”

(2)

Fpv= apAV- &Ap

and other symbols have their usual meaning. We take then the mean field approximation by assuming the meson and the photon fields to be the classical values, the details of which are written by many authors. We show in Fig.1 the results of the RMF model with the TMA parameter set.’ It is amazing to see that the RMF model is able to reproduce the masses of nuclei in the entire mass region. We mention that the RMF model has been applied to nuclei up to proton and neutron drip lines and also to the superheavy nuclei by allowing deformations and pairing correlations with great quantitative success. We remind here that if we were only to reproduce the masses and the sizes of nuclei, we can do so with the model without pions for nuclei with heavy nuclei ( A > 40) with 7 parametem2 The recent publications from the Argonne group, however, show very important results on the structure of light nuclei in terms of the role of pions.3 They performed the quantum monte carlo calculations on light nuclei ( A < 10) by using the nucleon-nucleon interaction with the three body forces, They were able to reproduce the energy spectra of these light nuclei. In addition, they stress the importance of the role played by pions, which

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Figure 1. The binding energies per particle for the proton magic nuclei as a function of the mass number, A. The TMA parameter results are shown by solid curves, and the NL1 results by dotted curves, while the experimental results are shown by dots.

provide 7 0 4 0 % of the attraction caused by the two body interaction. This fact indicates that the wave functions have strong pionic correlations, which should have consequence of various observables. We would like to remind that the D-wave component of the deuteron is caused by the pion and has the consequence to provide the quadrupole moment and the large amplitude in the form factor at large momenta. In the experimental side, there are many observables, which need theoretical attention with respect to the role of the pion in finite nuclei. Out of many, we would like to show t,he recent high resolution Gamow-Teller (GT) strengths obtained by (3He,t) reactions in Fig.2.* The GT excit,ation is made by the operator, ( Q T ) , which does not change the spatial wave functions. Yet, the GT strength is highly fragmented, which indicates that the single particle states are much more complicated than the ones the shell model provides. We have difficulty to reproduce the ratios of the longitudinal to transverse spin responses being very close to one, while tthe theoretical prediction of treating the pion as a residual int.eraction would provide the ratios be more than one. There are various phenomena, which need the inclusion of the tensor interaction to be worked out perturbatively. All these phenomena related with the need of the tensor correlations may be strongly relat.ed with the explicit role of the pion.

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0

2

4

6

8

10

12

Ex (MeV)

Figure 2. The high resolution G T spectrum of the (3He,t) reactions on 58Ni.4

3. Chiral sigma model in the relativistic mean field theory

The theoretical findings in light nuclei and also some indications in the experimental data associated with the tensor force for the necessity of the pion in finite nuclei urged us to look into a new framework to treat the pion at the mean field level. For this purpose, we introduced the pion mean field in the relativistic mean field f r a m e ~ o r kIn . ~ order to treat the pion at the mean field level, we have to break the parity symmetry. With the use of the pion nucleon coupling constant in the pseudo-vector form: we are able to show that the pion mean field becomes finite for finite nuclei. The mass dependence of the pion energy indicates that the pion mean field effect behaves surface like and hence we call the phenomenon of making the pion mean field finite as surface pion condensation. It has additionally an interesting effect that the pionic attraction is particularly large for the jjclosed shell nuclei. This fact indicates that, the jj-closed shell magic number may be caused by surface pion condensation. Hence, we have looked for a Lagrangian which can naturally needs the above mentioned role to be played by the pion mean field for the description of finite nuclei. In this effort, we have arrived at the linear sigma model

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with the omega meson field, which is defined by the following Lagrangian,‘

L,,

=

9(iypd’”- g,(u

1 1-2 - -wpww’A” + -g,

+

4

2

+ iys?. ii) - g w y p w q 9 (a2

(3)

+ ii2)wpwp

&U.

The fields 9,u and 7r are t.he nucleon, sigma and the pion fields. p and X are the sigma model coupling constants. Here we have introduced the explicit chiral symmetry breaking term, €0,and in addition the mass generation term for the omega meson due to the sigma meson condensation as t,he cme of the nucleon mass in the free space.7 The u - w coupling term of this structure may be derived from the bosonization of the Nambu-Jona-Lasinio model. In a finite nuclear system, it is believed to be essential t,o use the nonlinear representation of the chiral symmetry. This is because the pseudoscalar pion-nucleon coupling in the linear sigma model makes the coupling of positive and the negative energy stat,es extremely strong and we have to treat the negative energy states very carefully. We can derive the non-linear sigma model by introducing new variables and making a suitable transformation. After the transformation and redefinition of variables we get the non-linear chiral Lagrangian as18

1 + -8,iidpii 2 1 4

1

- Zm,2ii2

1 2

1,

- -wpwwpu + -mW2wpwp + z 2 f ? , p w p w f + i zgw2p2wpwp,

+

+

where we set M = g, f?,,m?,’ = p2 Xf?, 2 , mu2 = p2 3XfT2 and m, = The fields $, q5 and T are the t,ransformed nucleon, sigma and pion fields, which are related with the original fields in (3). The effective mass of the nucleon and omega meson are given by M + = M+g,cp and mu* = mu+ gwp, respectively. We take the following masses and the pion decay constant as, A4 = 939 MeV, m, = 783 MeV, m?, = 139 MeV, and f T = 93 MeV. Then, the other parameters can be fixed automatically by the following relations, go = M / f , = 10.1 and = mw/f?,= 8.42. The strength of the

zf?,. -

z

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cubic and quadratic sigma meson self-interactions depends on the sigma meson mass through the following relation, X = (mu2- mr2)/2fT2,in the chiral sigma model. The mass of t,he sigma meson, mu, and the coupling constant of omega and nucleon, g,, are the free parameters. If we use the KSFR relation for the omega meson, and the additional relation from t,he Nambu-Jona-Lasinio model, the mass of the omega meson is related to the pion decay constant by m, = (2fi/3)f,g,.s,10 The factor (2fi/3) stems from the g, = (3/2)g, where g is the universal coupling constant for the vector As we see below, this KSFR relation is very well satisfied in the present model within 6 %. In Fig.3 we provide the energy per particle of nuclear matter as a function of the density for t,he extended chiral sigma model.13 We take the parameters of the chiral sigma model from the properties of mesons as pion mass, m,, omega meson mass, m,, pion decay constant, f,. The free parameters, mu and g,, are adjusted to provide the saturation property in the case of the extended chiral sigma model. We have fixed the free parameters as, mu = 777 MeV, and g, = 7.03. Then, the strength of the cubic and quadratic sigma meson self-interaction are fixed as X = 33.8. The saturation properties are the density, p = 0.141 fm-3, and the energy per particle, E / A = -16.1 MeV. We find in this case the incompressibility, K = 650 MeV. The sigma meson mass chosen here is larger than that used in one boson exchange potential, which is around 500 MeV. If we take 500 MeV as the sigma meson mass, the attractive force becomes strong and the saturation curve becomes deep. We adjust then the omega-nucleon coupling constant , g,, to reproduce the binding energy per particle. The energy minimum point appears at quite a small density, p = 0.053 fm-3. The saturation condition is riot satisfied simultaneously both for the density and binding energy per particle using this meson mass. It is interesting to note that the value mu = 777 MeV is very close to the one when the chiral mixing angle is chosen at 45" in the generalized chiral model; mu M mp.8

As a comparison, the energy per particle of the mean field result with the TM1 parameter set is shown together with the present result.2 The R.MF(TM1) calculation reproduces the results of the relativistic BruecknerHartree-Fock ca1c~lation.l~ We see that the present equation of state is much harder than the one of RMF(TM1). The incompressibility comes out to be 650 MeV, while it is 281 MeV for TM1. In Fig.4 we plot the vector and the scalar potentials and compare with the ones of RMF(TM1). The values are about a half of the case of the TM1 parameter set. This is because the extended chiral sigma model has solutions at smaller sigma

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Figure 3. The energy per particle of infinite nuclear matter as a function of the density for the extended chiral sigma model (solid curve). As a reference the energy per particle in the RMF theory with the TM1 parameter set, RMF(TMI), is provided by dashed curve.

r

I

I

I

I

400 -

5

8

-

3 5 B

I

-400I

I

I

I

0.05

0.10

0.15

0.20

!5

P ( fm”)

Figure 4. The scalar and vector potentials are plotted as a function of the density for the extended chiral sigma model shown by solid curve and those for RMF(TM1) by dashed curve.

values than those for RMF(TM1). We would like to note the consequence of the smaller absolute values of

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the scalar and the vector potentials in finite nuclei as shown in Fig.4. The summation of the absolute values of the scalar and the vector potentials is directly related with the spin-orbit potential of finite nuclei. Hence, the fact that these absolute values are about half of the values of RMF(TM1) indicates that the spin-orbit splitting for finite nuclei will come out to be about a half of the necessary spin-orbit splittings. 9.4, 9.2

I

I

I

I

I

-

I

9.0 -

E

2ca

8.8 8.6 -

8.4 8.2 8.0 I 20

I

I

I

I

I

I

30

40

50

60

70

80

A (Mass number)

Figure 5. The binding energy per particle for N = Z even-even mass nuclei in the neutron number range of N = 16 34. The binding energies per particle for the case of the extended chiral sigma model without and with the pion mean field are shown by the dashed and the solid lines. As a comparison, those for the RMF(TM1) are shown by the dotted line. N

We would like now to discuss the properties of finite nuclei in terms of the extended chiral sigma model without introducing yet the pion mean field. We show the results of binding energies per particle of N = Z eveneven mass nuclei from N = 16 up to N = 34 in Fig.5. We take all the parameters of the extended chiral sigma model as those of the nuclear matter (Figs.3 and 4) except for gw = 7.176 instead of 7.033 for overall agreement with the RMF(TM1) results. We include the Coulomb interaction for actual calculations. For comparison, we calculate these nuclei within the R.MF approximation without pairing nor deformation. The RMF(TM1) provides the magic numbers, which are seen as the binding energy per particle increases at N = Z = 20 and 28. On the other hand, the ext,ended chiral sigma model without the pion mean field provides the magic number behavior only at N = Z = 18 instea.d of N = Z = 20. In order to see why the difference between the two models for the La-

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Figure 6 . The proton single particle energies for the N = Z even-even mass nuclei in the case of the RMF(TM1) theory, where the magic numbers a t N = 20 and 28 are visible.

Figure 7. The proton single particle energies for the N = Z even-even mass nuclei in the case of the extended chiral sigma model without the pion mean field. ls1j2orbit is pushed up and the N = 20 magic number is shifted to N = 18. The spin orbit splitting between Of712 and O f 5 / 2 is small and the magic number a t N = 28 is not visible.

grangian arises, we show in Fig.6 the single particle levels for the two models. In the case of the TM1 parameter set shown in Fig. 6, the shell gaps are clearly visible at N = 20 and 28. The magic number at N = 20 is due to the central potential, while the magic numbers at N = 28 comes from the spin-orbit splitting of the Of-orbit. This is definitely due to the fact that the vector potential and the scalar potential in nuclear matter are

128

large so as to provide the large spin-orbit splitting. On the other hand, the single particle spectrum of the extended chiral sigma model is quite different from this case as seen in Fig.7. Most remarkable structure is that the l s l / 2 orbit is strongly pushed up. Due to this reason the 0d3/2 orbit becomes the magic shell at N = 18 and the magic number appears at N = 18 instead of N = 20. We see also not strong spin-orbit splitting and hence there appears no shell gap at N = 28. The first discrepancy could be due to the large incompressibility as seen in the nuclear matter energy per particle as seen in Fig.3. The other is due to the relatively small vector and scalar potentials in nuclear matter as seen in Fig.4.

Figure 8. The proton single particle energies for the N = Z even-even mass nuclei in the case of the extended chiral sigma model with the pion mean field. The spin-orbit splitting is made large due t o the finite pion mean field, which is visible as centered a t the N = Z = 28 nucleus. We note that while the total angular momentum is a good quantum number, but the angular momentum is not exact, we write the dominant angular momentum beside each single particle state.

We give here an intuitive explanation to understand the energy curve of the magic structure in Fig.5 to be given by the finite pion mean field using the schematic picture in Fig.9. To proceed, we have to know first the effect of the finite pion mean field in terms of the shell model. The discussion of the parity projection, done in the previous publication,5 clearly shows that the pionic correlations due to the finite pion mean field is expressed by the coherent 0- particle-hole excitations, in which the coupling of the different parity states 1 and 1’ = 1 f 1 with the same total spin j in the shell model language. In the discussion of the contribution to the pionic correlations

129

from various single particle states, the highest spin state in each major shell has a special role. Only this highest spin state does not find the partner to form the 0- state in the lower major shells. However, if this state is filled by nucleons, those nucleons are able to find the 0- partners in the higher major shells by making particle-hole excitations. Hence, the position of the highest spin state in a major shell with respect to the Fermi surface is important for the strength of pionic correlations in nuclei.

9/2 f.512 '3/2

2

s1/2 d512

Figure 9. The schematic picture of the single particle states and the occupied particles in the 58Ni nucleus.

In the case of discussion, the highest spin state is the f7/2 state as shown in Fig.9. In the 40eacase, the occupied states can not couple with the f7/2 state to form 0- and the f7/2 level is not used at all for the pionic correlations. In the next 44Ticase, nucleons start to occupy the f7/2 level, and these nucleons are used for the 0- pasticle-hole excitations into g7/2 levels. The number of particles to be used by the pionic correlation increases as the nucleon number is increased until 56Ni, where the f 7 p level is completely occupied. For the nuclei above 56Ni, the upper shells as f5/2 are to be occupied and those states are not used for 0- particle-hole excitations from the d512 level below caused by the pionic correlation due to the Pauli blocking. For 56Ni,the pionic correlation becomes maximum. This is the reason why "Ni obtains the largest pionic correlation energy,

130

which leads to the appearance of the magic number at N = 28. We discuss now t,he effect of the finite pion mean field on the single particle energies. We show in Fig.8 the single particle spectra for various nuclei. We see clearly the large energy differences between the spin-orbit partners to be produced by the finite pion mean field as the energy differences become maximum for nuclei at N = 28. The pion mean field makes coupling of different parity states with the same total spin. The O s l p state repels each other with the Op,/, state and therefore the O s l p state is pushed down and the O p l p state is pushed up. The next, partner is O p 3 / 2 and Od3p. The Op3p state is pushed down, while the Od3l2 state is pushed up. The next partner is Odsp and 0f s p . The Od5p state is pushed down, while the 0f 5 p state is pushed up. This pion mean field effect continues to higher spin partners. This coupling of the different parity stat,es with the same total spin due to the finite pion mean field causes the splittings of the spin-orbit partners as seen clearly for the Op spin-orbit partner, Od spin-orbit partner and Of spin-orbit partner in 56Ni. It is extremely interesting to see that the appearance of the energy splitting between the spin-orbit partners for the case of the finite pion mean field is caused by completely a different mechanism from the case of t,he spin-orbit interaction.

4. Lambda hypernuclei

It is very interesting to apply the present finding on the mechanism of the energy splitting in the spin-orbit partner to lambda hyper nuclei, where one of the nucleon is replaced by the lambda particle. The quark content of the lambda baryon is uds instead of uud and hence the sigma and omega meson couplings to the lambda is 2/3 of that to the nucleon due to the QZI rule. On top, the lambda particle has the isospin zero and hence it?does not couple with the pion due to the isospin symmetry. Hence, the spin-orbit splitting due to the ordinary mechanism caused by the sigma and omega couplings is reduced to roughly 2/3 of the nucleon case. Furthermore, the pion mechanism of providing the energy splitting in the spin-orbit partner does not exist for the hyperon. We expect extremely small energy splittings in the spin-orbit, partners in the lambda hyper nuclei. We show in Fig.10 the numerical result of the single particle levels of the lambda hyper nucleus, where one lambda particle is placed in "Ni as has been worked out in the previous section using the ECS model with the surface pion condensation. Due to the fact that the sigma and omega couplings are reduced to 2/3 of those to the nucleon case, the single particle

131

r (fm) Figure 10. The single particle potential for the lambda particle embedded in 56Ni and the single particle levels of the lambda particle.

potential is about 213 of that for the nucleon and hence the binding energy for the state is about -30 MeV. The energy splittings in the spin-orbit partners; in the p state, d state and f state, are found extremely small due to the smaller meson-lambda couplings and also the lack of the pion condensation effect. These small energy splittings in the spin-orbit partners are in accordance with the experimental findings. We comment t,hat the rough behavior of the single particle potential should be smoothed out by introducing the parity projection. 5. Conclusion

We have studied infinite nuclear matter and finite nuclei with the nucleon number N = Z even-even nims in the range of N = 16 and N = 34 using the chiral sigma model, which is good for hadron physics. The direct application of the chiral sigma model is not able to provide the good saturat.ion property of infinite matt,er. We have then used the extended chiral sigma (ECS) model, in which the omega meson mass is dynamically generated by the sigma condensation as the nucleon mass. This ECS model is able to provide a good saturation property, although the incompressibility comes out to be too large. Another characteristic property of the ECS model is that the scalar and vector potentials are about a half of the case of the RMF(TM1)

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model in nuclear matter. We have then applied this ECS model to finite nuclei. The ECS model without the pion mean field gives the result that the magic number appears at N = 18 not at N = 20. This result comes from the large incompressibility found in the equation of state as K = 650 MeV. This property of the ECS model provides the mean field central potential repulsive in the interior region and the 1s-orbit is extremely pushed up. Due to this, the magic number appears at N = 18 instead of N = 20. We note that this problem originates from the ECS model treated in the present framework and the finite pion mean field under the mean field approximation does not remove this difficulty. There are several possibilities to be worked out to cure this problem as the effect of Dirac sea, the parity projection, and the Fock term. The ECS model without the pion mean field provides the result that the magic number does not appear at N = 28. This result comes from another characteristic property of the ECS model, which is the small scalar and vector potentials in nuclear matter. The scalar and vector potentials lead directly to the strength of the spin-orbit interaction in finite system. Since the spin-orbit interaction given by the ECS model is about a half of those of the standard RMF calculation with the TM1 parameter set, the energy splittings between the spin-orbit partners are small and, therefore, there appears no magic effect at N = 28. As for this point, it is important to introduce the pion mean field by breaking the parity of the single particle states in the ECS model Lagrangian. Since the role of the pion mean field on the jj-closed shell nuclei has been demonstrated in t,he previous publication5, we have introduced the parity mixed intrinsic single particle states in order to treat the pion mean field in finite nuclei. We followed the formulation of Sugimoto15 in the RMF framework. We have found that the magic number effect appears at N = 28. We have studied the change of the single particle spectrum due to the finite pion mean field. It is extremely interesting to find that the spin-orbit partners are split largely by the pion mean field effect. Namely, the parity partners as ( s l p and p l l z ) , (p3/2 and d 3 / 2 ) and (d5I2 and f 5 / 2 ) are pushed out each other due to the pion mean field and as the consequence the spin-orbit partners are split largely like the ones of t,he ordinary spin-orbit splittings. This is related with the energy differences of the spin-orbit partners caused by the energy loss of the tensor (pionic) correlations due to the Pauli blocking.16 It is gratifying t o observe that first the extended chiral sigma model, which has the chiral symmetry and its dynamical symmetry breaking, is able to provide the nuclear property with only a small adjustment of the

133

parameters in the Lagrangian. The energy splitting between the spin-orbit partners appears remarkably in the ECS model with the pion mean field. The most important consequence obtained in this st,udy is that this energy splitting is caused by the pion mean field which is completely a different mechanism from the case of the spin-orbit interaction introduced phenomenologically. This suggests the origin of the magic effect of jj-closed shell nuclei. The mechanism of creating the energy difference due to the surface pion condensation in the spin-orbit partners for nuclei is missing in the case of the lambda hyper nuclei. At the same time, the ordinary spin-orbit interaction is reduced due to the OZI rule for the hyper nuclei. Hence, the spin-orbit splitting should be much smaller for the lambda hyper nuclei as compared to the nucleon in nuclei as demonstrated experimentally. We have demonstrated the importance of the pion to provide the essential energy difference in the spin-orbit partner in finite nuclei using the extended chiral sigma model. Now, we have to work out the parity and also the charge projection in order to complete the many body prescription of finite nuclei. We are also studying the parity and charge projection using the Hartree-Fock method for light n ~ c 1 e i . lIt~ is also extremely important to work out the observables due to the finite pion mean fields.

Acknowledgement This is an invited talk presented by H. Toki at t,he International Workshop on Hypernuclei held through June 16-18, 2003 in Sendai.

References 1. 2. 3. 4. 5. 6.

7. 8.

9. 10. 11. 12. 13.

Y. Nambu and G. Jona-Lasinio, Phys. Rev.122 (1961)345;1 2 4 (1961),246. Y.Sugahara and H. Toki, Nucl. Phys. A579 (1994), 557. C. Pieper and R.B. Wiringa, Annu. Rev. Nucl. Part. Sci. 51 (ZOOl), 1. Y.Fujita et al., Eur. Phys. J. A 1 3 (2002),411. H.Toki, S. Sugimoto and K. Ikeda, Prog. Theor. Phys.108 (2002),903. M. Gell-Mann and M. Levy, Nuovo Cimento 16 (1960),705. J. Boguta, Phys. Lett. B120 (1983),34;B128 (1983),19. S. Weinberg, Phys. Rev.166 (1968), 1568;177 (1969),2604. K. Kawarabayashi and M. Suzuki, Phys. Rev. Lett.16 (1996),255. Riazuddin and Fayyazuddin, Phys. Rev.147 (1966),1071. A. Hosaka, Phys. Lett. B 2 4 4 (1990),363. 0.Kaymakcalan, S. Rajeev, and J. Schechter, Phys. Rev. D30 (1984),594. Y.Ogawa, H.Toki, S. Tamenaga, H. Shen, A. Hosaka, S. Sugimot,o and K. Ikeda, RCNP prepring (2003).

134 14. R. Brockmann and R. Machleidt, Phys. Rev. C 4 2 (1990), 1965. 15. S. Sugimoto, Docter thesis in Osaka University (2002). 16. S. Takagi, W. Watari, and M. Yasuno, Prog. Theor. Phys.22 (1959), 549; T. Terasawa, Prog. Theor. Phys.23 (1960), 87; A. Arirna and T. Terasawa, Prog. Theor. Phys.23 (1960), 115. 17. S. Sugimoto, K. Ikeda and H. Toki, RIKEN preprint (2003).

3. Experimental Aspects of Strangeness Production on Nucleons and Nuclei

LAMBDA POLARIZATION IN EXCLUSIVE ELECTROAND PHOTOPRODUCTION AT CLAS

M. D. MESTAYER* Thomas .Jefferson National Accelerator Facility, 12000 Jefferson Awe., Newport News, Va. 23606 USA E-mail: [email protected]

The CLAS collaboration at JLab has recent results on A polarization for both electroproduction and photoproduction of K + A exclusive states. I note the striking phenomenological trends in the data and discuss the underlying physics which might give rise to these phenomena; both in the context of an effective Lagrangian formalism, where the degrees of freedom are intermediate mesons and baryons, and also in the context of a simple quark picture. The quark model argument leads to the conclusion that the s and 5 quarks are produced with spins anti-aligned, in apparent contradiction to the popular 3Po model of quark pair creation in which the pair is created with vacuum quantum numbers (J=O and positive parity), i.e. in an S=l, L=l, J=O angular momentum state.

1. Introduction

One of the important goals of particle and nuclear physics is to understand strong interaction dynamics. Studying hadron production sheds light on these dynamics because it focusses on just how quark pair creat,ion (QPC) neutralizes the strong forces which bind quarks into hadrons. Because sS creation is the lowest energy manifestation of QPC of a flavor which is not a valence quark in a nucleon, it is of special interest. By a happy circumstance, the A’s decay is self-analyzing, and its assumed SU(3) wavefunction has all of its spin carried by the s-quark , so its decay distribution is directly related to the spin of its s-quark . Thus, we have studied A polarization in exclusive production in an attempt to understand the spin-dynamics of QPC and its role in neutralizing t,he strong force field, i.e. “breaking the gluonic flux-tube” . *representing the CLAS collaboration.

137

138

In this contribution, I will describe two recent experiments which have been published1p2 by the CLAS collaboration. The first is a measurement of induced A and Co polarization in photoproduction of K + A and K+Co from a proton target where neither beam nor target were polarized. The second is a measurement of spin transfer from a polarized electron beam to the polarized A, also in K + A production from an unpolarized proton target. Both measurements can be used to constrain hadrodynamic models in which the effective degrees of freedom are the intermediate mesons and baryons; the relevant parameters being the choice of baryons participating in s and u-channel exchanges and the choice of mesons exchanged in the t-channel, the vertex coupling constants and the hadronic form factors. Alternatively, by using a qualitative, semi-classical argument, I argue that both measurements are sensitive to the spin state of the produced quark pair.

2. Experiment Description These scattering experiments were performed on a hydrogen target, situated within the CLAS detector in Hall B at Jefferson Lab. These studies required the simultaneous detection of the scattered electron and the K+, as well as the proton from the decay of the A . For the photoproduction experiment the beam electron was detected in the CLAS tagger, providing a measure of the photon's energy. For the electroproduction experiment, both the scattered electron as well as the K+ and proton were detected in the CLAS detector. In the latter case, the electron beam was polarized with typical values of 75%. The CLAS is a large-acceptance detector used to detect multi-particle final states init,iated by photon or electron beams. The central element of the detector is a six-coil superconducting toroidal magnet which provides a mostly azimuthal magnetic field. Drift chambers (DC) situated before, within and outside of the magnetic field volume provide charged particle tracking. The outer detector surrounding the magnet and chambers consists of large-volume gas Cerenkov counters (CC) for electron identification, 5 cm thick scintillators (TOF) for triggering and charged particle identification via time-of-flight, and a lead-scintillator electromagnetic shower counter (EC) used for electron/pion separation as well as neutral particle detection and identification. The offline event reconstruction first identified a viable electron candidate, either a tagger hit for the photoproduction experiment or a negatively

139

charged track in the DC’s which matched in position and energy with a hit in the outer detectors for the electroproduction case. Kaon candidates were positively charged tracks found in the DC which were spatially matched to a TOF hit. The time of flight and the measured path length yielded the particle velocity; combining this with the momentum of the DC track yielded the kaon-candidate mass. Cuts on the calculated mass and time of flight typically acceptcd >99% of real kaons, but allowed some background from positively charged T+’S and protons. The data were binned in the independent kinematic variables cosO;( and W where cos 0; is the cosine of the K+ angle and W the total energy in the hadronic center-of-mass system. For the electroproduction experiment, we have the additional variables, Q2, the 4-nlomentunl squared of the virtual photon, as well as 4, the angle between the leptonic and hadronic planes. Using the 4-momenta of the real (or virtual) photon and the K+ candidate, we calculated the missing mass of each event. Within each bin the missing mass spectra showed peaks at the A and Co mass, situated on a smooth background. The A and Co peaks were fit to templates produced with a radiative event, generator and a detector simulation program, along with a low-order polynomial representing the background. For the photoproduction data, the absence of radiative corrections meant that we could use Gaussians and a polynomial background to fit the missing mass spectra. Fiducial cuts were used to eliminate inefficient areas of the detector and the acceptance was calculated using a Monte Carlo package, GSIM, based upon the GEANT code. Our acceptance correction was combined with a bin-migration or “smearing” correction, as well as with a radiative correction factor.

3. Photoproduction Results

In addition to determining that the event was a K + A event by detecting the I(+ and tagged photon, we also detected the decay proton (from the A --t PT- decay mode) in order to measure the polarization of the A sample. The weak decay of the A is self-analyzing, in that the angular distribution of the decay protons is proportional to 1 a . P cosO, where a is the decay analyzing power value of 0.642, P is the polarization ofthe sample of A’s and cosO, is the cosine of t8heangle that the proton’s momentum vector makes relative to the particular axis chosen, evaluated in the A rest-frame. For photoproduction the measurement axis is chosen to be normal to . parity the plane containing the photon and the K+, A = q x f i ~ Because

+

-

140

is conserved in K + A production, this pseudo-vector is the only one available with which to form a Lorentz-invariant, parity-conserving term in the Lagrangian when dotted into the A spinor, u. So, for photoproduction, the polarization can only be non-zero along the normal ( f i ) axis. The analysis proceeded in a straightforward manner: for each bin in W and cos Ok an acceptance-corrected yield of protons was binned according to the cosine of the direction of the proton momentum relative to ii and then fit to 1 a.P cosOp,with the value of the polarization, P , being the free parameter.

+

1 -_ 0.8 0,6 + 0.4 0 0.2 - ' N 0I L U -0.2 0 -0.4 -0.6 i-0.8

4c

-4

& = Sum

W =All i

*

4

*

.-

a

t

-1*2-','

"

" -0.5

"

"

0I

'

"

"

0.5

"

'

Figure 1. Recoil polarization in yp + K+A events averaged over all E,. The curve is a phenomelogical fit which is constrained to equal 0 at the endpoints.

To determine the polarization of the Co we measured the polarization of its daughter A produced from the electromagnetic decay, Co + A y. The C" 's polarization signal is diluted during its electromagnetic decay to the A and a y with the daughter A's polarization being opposite in direction

141

and 1/3 the strength of that of the parent, Co. Thus, the coefficient has an additional factor, ax = -0.333 and the proton's angular distribution is fit to 1 QX a . P cosf3,. In Figs. 1 and 2, I show the A and the Co polarization versus cos 6); averaged over all incident photon energies.

+

Recoil Polarization f o r y

+ p + K+ + 1''

1 . 2 , " ~ ' " " ' " " ' " " ' ~

I 0.8

N ,0 L 0 -0.2 0 -0.4

a,-0.6 -0.8 -1

4

I-

c0 s (0y) Figure 2. Recoil polarization in ~p .+ K+Co events averaged over all E7. The curve is a phenomelogical fit which is constrained to equal 0 at the endpoints.

First, note the simple phenomenology: the A's are negatively polarized (opposite the normal to the hadronic plane) for kaons produced in the forward hemisphere and positive for backward-going kaons. Interestingly, the Co polarization vaIues are approximately equal in magnitude but opposite in sign from the A values. This finding has a natural explanation within quark models if one assumes that in I ~ He e' K( e+,) y H are very important for revealing more precise information about the hypernuclear wave functions 8

150

0.14

0.16

0.18

0.2

0.22

0.a

0.26

0.a

-t (ceV'>

Figure 3. Differential cross section in the center of mass for electroproduction of H as a function of - t . The experiment cannot resolve the ground and the 1st excited states (cf. text).

4. Summary

The measurements on H ( e ,e'K+)Y established the basic high precision data needed to extend the experiments on associated hyperon production to nuclear targets. For A 2 2 targets a full spectral function is used to describe the struck nucleon in the nucleus. In each case the kinematic model derived from hydrogen is used in impulse approximation to describe the quasifree production of hyperons off nuclear targets. Moreover, for A = 3,4, we observe clear evidence for the i H , t H bound states produced in electroproduction. It is the first time, these hypernuclei have been measured in electroproduction. After completing the analysis, we expect to obtain quantitative measurements of the electroproduction cross section for all of the targets studied: ' H , 2 H , 3He, 4He. 5. Acknowledgements This work was supported in part by the U.S. Department of Energy and the National Science Foundation. Support from Argonne National Laboratory

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and the U.S. Dept. of Energy under contract No. W-31-109-Eng-38 is gratefully acknowledged. The support of the staff of the Accelerator and Physics Division of Jefferson Lab is gratefully acknowledged. F. Dohrmann acknowledges the support by the the A.v.Humboldt Foundation through a Feodor Lynen Research Fellowship as well as the support by Argonne National Laboratory as the host institution for this research. References 1. 2. 3. 4.

5. 6. 7. 8.

J.-M. Laget Nucl. Phys. A691, llc(2001) D. Abbott et al, Nucl. Phys. A639, 197c(1998) B. Zeidman et al, Nucl. Phys. A691, 37c(2001) J. Cha, PhD thesis, Hampton University, 2000. 0. Benhar et all Nucl. Phys. A679, 493(1994) D. Gaskell et al, Phys. Rev. Lett. 87, 202301(2001) A. Uzzle , PhD thesis, Hampton University 2002. T. Mart et all Nucl. Phys. A640 , 235(1998); T.Mart, C. Bennhold these proceedings.

KAON ELECTROPRODUCTION AT LARGE FOUR-MOMENTUM TRANSFER

P. MARKOWITZ For the JLab Hall A and E98-108 Collaborations Physics Department Florida International University Maami, F L USA E-mail: [email protected] Exclusive H(e,e’K)Y data were taken in January, March and April of 2001 at the Jefferson Lab Hall A. The electrons and h n s were detected in coincidence in the hall’s two High Resolution Spectrometers (HRS). The kaon arm of the pair had been specially outfitted with two aerogel Cerenkov threshold detectors, designed to separately provide pion and proton particle identification thus allowing kaon identification. Preliminary data show the cross section’s dependence on the invariant mass, W, along with results of systematic studies. Ultimately the data will be used t o perform a Rosenbluth Separation as well, separating the longitudinal from the transverse response functions.

1. Introduction

The electromagnetic production of kaons allows measurement of the structure of mesons containing a strange quark and was one of the motivations for building the Thomas Jefferson National Accelerator Facility. Jefferson Lab is able to measure strange quark electroproduction from threshold through the deep-inelastic hard scattering (DIS) region. Experiment E98-108’ was approved to measure kaon electroproduction over a broad kinematical range. The experiment separates the longitudinal, transverse, and longitudinal-transverse interference responses to the unpolarized cross section. One goal is to obtain a data set allowing the extrapolation in the Mandelstam variable t of the isolated longitudinal response to the kaon mass pole. Such a reaction would correspond to the scattering of an electron off of a free kaon. A second goal is to examine the behavior of transverse response in this kinematical region, which overlaps with both the resonance region and extends DIS region. 152

153

es,,9(GeV,c),

Online Missing Moss (MeV)

Figure 1. The online missing mass yield taken in March 2002 at Q 2 = 1.9 (GeV/c )’, W = 1.95 GeV and t = tmin.

The E98-108 collaboration collected data initially in January, March and April 2001 and finished running in March 2002. [Shown above in Fig. 1 is the online missing mass spectra from the March 2002 kinematics.] At a total of 30 kinematics points, the experiment measured the H ( e ,e’K+)Y cross section. Kinematics used momentum transfers of 1.90 and 2.35 (GeV/c)2 and invariant masses between 1.8 and 2.2 GeV to measure the cross section as a function of E (the photon longitudinal polarization), as well as measurements left and right of the direction of 4: Preliminary ah, U T , and ~ L Tcross sections have been extracted from the data. The transverse cross section U T , and longitudinal-transverse interference cross section (TLT is used to constrain the reaction mechanism. The behavior of the longitudinal cross section UL is mapped as a function of the Mandelstam variable t at fixed Q2. The kaon form factor is expected to be senstivity to OL, albeit in a model dependent way. The data will allow the kaon electroproduction reaction mechanism to be determined and eventually allow the kaon form factor to be modelled as well. The experiment required building two new aerogel Cerenkov radiation detectors with indices of refraction of 1.015 and 1.055. The first detector,

154

due to the low index of refraction, required special handling of the delicate aerogel radiator. The first detector fired only on pions or lighter particles, but not on kaons or protons. The second aerogel was built primarily by the MIT group and fired on either kaons or protons but not pions. The use of two aerogels in anticoincidence is a novel PID idea. The response of the two new aerogels as a function of momenta has been studied in detail for protons, kaons and pions. 2. Present Status

+

+

+

Measurements of the y p -+ K+ Y and e p + e' + K+ + Y (Y = A, Co) reactions are 'limited by short lifetimes ( c . TK = 370 cm, c . TA = 8 cm), small production rates (an order of magnitude smaller than for pions) and high thresholds [Eth(KA)= 911 MeV, Eth(KCo)= 1.05 GeV]. The unseparated cross sections are known with an accuracy of about 10%. Older, previous data from CEA, Cornell, and DESY provided an empirical fit to the unseparated cross section based on phase space, a simple monopole Q2-form factor, and an exponential drop with t. The past ten years have seen the first new data on electromagnetic kaon p r o d u ~ t i o n . ~ 3 ~ However the current situation for kaon electroproduction remains less satisfactory, both from the experimental and theoretical point of view. Jefferson Lab experiment E93-1083 was the first actual Rosenbluth separation, and demonstrated that the longitudinal response is large (approximately three-quarters the size of the transverse response) at t = tmin or O,, = 0. That experiment also demonstrated that Jefferson Lab is well suited for such precision separations, with the small emittance of the beam, the good particle identification of the detectors, and the accuracy of the spectrometers for cross section measurements. In kaon electroproduction, the mass pole is in the unphysical region where t > 0. The only unambigous data on the kaon form factor is from high-energy scattering of kaon beams from atomic electron^.^ Due to the inverse kinematics, the measurements were limited to low 4-momentum transfers (.02 < Q2 < .12 (GeV/c)2). The measurements were able to determine the kaon charge radius by looking at the slope of the cross section with respect to Q2. 3. Experimental Setup

The experiment took place in Hall A at the Thomas Jefferson National Accelerator Facility's CEBAF accelerator. The standard equipment in Hall

155

2

Figure 2. The longitudinal (upper) and transverse (lower) response function a t Q2- 2.35 GeV/c2 for H(e,e'K+) as a function of the invariant 4-momentum, t .

A has been described e l ~ e w h e r eElectron .~ beams of energies upto 5.7 GeV were incident on liquid hydrogen targets of nominal 4 cm and 15 cm lengths. Electrons and h n s were detected in coincidence in the two magnetically symmetric high resolution spectrometers (HRS). The HRS spectrometers were outfitted with special particle identification: on the electron side there were a gas Cerenkov counter and a lead glass calorimeter t o veto 7r- mesons, while on the hadron side two different aerogel Cerenkov counters were used to separately veto pions and protons. The pions were vetoed in the A1 aerogel which has a refractive index of 1.015 by requiring that the detector A1 not fire. Protons were vetoed in the A2 aerogel which has a refractive index of 1.055 by requiring that the detector did fire. 4. Experiment Status

The doctoral students analyzing the data (Marius Coman of Florida International University) is presently focussing on the systematic analysis (acceptance, normalizations, efficiencies and calibrations). For example, target "boiling" corrections are typically 4-6%, while VDC efficiency cor-

156

rections (both for the detector firing all four planes and for reconstructing one unique track) typically total 20%. The wire chamber efficiency, electronic and computer deadtimes, and cut efficiencies have been determined. Radiative corrections have been done using the MCEEP simulation code; a comparison to the SIMC simulation code is underway.

5. Prelimnary Results

L

Figure 3. Shown are ratios of the longitudinal to transverse responses as a function of Q2 from the previous E93-018 and from this experiment.

Prelinimary separated longitudinal and transverse response function results as a result of the invariant 4-momentum transfer t a r e shown in Fig. 3. The upper panel shows the Hall A data at Q”2.35 (GeV/c)2 while the lower curve shows the transverse response fucntion. The error bars will decrease by a factor of 2-3 when the analysis is final. The response functions were previously measured at lower Q2 in Hall C by experiment E93-018. Plotted in Fig. 5 is the ratio of the longitudinal to the transverse response function from E93-018 and a point at the higher Q2 of this experiment.

1 57

References 1. Electroproduction of Kaons upto Q2 = (3 GeV/c)2, Jefferson Lab Experiment E98-108, P. Markowitz, M. Iodice, S. F'rullani, C. C. Chang, 0. K. Baker spokespersons2 (1998). 2. Measurement of yp-@ A and rp-@ C at photon energies up to 2 GeV, M.Q.Tran et. al., SAPHIR , Phys. Lett. B 445, 20 (1998) and http:/flisalZ.physik.uni-bonn.de/saphir/klks.txt 3. Longitudinal and Transverse Cross Sections in the ' H ( e ,e'K+)A Reaction, G.Niculescu, et. al.,Phys. Rev. Lett. 81,1805 (1998). 4. A Measurement of the Kaon Charge Radius S.R.Amendolia et. al., Phys. Lett. B 178 435 (1986). 5. See, e.g., http://hallaweb.jlab.organd Nucl. Instr. and Meth. in preparation.

PHOTOPRODUCTION OF NEUTRAL MESONS WITH THE CRYSTAL-BARREL DETECTOR AT ELSA

V. CREDE Helmholtz-lnstitut f i r Strahlea- und Kemphysik, Nupalle 14-16, 531 15 Bonn, Germany E-mail: [email protected] The general succesa of quark models led to the problem of missing resonances. Many states predicted by constituent quark model calculations have not been observed experimentally or are only weakly established. This open question is discussed on the basis of experimental results of the CB-ELSA experiment at the e- accelerator ELSA in Bonn. Differential cross sections of y p + p r o and y p --t p q are presented for incident photon energies up to E, = 3 GeV. At low energies, results of experiments such as GRAAL and CLAS are reproduced to a good accuracy. New data points have been added for forward angles of the meson and at energies above 2 GeV. In the differential cross sections of both no and q photoproduction, a transition from dominant resonance production to a strong peaking in the forward direction can be observed around E, = 2 GeV. Moreover, total cross sections of y p + p r o ro ( T O T ) are discussed. Resonance production and even cascades of the type .**(A**) + N*(A*) + prOrO(pnOq) are observed. Indications for at least one A resonance around 1900 MeV are seen. The latter would be particularly interesting if it had negative parity because this state would be in contradiction with constituent quark models 1 ) 2 .

1. Introduction

Photon-induced reactions on the nucleon are a rich source of information for the baryon resonance spectrum. The full knowledge of possible baryon excitations and their properties would allow the extraction of the relevant degrees of freedom. Spectroscopic predictions are not possible in the nonperturbative regime of QCD. For this reason, effective theories and models are necessary in order to determine the masses, couplings and decay widths of resonances. Various constituent quark models are quite successful in describing the spectra. However, many open questions still remain. All models predict a series of hitherto unobscrved states, for instance. The persistent non-observation would be a big problem as those models would 158

159 TOF

am

Figure 1. Start configuration for a first series of measurements

have failed to describe physical reality. One explanation is that baryons have a quark-diquark structure. This would reduce the internal number of degrees of freedom and thus, the number of possible baryon resonances. On the other hand, almost all existing data result from 7rN elastic scattering experiments and models focussing on baryon strong decays predict baryon states to be missing in 7rN analyses but to show up however in electromagnetic production 3 . Therefore, photoproduction experiments offer a large discovery potential. The decay chain y p -+ A* -+ (Aq)(I = + p r 0 v is a suitable reaction to study A states and to search for missing A*. Additionally the region of A resonances with masses around 1950 MeV is of special interest in baryon spectroscopy. The PDG lists four well established states with positive parity in this mass region. In comparison only three A* with negative parity and poor experimental evidence are listed: A( 190O)S31 (**), A(1940)D33 (*) and A(1930)D35 (***). A confirmation of those states with negative parity would be in contradiction with constituent quark models predicting the three states at masses clearly above 2 GeV

g)

2. The Crystal-Barrel Experiment at ELSA

The ELSA accelerator complex in Bonn provides electron beams up to energies of 3.5 GeV. A LINAC preaccelerates the particles which are then injected into an electron synchrotron. The latter provides electrons with energies up to 1.6 GeV which are finally transferred to the stretcher ring

ELSA. For the data presented here, electrons extracted from ELSA with energies EOhit a primary radiation target and produced bremsstrahlung. The corresponding energy of the photons ( E , = EO- E e - ) was determined in a tagging system by the deflection of the scattered electrons in a magnetic

160

field. This detector provided a tagged beam in the photon energy range from 0.8 GeV up to 3.0 GeV for an incoming electron energy of 3.2 GeV. The setup of the CB-ELSA detector used for a first series of experiments is shown in Fig. 1. The calorimeter (Crystal-Barrel) consisting of 1380 CsI(T1) crystals covering about 98 % of 47~solid angle is an ideal detector for photons. The photoproduction target in the center of the Crystal-Barrel (5 cm in length, 3 cm in diameter) was filled with liquid hydrogen. The target was surrounded by a scintillating fibre detector built to detect and to trigger on charged particles leaving the target (proton trigger). In addition, it provided an intersection point of a particle's trajectory with the detector and hence helped to identify clusters of charged particles in the barrel. The general concept of the experiment is to combine the calorimeter with suitable forward detectors. Besides Time-Of-Flight walls in the start configuration, the TAPS detector (calorimeter consisting of 528 hexagonal BaF2 crystals) was used in a second series of measurements. The latter

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cose,

Figure 2. Preliminary differential cross sections for x o photoproduction from 300 MeV up to 3.0 GeV. The solid line indicates predictions by the SAID model. Systematic errors are given as grey-shaded area at the bottom of each energy bin. For energies below 1.3 GeV, the photon flux was determined by a x2 fit to the SAID predictions. Above 1.3 GeV, normalisation is taken from a measured photon flux scaled by a global factor of 0.75 in order to account for experimental uncertainties.

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cos o,,

Figure 3. Preliminary differential cross sections for 7 photoproduction from 750 MeV up to 3.0 GeV. Normalisation is the same as for xo production. Systematic errors are given as grey-shaded area at the bottom of each energy bin. Symbols indicate: CB-ELSA (m TAPS (k), CLAS (o), GRAAL (A), MAID (dotted line), SAID (dashed line).

has fast trigger capabilities and provides high granularity in the forward direct ion. Data was taken from December 2000 with the whole apparatus fully operational. Measurements at three different ELSA energies were performed: EO=1400,2600 and 3200 MeV.

162

3. Investigations of T O and

final states

Fig. 2 shows differential cross sections for single no photoproduction. The CB-ELSA results are in excellent agreement with the predictions of the SAID model. The latter is a parametrisation of a large amount of previously measured no data. Towards higher photon energies, i.e. above 2.2 GeV, resonance contributions disappear and a strong forward peaking can be observed. The latter can be described by t-channel exchange of p and w mesons and thus helps to identify resonant contributions. Exploring the high energy part of the spectrum allows extrapolation of t-channel contributions at lower energies. Photoproduction of q mesons ( I = 0) serves as an isospin filter because only nucleon resonances can be excited. The preliminary results are given in Fig. 3 and are consistent with measurements from TAPS 5 , GRAAL 6,7, CLAS and, for photon energies below 1.5 GeV, with the two models SAID and MAID g. The dominance of the s11(1535) can clearly be seen as isotropic behaviour of the differential cross section close to threshold. As in the case of 7ro photoproduction, a transition from resonance production to a strong forward peaking is observed (t-channel exchange). A small rise of the q differential cross section for higher energies in the backward direction of the meson may indicate u-channel contributions. Fig. 4 shows the high quality of the data. Background subtraction was applied only for the q channel. The background underneath the 7ro signal is very small and, thus, not explicitely treated.

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4. Preliminary results on the reaction 7 p

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In the following, results are presented for a data run at EO = 3.2 GeV resulting in M 22 000 nor)events. Figure 5 (a) shows the total invariant mass for the p TO q final state. No structures are visible at first sight. Different mass regions are indicated and the corresponding p r o mass spectra given. Hints for baryon resonances decaying into Aq now become visible. In the total mass region around 1700 MeV, no structure can be seen, Fig. 5 (b). However, a clear peak at the A mass can be observed in the mass region around 1900 MeV, Fig. 5 (c). We expect a series of resonances in this mass region with positive as well as with negative parity. In principle, it would be very difficult to disentangle them. However, in the Aq threshold region we expect a small angular momentum between the q meson and A(1232). Hence, it should be possible to excite some resonances selectively. For orbital angular momenta 1 = 0 or 1, we should expect contributions from the A(1910)P31, A(192o)P33, A(1905)F35 (1 = 1) and A(1940)D33 (1 = 0 ) . For higher p no masses, further resonance intensity may be hidden in a structure around 1600 MeV, Fig. 5 (e). One has to be careful interpreting structures in the mass projections as those are often reflections of the corresponding Dalitz plots (Fig. 5 (d) and (f)).

7600

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Figure 6. Preliminary total cross sections for 7 p -+ p r o 9 and y p + p T O T ' . The low-energy part of the CB-ELSA double-pion c r o s section agrees well with the GRAAL data. It should be mentioned that no proper five-dimensional acceptance correction has been applied yet.

165

L

d

Figure 7. Preliminary total cross section for the reaction y p -+ p T" T". The solid line indicates the CB-ELSA PWA result based on a data sample using an incoming ELSA electron energy of Eo = 1.4 GeV. This energy range corresponds to a mass range of 1240 MeV/c2 - 1900 MeV/c2.

Fig. 6 shows the total cross sections for the reactions y p pi no q and y p + p 7ro 7ro. The latter agrees very well with the GRAAL data in the low energy region. Above 2 GeV both cross sections are almost equal in magnitude. However, it should be mentioned that no proper five-dimensional acceptance correction has been carried out yet. Preliminary solutions of a partial wave analysis are based on an unbinned maximum likelihood fit taking all correlations among five independent variables properly into account (event-based fit). New resonances are needed to describe the data. There is evidence for a new A state at M 2.2 GeV as well as hints for A* -+ ~ ( 9 8 0as ) the ~ dominant contribution for ~ ( 9 8 0 production. ) Solutions can be ambiguous and therefore the question of negative-parity A states around 1950 MeV cannot be answered yet. Polarisation data is needed to discriminate between different contributing amplitudes. 5. Preliminary results on the reaction 7 p

+

p 7ro 7ro

Fig. 8 (left side) shows the total invariant mass of the reaction y p + p7r07ro for an ELSA energy of EO = 1.4 GeV. A clear peak

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Invariant pnOno mass [MeV/c2] Figure 8. Different plots on the reaction y p

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-+

p r o x o . See text for details!

around 1500 MeV/c2 as well as a structure at 1700 MeV/$ can be observed. The right side of Fig. 8 shows the p r o mass for the indicated mass range (1600 MeV/c2 - 1800 MeV/c2). Baryon cascades of the type N**(A**) + A(1232)r.O + p r o r o become obvious. A structure a t higher masses is also observed. The preliminary result of an event-based partial wave analysis confirms the parameters of known (***) and (****) resonances in the lowenergy spectrum below 1.4 GeV. Dominant contributions are N( 1520)DI3, A(1700)D33, N(1680)F1:, and N(1720)P13. Contributions of the nucleon resonance N(1700)D13 are less dominant. 6. Conclusions and outlook

The good agreement between CB-ELSA ro data and predictions by the SAID model shows that the detector acceptance is understood, which forms the basis for partial wave analyses. Furthermore, high quality 7 data have been measured and differential cross sections determined up to ET = 3.0 GeV. New resonances are in fact needed to describe the data. For example, there is cvidence for a new A state around 2.2 GeV. Simulations however, have shown that the mass and angular distributions of a A* resonance ( J p = 3/2-) cannot be distinguished from those of a A* ( J p = 1/2+), at least when interference effects are neglected. The CB/TAPS collaboration has taken data with linearly polarised photons created by coherent bremsstrahlung in a well-oriented diamond crystal. In general the use of linear polarisation breaks the symmetry. Thus,

167

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1

Figure 9. distributions for different Q,o bins. The data are not acceptance corrected. The incoming photon energy is limited to 1440 MeV 5 E, 5 1640 MeV, i.e. the polarisation maximum.

polarisation allows a better determination of contributing amplitudes by adding further constraints in the PWA, e.g. small contributions may have large effects in certain polarisation variables. In a two-body decay, the use of linearly polarised photons (polarisation PT) leads to a photon asymmetry E: =~O(l+PT'~'c0~(2~)) In a three-body final state like p7roq, there is more than one asymmetry depending on the choice of the corresponding a distribution. Fig. 9 shows the first results from a 2003 data-taking period. A photon asymmetry can clearly be extracted from the @o, distribution for different 0,o bins, for instance. Even considering only 40 % polarisation and contributions from background processes, statistics should be sufficient to investigate the 1950 MeV/c2 mass region and contribute to the question of negative-parity states as well as to the problem of missing resonances.

References 1. S. Capstick and N. Isgur, Phys. Rev. D34, (1986) 2809. 2. U. Lohring et al., EPJ A10, (2001) 309. 3. E. S. Ackleh et al., Phys. Rev. D54, (1996) 6811.

4. http://www.gwdac.phys.gwu.edu 5. B. Krusche et al., Phys. Rev. Lett. 74 (1995) 3736. 6. F. Renard et al., Phys. Lett. B528 (2002) 215. 7. J. Ajaka et al., Phys. Rev. Let. 81 (1998) 1797. 8. M. Dugger et al., Phys. Rev. Lett. 89 (2002) 222002. 9. http://www.kph.uni-mainz.de/maid

KAON PHOTOPRODUCTION AT SAPHIR FOR PHOTON ENERGIES U P TO 2.6 GEV*

K.-H. GLANDER, representing the SAPHIR Collaboration Physikalisches Institut, Una'uersititBonn, Nussallee 12, 531 15 Bonn, Germany E-mail: [email protected]

The measurement of photoproduction reactions with open strangeness is one of the central issues of the physics program at SAPIIIR. We report here on the analysis of the reactions y p + K + A and y p -+ K + C o using data taken in the years 1997/98. A substantial variation of the differential cross sections as a function of the K+ production angle throughout the measured photon energy range between threshold and 2.6 GeV is observed. The measured cross sections together with their angular decompositions into Legendre polynomials suggest contributions from resonance production for both reactions. The induced polarization of A has negative values in the kaon forward direction and positive values in the backward direction. The magnitude varies with energy. The polarization of Co follows a similar angular and energy dependence as that of A, but with opposite sign. Preliminary results for the reactions y p -+ K ° C + , y p -+ K+C-n+ and y p -+ K+Ano and published results on @J vectormeson photoproduction were shown at the conference.

1. Introduction The SAPHIR detector' at the electron stretcher facility ELSA was built to measure photon induced reactions in the threshold and resonance regions up to photon energies of 2.6 GeV. Of large interest was the measurement of photoproduction processes with open strangeness, especially the reactions y p + K + h and y p + K+Co. These reactions were already studied using SAPHIR data from the first data taking period from 1992 to 19942. During this first period 30 million triggers were taken for photon energies up to 2.0 GeV. In the second data taking period from 1997 to 1998 180 million triggers were recorded for photon energies up to 2.6 GeV. Equivalently, for *This work is supported in part by the Deutsche Forschungsgemeinschaft (DFG) (SPP 1034 KL 980/2-3)

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the analysis of the reactions y p -+ K + A and y p -+ K+Co, with respect to previous SAPHIR measurements', the photon energy range has been extended into the continuum region and the differential resolution in both, kaon production angle and photon energy, were improved by a factor of two. The results presented here are final and to be published in Eur. Phys. J. Details of the analysis can be found there and even in more detail in3l4. Because of lack of space there will be no discussion on the following topics, which were presented during the workshop: a

a

a

In my talk I presented preliminary data on the reaction y p -+ K°C+, which is important to constrain models for the reaction y p -+ K+Co with help of isospin invariance. Three body final states K Y T provide a good tool to study excited hyperons which decay to Y 71. There might be signals from nucleon (and A) resonances, which couple to K Y . So (as for the final states K Y ) the search for so called missing resonances, which were predicted by quark models (see e.g.5>6),but so far not established experimentally, can be addressed. I showed preliminary data on the reactions y p -+ K+C-.lr+ and y p -+ K+A./ro. Furtheron I showed data on the CP vectormeson photoprod~ction~.

2. Cross sections

Figures 1 and 2 show the differential cross sections for the reactions y p -+ K + A and y p -+ K+Co from threshold up to a photon energy of 2.6 GeV. The kaon production angular range in the overall cms is fully covered. In view of the statistical and systematic errors the data are splitted into 20 angular bins for 36 (33) photon energy ranges. For every data point the error includes the Statistical error and an estimate of systematic errors added in quadrature. The data shown here are selected with restrictive cuts to avoid background contributions. The curves to the data are Legendre fits of the form:

where q and k are the momenta of the kaon and photon in the crns. In Figures 3 and 4 the fit coefficients are shown for both reactions as a function

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+

angle of KO, from the elementary process, are 7OOMeV/c and 60 degrees, respectively, as shown in Fig.2 (a). The momenta of pions from the decay of Kg are shown in Fig.2 (b). From these figures, the spectrometer is required to have a momentum acceptance for charged pions from the threshold to 7OOMeV/c with as large solid angles as possible. Secondly, it should be taken into account that flies in a short distance since it has a finite lifetime of a-= 2.678cm. Therefore, good vertex resolution is required in order to distinguish background 7rcT+-xTTevents which come from N*'s or a multi-pion production. The NKS at LNS, Tohoku University is one of detectors to satisfy such requirements. 3. Experimental Setup

Experiments were performed at the internal tagged photon facility at LNS. The BMCTagger system' is located at the one bending corner of the Stretcher Booster (STB) ring. It consists of a carbon fiber radiator of l l p m diameter, an analyzing magnet which is common to the bending magnet (BM) of STB ring, segmented plastic scintillator counters in the magnet gap, and a control computer system. The 200MeV electron beam from LINAC is injected to the STB ring and accelerated up to 1.2GeV. At the flat-top, the radiator fiber is inserted to beam. A recoil electron associated to bremsstrahlung is momentum analyzed by BM and detected by the plastic counters. The radiator is smoothly moved from outside being controlled to keep flat photon intensity during the STB flat-top time of 20 sec. Typical tagged photon intensity was 2MHz. Duty factor was about 60

202

Figure 3. Neutral Kaon Spectrometer (NKS).

%, limitted by available power. The photon beam is extracted through a thin window (Al, 2mm) and is delivered to the experimental target. On the beam line, a magnet (SM) is placed in order to sweep out electrons and positrons from the conversion at the window or in the air. Helium bags are installed downstream of the SM to reduce the electromagnetic conversions in the air which produce background triggers. A lead collimator is placed at the entrance of the SM in order to define beam size and eliminate beam halo which causes huge background triggers. Tagging efficiency, which is the ratio of the signal accompanying with the photon to tagger signal, was measured to be 80f3 % under this condition. A 2.14g/cm2 natural carbon target was placed at the center of the NKS (figure.3). The NKS consists of a dipole magnet of 107cm diameter and 60cm gap, inner and outer plastic scintillator hodoscopes (Mand OH), straw and cylindrical drift chambers (SDC and CDC) in the magnetic field of 0.5Tesla, and narrow plastic counters in the beam plane (EV). The trajectory of charged particles is reconstructed by SDC and CDC and momentum is obtained. Time of flight is measured with IH and OH, whose distance is about 80cm. A huge background from e+e- are suppressed by EV’s in a trigger level. These detectors are divided into left and right parts and cover

203

a solid angle of 7r sr. For the trigger, we required two charged particle in both sides in addition to tagger signal, namely, 8 ( I H R @ OHR @ Trigger = Tagger 8 ( IHL 8 OHL 8

m).

m)

Because of the measurement in the threshold region, absolute beam energy is crucial in the present experiment. Therefore, beam energy was calibrated using y + e+ e- process. Momenta of electron and position pair were measured with the pair spectrometer system, which consists of a magnet with pentagonal pole shape, drift chambers, and trigger counters. In the analysis, field distribution was calculated by TOSCA and normalized to the measured value at the tenter of the magnet. The calibrated photon energies corresponding to each tagger segment are given in Fig.4. The photon energy ranges

+

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Figure 4. The calibrated photon energies corresponding t o each tagger segment. The me& surements were performed at 4 current setups as shown in figure. The results agrees with each other within the systematic uncertainty

of 10MeV.

from 800 to 1lOOMeV with the resolution of -6MeV determined by the counter width. Accuracy of the magnitude was estimated to lOMeV, which is dominated by the uncertainty of the fringing field shape. 4. Preliminary Results of Analysis

Trajectories and momenta in the horizontal plane were reconstructed using spline methods' from SDC and CDC hits and the calculated field map. Vertical position at OH was determined from the transmission time difference between signals from top and bottom photomultipliers. The vertical direction was evaluated by assuming the same vertical position at the target as that of the beam. Particle velocity was obtained from time difference between IH and OH after correcting pulse heights and flight path length. Figure.5 shows a scatter plot of inversed velocity (B-') and momentum of particles. Proton and pions are clearly separated. The regions drawn in the figure were defined as 7r+ and 7r- in the analysis.

204

Vertex position was calculated as the crossing point between two trajectories in the left and right arm detectors in the horizontal plane. In the calculation, the bending effect in the magnetic field was taken into account. Thus, 3momentum of the particles and opening angles ( q ) between two trajectory were fully determined. Figure.6 (a) shows a distribution of vertex for n+n- events. Vertex resolution was estimated to be 1.7 m m rms after selecting events of -0.8 < cosq < 0.6. Most of the events were originated in the target area drawn by the box (TGT). These events are background such as multi-pion production or N* decay. No peak was observed in an invariant mass spectrum for those events. ( Fig.6 (b) ) On the other hand, when the decay volume (DV) was chosen as mentioned before, a peak of KS was clearly observed as shown in Fig6 (c).

0

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1 /B Figure 5. Inversed velocity and momentum for reconstructed charged particles. Sign of the momentum means particle charge. Pion gates are drawn in the figure.

In order to extract Kg contribution, invariant mass gates for Kg and background were defined as follows,

KO 0.445< M(?r+n-) ^. Question is, 208

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however, the strangeness has to be in a specific hadron which is either in hyperons or kaons. So far acquired date suggest that antikaon nuclear potential is attractive qualitatively. However, no quantitative number has been given experimentally. Atomic levels of K - atoms which are dominantly determined by the Coulomb interaction are affected by the existence of the strong antikaon nucleus potential. One can derive the potential by detailed analysis of atomic X-ray data. The shifts and widths of observed atomic levels were reproduced by introducing an appropriate optical potential. Recent extensive analysis of kaonic X-ray data concludes that the potential is strongly attractive '. The derived depth is around -200 MeV which opens a possibility of kaon condensation at around three times normal nuclear density. The optical potential derived from the kaonic atom data, however, is not unique since the atomic state is sensitive only to the phase shift of K - wave function at the nuclear surface. The phase shift alone cannot determine the depth of the potential since the K - wave function has an ambiguity in number of nodes in the nucleus especially when the potential depth is quite deep. The strong imaginary part of the potential further obscures the nodes. Earlier studies with a different treatment of the nuclear surface gave much shallower potentials '. The X-ray from K - hydrogen shows that the antikaon nucleon interaction is repulsive at the threshold '. It is known that h(1405) can be a bound state of antikaon and nucleon although it can also be explained as the excited state of A where one of u, d, and s quarks is in a porbit. The strongly attractive interaction makes a bound state and the interaction at the threshold derived from the energy shift of the X-ray appears to be repulsive. Thus X-ray data of the K - hydrogen is consistent with that the h(1405) is the bound state and antikaon nucleon interaction is strongly attractive. Enhancement of the K - / K f ratio observed in the heavy ion reactions suggests a strong attractive interaction although quantitative argument requires understanding of details of the reaction mechanism , in particular, its temperature and density dependence lo for which further study would be needed. Calculations based on Chiral Lagrangian 1 1 J 2 J 3 or meson exchange potential l4 predict relatively shallow potential of 50-80 MeV. Later analysis showed that the same atomic X-ray data can be reasonably reproduced by such relatively shallow potential 15. On the other hand, theoretical calculations based on phenomenologically obtained antikaon nucleon interaction predicts deep potential ". The antikaon nucleus potential is the key in778

210

formation to constrain the properties of kaon in neutron star l7 although further experimental data are needed to further constrain theoretical models.

2. Kaonic nuclei and the in-flight ( K - , N ) reaction

If I?-nuclear potential is as deep as 200 MeV 5, then deeply-bound kaonic nuclei exists 18. The general properties of the kaonic nuclei can be predicted as follows. The potential depth is roughly four times deeper than that for nucleon and the kaon mass is about half of that of a nucleon. Thus the major shell spacing ( f i w ~ is ) f i times the 40A-lI3 frequently used for nucleon. Since the kaon has no spin, no spin dependent splitting has to be considered. The t i W ~is roughly 40 MeV, for instance, for the kaonic ESi nucleus. The 1s state appears at around -140 ( $ t i W ~- 200) MeV bound, which is the deepest bound state ever observed in nuclear physics. In order to observe the state its width has to be reasonably narrow. The width is given by the imaginary part of the potential, which decreases for the deeply bound state and is around 10 MeV 19. The production of kaonic nuclei can be achieved by the in-flight ( K - , N ) reaction l 8 which is graphically shown in fig. 1. This reaction provides a virtual K - or K O beam which is thus appropriate to excite kaonic nuclei. Other strangeness transfer reactions like ( K - , r), (r*,K + ) and (y, K + ) primarily produce hyperons and thus are sensitive to states mostly composed of a hyperon and a nucleus.

Figure 1. Formation of kaonic nuclei via the ( K - , N ) reaction is shown diagrammatically. The kaon, the nucleon, and the nucleus are denoted by the dashed, thin solid and multiple lines, respectively. The kaonic nucleus is denoted by the multiple lines with the dashed line. The filled circle is the K N -+ K N amplitude while the open circles are the nuclear vertices. The bubbles represent distortion.

21 1

The momentum transfer of the reaction depends on the binding energy of a kaon. We are interested in states well bound in a nucleus ( B E = 100 -150 MeV). The momentum transfer for the states is fairly large (q = 0.3 0.4 GeV/c) and depends little on the incident kaon momentum for PK = 0.5 w 1.5 GeV/c, where intense kaon beams are available. Therefore one can choose the incident momentum for the convenience of an experiment. It is a little beyond the Fermi momentum and the reaction has characteristics similar to the ( T + , K+) reaction for hypernuclear production where so-called stretched states are preferentially excited 20. The calculated cross sections of the kaonic nuclei are given elsewhere l 8 which employed the distorted wave impulse approximation (DWIA). The DWIA calculation requires: (a) distorted waves for entrance and exit channels, (b) two body transition amplitudes for the elementary ( K - , N ) process, and (c) a form factor given by initial nuclear and kaonic-nuclear wave functions. Relevant formulas used in the ( K - , N ) reaction are essentially the same as those used in the (&, K+) reaction which can be found elsewhere 20. The calculated cross section is around 100 pb/sr for I2C at forward scattering angle. Recent calculation showed that the cross section is reduced further half due to distortion although general characteristic of the reaction is the same 21. The cross section of the elementary reaction was given by the phase shift analysis of available data22 which is shown in figure 2.

-

3. Exploratory experiment at BNL We have carried out an experiment to look for kaonic nuclear state. The K - beam was provided by the D6 beam line of the alternating-gradient synchrotron (AGS) of BNL. The 160(K-,n) reaction was used to produce kaonic nuclear states. The experiment was carried out as a parasite of the E930 experiment which looked for y rays from AGOhypernuclei. The incident K - momentum of P ~ = 0 . 9 3GeV/c, which gave the maximum yield for hypernuclei, was also almost best suited for the production of kaonic nuclei as seen in figure 2. The K - beam intensity was typically 8 x 104/spill for 5 x 10l2 proton/spill. A spill consisted of 1.4 seconds of continuous beam every 4 seconds. Figure 3 shows the setup of the experiment. The beam-line spectrometer measured the incident K - momentum. An array of Ge detectors which is called Hyperball was placed at around the target. We used it to tag charged particles from the target which enhance kaonic nuclear events al-

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212

Figure 2. The CM differential cross sections of the three reactions are shown m a function of incident kaon lab momentum.

though its primarily purpose was to measure y rays from hypernuclei. The 48D48 spectrometer system measured T - from the ( K - , T - ) reaction to tag hypernuclei. It is irrelevant for the present measurement although was useful to sweep out vast amount charged particles from the target which would have give intolerable rate to the neutron counters. Neutrons were measured by an array of neutron counters placed 6.8 m downstream of the target. There are many elements in the beam line to identify K - . Details of the setup of the E930 experiment can be found elsewhere 23. The biggest background is the K - decay in-flight mostly from K - + ~ - 7 r O . We confined the decay region by placing a veto counter just downstream of the target which reduced the background from the K - decay although we still had appreciable amount of y ray backgrounds from TO’S. The target was water which contains not only oxygen but also hydrogen. The water was contained in a container of 200(thickness) x 15(height) x 60(width) mm3. Kaonic nuclear states excited by the reaction leaves strangeness in the nucleus. We naturally expect emission of energetic particles from the state as described later. Hyperball tags such particles reducing backgrounds.

213

I

Figure 3. Setup of the test experiment is shown schematically. It was a parasite of the BNL AGS-E93O. See text for the description of each detector element.

4. Neutron momentum spectra The neutron momentum spectrum was obtained by the time-of-flight (TOF) spectrum. Calibration of timing was achieved by using K - and 7r- beams that hit the neutron counter by setting magnetic field of the 48D48 spectrometer off. Incident beam momenta were measured by the beam line spectrometer thus precise calibration was achieved. Time resolution of neutron counters were around 100 ps which is the dominant source of the momentum resolution of neutrons. The momentum resolution depends on neutron momentum. It is around 15 MeV/c for 1.3 GeV/c neutrons which corresponds -100 MeV bound region for kaonic nuclei. Detection of neutrons is not straightforward and we usually have backgrounds. In order to reduce them, it was required that more than two successive neutron counters

214

fired and their pulse heights were consistent with a dE/dX for a measured neutron momenta. The TOF spectrum is shown in figure 4. The inclusive spectrum is in the left side. A distinct peak in the spectrum corresponds to y rays (p = 1). The y rays are from no decay which is from the K decay as discussed above. Around 1/P = 1.15 we see a broad peak. This is due to KL which is from the charge exchange reaction of K- at the target. The KO produced by the K - + p + Ron reaction became either K , or K L . Only the KL reach the neutron counter and the K L again produces charged kaon at the neutron counter by the charge exchange reaction. The peak position in the TOF spectrum is almost the same as that of K - beam which verifies this consideration. In order to reduce such backgrounds, hits in Hyperball were required. Hyperball consists of Ge and BGO detectors. In the current analysis we employed only the Ge detectors. We took events that are accompanied by charged particles. The charged particles leave energy much higher than y rays in Ge detectors. We thus set 7 MeV for the threshold of the Ge detectors. BGO counters had so high gain to be sensitive to low energy y rays that the gain setting was inappropriate to tag charged particles. The TOF spectrum with the cuts is shown in the right side of figure 4. One can clearly see that the peak due to KL disappears. It is particularly important that we can almost eliminate the background due to KL since it could be the most serious backgrounds in high neutron momentum region which corresponds to deeply bound kaonic nuclei. The momentum spectrum of the 1 6 0 ( K - ,n ) reaction is shown in figure 5. Here the horizontal axis is the difference of measured neutron momentum from that of calculated for the kinematics of the K - + p + n+Ko reaction. In the calculation we used K - beam momentum measured by the beam line spectrometer. Since water (HzO) target has two protons over one l6O, we should observe dominant contribution from the proton target. The distinct peak appears at zero corresponds the reaction on the proton. This also means that calibration of timing was correctly carried out.

5. Decay properties of Kaonic nuclei The kaonic nuclei are made up by the strong attractive interaction between antikaon and nucleon. The two body attractive interaction makes A(1405) which is an 1=0 state. Therefore it is reasonable to assume that the decay of kaonic nuclei dominantly through the same decay modes as that of A( 1405). It dominantly decays to 7rC (n+C-, n°Co or n-C+) and decay to the 7rA

Figure 4. TOF spectrum of neutrons detected by the neutron counter at 0 degrees are shown. The left side is inclusive spectrum with dE/dX cut and right side has additional cut of more than one hit in Hyperball.

channel is strongly suppressed due to its 1=0 character. If binding energy of kaon is less than 100 MeV the kaonic nuclei can decay into TC. The C- and C+ produce charge pions and A produced by the decay of Co also produce charged pions. Thus the kaonic nuclei are likely to produce charged pions. If the binding energy is deeper than 100 MeV, nC channel is effectively closed. channel is of minor importance since it is possible only through an The ~ T A isospin mixing of 1=0 into I=l. A kaon interacts with two nucleons leaving hyperon and nucleon in the final state. Experimentally one can still observe pions that are provided from the decay of hyperon although multiplicity of pions are less. We used GEANT simulation to estimate the efficiency of the Hyperball tagging. We, however, note that the efficiency depends on the decay modes assumed for which we need further study. 6. Discussion

In the present experiment it is proved that we can have a neutron spectrum almost free from backgrounds. It is due largely to the fact that we are detecting almost highest energy neutrons. There are, however, background processes that could produce neutrons more energetic than that of the quasifree process. The ( K - , n - ) reaction where pions are scattered backwards can produce energetic hyperons. In this case the hyperons are scattered forward and their decays produce neutrons. The pions scattered

216

5

Figure 5. Momentum spectrum of the outgoing neutrons. Zero corresponds to the momentum of a neutron from the p ( K - , n ) K O reaction which is around 1.2 GeV/c in this particular experiment.

backwards give hits in Hyperball thus signal becomes similar to the kaonic nuclei. The process was estimated by the GEANT simulation with known cross sections 22. The process was found to be of negligible importance from the consideration cross section and properties of decay. Energetic neutrons can also be produced by the K - absorption by two nucleons. It is K - + p N + Y n . The neutron or proton process has to involve another nucleon in addition to the ( K - , N ) reaction. Thus one expects the process gives smaller cross section than that of the ( K - , N ) reaction. The process can be interpreted as a spreading width of the kaonic nuclei. From the simple consideration of kinematics the kaon absorption produces neutrons around 1.5 GeV/c thus appears at 0.3 GeV/c in figure 5. The width is around 0.1 GeV/c which is obtained by a simulation. We see no peak in figure 5 which shows that our spectrum is free from the two-nucleon absorption background. Use of energetic kaon reduces two-nucleon absorption process since short wave length of incident particle makes simultaneous participation of two nucleons in the process difficult.

217

The physics we learn from the neutron momentum spectrum is the following. First we observed the sharp peak at 0 which corresponds to K - p --t KO n. Secondly we observe appreciable amount of strength in the bound region. Bound region starts around 0.05 GeV/c and we see some enhancement at 0.06 and 0.13 GeV/c. This means that interaction is strongly attractive. Implication of the spectrum is clearer in the excitation energy spectrum. We see evidence of a peak corresponding to the excitation of kaonic nuclei. However, excitation energy spectrum needs further analysis particularly for consistency between experimental resolution and observed peak in the spectrum. Since it is subject to future change, we leave the excitation energy spectrum of kaonic nuclei in a future publication.

+

+

7 . Prospect

Recently we have carried out an experiment to study the 12C(K-,p) reaction at KEK. This was parasite of the KEK-PS E522 where the ( K - , K + ) reaction was studied to investigate AA at the threshold. The K - beam momentum of 1.6 GeV/c was high for the present study since KN scattering cross section is already quite small although can give important information. The analysis of the reaction is under way. Preliminary studies indicates appreciable amount of events in the bound region. This again suggest attractive interaction. It is shown that the ( K - , p ) and ( K - , n ) reactions can be used for the study of the kaonic nuclei. Study of the reaction requires intense low energy kaon beam for which AGS of BNL and probably PS of KEK are particularly suitable. The beam momentum can be chosen by considering the cross section, beam intensity and momentum resolution of spectrometer. There are beam lines which provide K - beam 0.5-2 GeV/c at BNL and KEK. The relatively broad width (-10 MeV) and simple structure of the state need spectrometers of only modest momentum resolution but wide momentum acceptance. The kaon-nucleus potential is particularly interesting thus there are many efforts to carry out experiments recently The ( K - , n ) reaction with stopped kaon is one possibility and the ( K - , T-) reaction is another possibility. One can also think of reactions using electromagnetic probes. There are also many theoretical works. It is very hard to list all of them though once the strongly attractive interaction is proved by experiments many interesting possibility will surely arise. We demonstrated that the ( K - , p ) and ( K - , n ) reaction can be used to 24925.

218

obtain direct information on the KN interaction in nuclear matter. The calculation employed here is rather crude although it is based on well-known general concepts in nuclear physics.

Acknowledgements The anther (TK) is grateful to discussions with Professors A. Gal, Y. Akaishi, and T. Tatsumi. This work is financially supported in part by Japan Society for the Promotion of Science under the JapanU.S.Cooperative Science Program.

References 1. D. B. Kaplan and A. E. Nelson, Phys. Lett., B175 (1986) 57 2. G. E. Brown, Nucl Phys A574 (1994)217, G. E. Brown, M. Rho, Phys. Rep. 269 (1996) 333, C. H. Lee, Phys. Rep. 275 (1996) 255 3. M. Prakash and J.M. Lattimer, Nucl.Phys. A639 (1998)433 4. P. J. Ellis, R. Knorren, M. Prakash. Phys.Lett.B349 (1995)ll 5. C.J. Batty, E. Friedman, A. Gal. Physics Report 287 (1997) 385 6. M. Iwasaki, et al., Phys. Rev. Lett. 78, (1997) 3067 7. R. B a t h et al., Phys. Rev. Lett. 78 4027 (1997) 8. F. Laue et al., Phys. Rev. Lett. 82 1640 (1999) 9. G.Q. Li, C.H. Lee, and G.E. Brown, Phys.Rev.Lett.79 5214 (1997); G.Q. Li, G.E. Brown, C.H. Lee, Phys.Rev.Lett.81 2177 (1998) 10. L. Tolbs, A. Ramos and A. Polls, Phys. Rev. C65, (2002) 054907 11. M. Lutz, Phys. Lett. B 426, 12 (1998) 12. A. Ramos and E. Oset, Nucl. Phys. A671, 481 (2000) 13. J. SchafFner-Bielich,V Koch and M. Effenberg, Nucl. Phys. A669, 153 (2000) 14. L. Tolbs, A. Ramos, A. Polls and TTS Kuo, Nucl. Phys. A635, 99 (1998) 15. S. Hirenzaki et al., Phys. Rev. C61, (2000) 055205 16. Y. Akaishi and T. Yamazaki, Phys. Rev. C65 044005 (2002) 17. A. Ramos, J. Schaffner-Bielich and J. Wambach, Lecture Notes Phys 578, 175 (2001) 18. T. Kishimoto, Phys. Rev. Lett. 83 (1999) 4701 19. T. Waas, N. Kaiser and W. Weise, Phys. Lett. B379 (1996) 34 20. C. B. Dover, L. Ludeking and G. E. Walker, Phys. Rev. C22 (1980) 2073 21. A. Cieplj., E. Friedman, A. Gal and J. Mares, Nucl. Phys. A696 (2001) 173 22. Gopal et al., Nucl. Phys. B119 (1977) 362 23. H. Akikawa et d.,Phys. Rev. Lett. 88 (2002) 082501 24. M. Iwasaki,et al., Nucl. Inst. Math. A, 473 (2001) 286 25. T. Nagae et al., private communication (2003)

4. Spectroscopy of Hypernuclei


PROSPECT OF PHOTOPRODUCTION OF MEDIUM-HEAVY HYPERNUCLEI-

T. MOTOBA Lab. of Physics, Osaka Electro-Communication University, Neyagawa 572-8530, Japan+ and Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, U.S.A. P. BYDZOVSKY AND M. SOTONA Nuclear Physics Institute, 250 68 R e i near Prague, Czech Republic K. ITONAGA Miyazaki Medical College, Miyazaki 889-1 698 Japan K. OGAWA Department of Physics, Chiba University, Chiba 263-8522, Japan

0. HASHIMOTO Department of Physics, Tohoku University, Sendai 980-8578, Japan

Basic characters of the elementary hyperon photoproduction process are clarified. Novel aspects of photoproduction of hypernuclei are demonstrated by choosing typical medium-heavy nuclear targets, which should provide a n important opportunity of studying dynamical coupling between a hyperon and nuclear core excitation.

1. Introduction

In the spectroscopic study of hypernuclei, the "(-ray measurements in recent years have achieved a great success in providing us with remarkably high *Work done in part of the Japan-Europe Joint Research Projects supported by Japan Society for the Promotion of Science (2000-2002). t Permanent address; E-mail:[email protected]

221

222

’.

resolution data on their energy levels However, it is not always easy t o produce hypernuclei abundantly enough t o make such measurements possible, in view of the practical kinematical conditions. As for the reaction spectroscopy, there are many challenges to be done for investigating hypernuclear structures. Recently the photo-/electro-production of hyperons and hypernuclei has attracted much attention in strangeness nuclear physics. First, the high-energy electron beams became available a t the Jefferson National Laboratory (JLab) and its beam intensity is so high that can overcome practically the small hyperon production cross sections. In addition t o the elementary process experiments, the first experiment on the nuclear target, 12C(e,e’K+)i2B, was successfully carried out 2 , providing a promising result which is consistent with the theoretical calculation 3 . Secondly, the photoproduction of hypernuclei has a characteristic novel merit of exciting unnatural parity high-spin states which cannot be reached through the ( K - , T - ) and ( T + , K + ) reactions. Another merit t o be added is t o convert a proton into A so that proton-defficient mirror hypernuclei are produced. Next, an emphasis should be put on the energy resolution of the electroproduction which is expected t o be several times better than the secondary mesonic beams: the former typical value is A E N 0.5 MeV 4 , whereas the latter best value is 1.45 MeV in the KEK-SKS achievement 5,6. In this report, first we discuss basic properties of hyperon photoproduction process and, secondly, theoretical predictions are demonstrated by choosing medium-heavy nuclear targets such as 28Si and 40Ca. Determination of energy position of typical high-spin states with unnatural parity helps us test various models of Y-N potential models

’.

2. Kinematics and Nature of the yp + A K + Reaction

Characteristics of hypernuclear production reaction depend basically on the magnitude of the momentum transfer and the nature of the elementary amplitudes describing the hyperon photoproduction process. First we compare the n ( K - , T-)A, n ( ~ + K ,+ ) A , and p(y, K + ) A reactions. In Fig. 1 the hyperon recoil momenta q1\ in these reactions are plotted as a function of the projectile momentum. It is well known that the small values of qiKK’?i) = 50 - 150 MeV/c involved in the ( K - , T - ) reaction at p~ N 0.8 GeV/c favor the hypernuclear excitation with recoilless or very small angular momentum transfer (AL 5 1, AS = 0). As for the ( T + , K + ) reaction, the sizable momentum transfer q r ’ K ) N 400 MeV/c

223

(R, %-) ...."............(nt,,Kt)

Igz:

-(Y,

Kt)

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

. . . .

.

.

.

.

1:

n 0.0

0.5

1.0

1.5

2.0

2.5

FmJECTILE yoyBrrm( (CeV/c) Figure 1. Hyperon recoil momentum qh as a function of projectile lab momentum. Two curves for each reaction correspond to the meson lab scattering angles: ela),= 0 and 10 deg.

together with the spin-nonflip dominance leads to the selective excitation of hypernuclear natural parity states with maximum aligned angular m e mentum ( J = L,, = I, I^ of [(nlj);l(nlj)^]J in case of Jtarget= o+). It is interesting to see that the momentum transfer q p Y K )is quite similar to q r ' K ) ,suggesting its high-spin selective excitation as in the ("+,IT+) reaction. The A recoil amounts to 353 MeV/c (Olab=O deg) - 425 MeV/c( 10 deg) at pr = 1.3 GeV/c which is chosen in the actual experimental kinematics. Many theoretical attempts have been made to describe the elementary hyperon photoproduction processes. In the hypernuclear calculations, we adopt four isobaric models denoted hereafter as Adelseck-Wright (AW2) 11, Adelseck-Saghai (AS1) 12, Williams-Ji-Cotanch (C4) l3 and Saclay-Lyon A (SLA) 14. In Fig. 2 we show how well these theoretical amplitudes reproduce the experimental differential cross sections at a fixed kaon scattering angle. Predictions of all models are in good agreement with the data for energies up to 1.4 GeV, but for the higher energies the 3 models AW2, AS1, and C4 deviate remarkably from the new SAPHIR data lo (triangle data points) which were not included in the fitting procedure. In the present hypernuclear calculations the cross section estimates are performed at E$b x 1.3 GeV where all the four models provide acceptable description of the elementary process. In more detail the SLA model gives 15 - 20% overestimates with respect to the experimental differential cross sections at < 15 deg(0gb < 6.5 deg) This suggests the amount of theoretical

+

OgM

224 3

I

.

,

.

,

.

J

I---

Figure 2. Experimental and theoretical differential cross sections for the -yp

-+

hK+

reaction are plotted as a function of the photon lab energy at a fixed kaon scattering angle. See text for the models denoted as AW2, AS1, C4,and SLA. The data are from Refs.

(solid circles),

(empty circles), and

lo

(triangles).

uncertainty in predicting the hypernuclear production rate with this model. Next we emphasize that the unique character of hypernuclear photoproduction comes from the spin-flip dominance. The elementary transition matrix for -p -+ AK+ can be expressed in terms of four complex amplitudes (fo, go, 91,and 9-1)defined in the lab frame of Fig. 3 as:

M =< k - P,pltlk,O >Lab=

C O ( f 0 f 9000)

+ Ex(gl0l + 9-la-1)

(1)

Here ex and €0 denote the unit vectors describing the photon polarization and om is the Pauli spin operator for the baryon. The amplitudes are normalized as follows:

where the energies, momenta, and angle are all in the laboratory frame. In order to demonstrate the spin-flip dominance, we list in Table 1 the squared magnitudes of the four complex amplitudes. One sees that, at small angles concerned here, the spin-dependent amplitudes (go, 91,g+1) clearly

225

Figure 3. Hyperon photoproduction kinematics in the laboratory frame

dominate over the the spin-nonflip one (fo). Although all of the models were obtained in fitting to the available scattering data, one also notices that these amplitudes are considerably different from each other. Especially these models predict very different polarization values, respectively, for which the experimental data are very few. We remark that the important two factors in the elementary process - its large momentum transfer and spin-flip dominance - give rise to the selective excitation of hypernuclear high-spin states with unnatural parity. Table 1. Magnitudes of the spin-independent (fo) and spin-dependent amplitudes (g’s) in units of nb/sr/GeV2. The evaluation is made at EYb = 1.3 GeV. The laboratory cross sections are in pb/sr.

3 deg

10 deg

A W 2 l1 AS1 l2 C4 l3 SLA l4 A W 2 l1 AS1 l 2 C4 l3 SLA l4

0.0001 0.0071 0.0002 0.0024 0.0011 0.0548 0.0011 0.0255

0.369 0.398 0.609 0.451 0.296 0.375 0.569 0.392

0.188 0.191 0.290 0.224 0.209 0.175 0.190 0.186

0.192 0.206 0.299 0.222 0.218 0.205 0.217 0.178

1.78 1.91 2.85 2.14 1.65 1.84 2.23 1.78

-0.005 -0.055 -0.019 -0.016 -0.007 -0.142 -0.066 -0.053

3. Excitation Spectra Predicted for 28Si(y,K+)i8Al In order to demonstrate the characteristics of photoproduction of hypernuclei, here we choose 28Sias a typical nuclear target. The excitation spectra have been evaluated at E7 = 1.3 GeV and 0; = 3 deg which correspond to the kinematical condition in the experimental proposal. In the first subsection, for demonstration the 28Sitarget ground state is assumed to have the lowest proton-closed shells [ ~ ~ p ~ ~ ( O d 5 /In 2 )the g ] .second subsection, we extend the calculation to employ realistic wave funtions solved in the

226

[s4p"(sd)~~ full ] shell model space.

3.1. A Demonstrative Model with (OdsI2)E

As the proton shells are closed up t o (Od5/2);, the final hypernuclear states are described, respectively, with l p - l h configurations [(nlj);'(nlj>"]~. For the single-particle wave functions, we employ the DDHF solutions so as t o be as realistic as possible. The calculated cross sections are summarized in Table 2. Table 2. Differential cross sections (in pb/sr) for the 28Si(y,K+)i8A1 reaction calculated at E, = 1.3 GeV and O& = 3 deg with the SLA amplitude 14. The final hypernuclear states are expressed by [(lj);' ( l j ) " ] ~ .

(EA)

(p-hole) J=O J=1 ( O r 1 ) J=2 5/2 J=3 J=4 J=5 J=O (op-' ) J=1 1/2 J=2 J=3 J=O J=l @P&) J=2 J=3 J=4 J=O (0s-1 ) J=1 1/2 J=2 J=3

0472 (-16.92)

op:/ 2 (-8.60)

op:/2

(-8.00)

Od$2

Od$2

(-0.29) 0.0 36.7 0.0 27.2 0.0 221.7

(1.29)

-

-

0.1 26.2

-

-

-

-

20.9 115.2

-

6.9 4.1 5.8 189.1

-

-

-

0.4 51.0

-

0.0 37.1

-

-

-

-

1.5 51.5

43.4 87.8

-

-

0.9 99.3

-

-

-

11.4 115.7

-

0.0 15.0 0.0

-

-

0.8 90.9

3.6 2.5 6.1 194.8

23.3 70.6

-

148.1

0.0 24.0

-

-

-

19.5 58.9

-

-

-

-

-

9.8 44.6 41.4 164.4

2.1 4.2

-

-

-

-

0.0 6.4 21.0 144.2

12.8 38.8

-

-

-

-

0.0 75.9

0.2 39.0

-

-

-

-

39.0 78.6

19.8 58.4

-

1s:/2 (0.32)

-

-

-

The charcteristic result to be emphasized first is the selective excitation of the highest-spin state within each l h - l p multiplet. In fact one sees in - ' d A5/2 ] 5+ and Table 2 that the [di/2S$213+ 7 [di/2P$z]4- > [dg/2P1/213-1 A 7 ld5p 1

[d;/zd$/2]4+ states are very strongly excited and that the cross sections t o the lower-spin states are very smaller. The preferential excitation of the high-spin states are attributed t o the large momentum transfer (about 300 MeV/c) as similarly as in the case of the ( T + , K + ) reaction. Secondly, such a novel fact is revealed that the selectively excited state in each combination [j;'jS]~ has an unnatural parity with the maximum

227

+

+ +

+

spin valiue of J = JmaX= j , j $ = IN 1~ 1 = L,, 1. In Table 2, one may refer t o the [ d ; / 1 2 ~ t / 2 ] 3[d;f,p$,]4-, +, and [di/2dt/2]5+cases for reconfirmation. The I p-13 / 2.A~ >5=2] ,3+ ,4- states in the lowest block of Table 2 have the similar nature. This kind of selectivity is not seen in the other hypernuclear production processes such as (T+ , K+) and ( K - , T - ) reactions. This is attributed t o the spin-flip transition dominance in the elementary hyperon photoproduction reaction. It is also noted that, in the other combinations such as [ j ; ' j 2 ] 5 or [ j 7 1 j p ] 5 ,the highest spin is limitted to JLaX= IN 1~ and accordingly the natural parity The numerical results of Table 2 are schematically shown in Fig. 4 where relative strengths in each J-multiplet are easily understood.

+

(nb/sr) 350

I

d5/2-proton hole

I

*s

300

0

2

g

250 200

a

150

$

100

'

50 0

Figure 4. Divided contributions to the particle-hole state [ j ; ' j * ] ~ as calculated for the 28Si(y,K+)i8A1 reaction at E, = 1.3 GeV and = 3 deg.

Okb

Figure 5 shows the calculated angular distributions for the pronounced peaks. All these differential cross sections decrease quickly as the kaon lab scattering angle increases. It is interesting t o note that the relative strength for the [d;,?2df/2]J=4+and [ d-1 5 / 2 Ap 3 / 2 ] J = 4states changes at 0; N 7 deg. 3 . 2 . Use of the ( s d ) n Full Space W a v e Functions

Here we use sophisticated wave functions solved in the ( O d 5 / 2 0 d 3 / 2 1 ~ ~full / ~ space ) ~ ~ ~for ~ 27,28Si. It is remarked that the use of such detailed wave functions should predict several new but minor states in addition t o the pronounced peaks which are predicted in the simplified configuration. In order to predict a realistic strength function for the 28Si(y,K+)i8A1 reaction, one has t o take the empirical proton-hole widths into account, although they are not always available. Figure 6 shows the result where

228

120

0

5 10 15 20 Kaon Scattering Angle 8, (deg)

25

Figure 5. Calculated angular distributions of the states excited strongly in "Si(y, K+)i8Al reaction at E, = 1.3 GeV.

the following proton widths are employed tentatively: rN(Os;f2)

=

10 MeV,

= 3 MeV, and I'N(Od&) = 0 MeV. At the bound states the width I ' A ( j ) = 0.3 MeV is used which

FN(Op$2) = 6 MeV, I'N(Op;,?,)

same time, for the A is about half of the energy resolution expected at the Jefferson Lab, while r A ( j ) = 1.0 MeV for 0 < EA < 2 MeV and r A ( j ) = 3 MeV for EA > 2 MeV are assumed rather arbitrarily. Furthermore the energy splittings between members of the [ j ; ' j ; ] ~ multiplet are taken from the YNG(AN) h-p interaction l5 derived from the Nijmegen model-D, and it is notable that the splittings are mostly of the order of 0.1 MeV. Major 3 doublets (6 peaks) structure obtained with the simlified wave fuctions [ d i , 2 j A ] (see Table 2 ) well persist also in the new estimates. It is quite interesting t o note that, for the major peaks, the use of the full space wave functions result in the reduction of the cross sections by a factor of about 0.65 in comparison with the single-j estimate with (Od512);. It should be also remarked that two pronounced peaks obtained at EA -8.5 MeV correspond to the and [ d ; l ' , ~ : ~ , ] ~ -structure, respectively. As the hole-particle interactions for high-spin states are generally very small, the energy difference between these two peaks, if separated experimentally, provides us the spin-orbit splitting of the A pstate. The third major doublet obtained a t EA 0 MeV includes the unnatural parity highest-spin state [d;j2dt12]5+ which should get the biggest cross section. If the dt,2 state is bound, or if it is not bound but the energy N

N

229 500

CI

32 " \

2

300

v

%

c: a

200

\ N b

a

100

0 -20

-15

-10

-5

5

0

Excitation Energy E,,

10

15

(MeV)

Figure 6. Theoretical excitation function calculated with the full (sd)" wave functions for the %i(y, K+);*Al reaction at E, = 1.3 GeV and = 3deg.

OFb

position is not so high above the threshold, then this peak width might be sharp enough t o be identified in the experiment with the good energy resolution expected at JLAB. As the partner has the dominant structure of [d;l',d$,]4+ and the AN particle-hole interactions in high-spin states are very small, the energy difference between these two peaks is almost equal to the spin-orbit splitting of the d-state A. Thus the photo/electro-production reaction will provide a nice opportunity of looking at such splittings in heavy systems if the energy resolution is good enough. The present treatment is a direct extension of that for pshell hypernuclear photoproduction calculation where always the full pshell wave functions have been easily employed. For the readers' reference, Fig. 7 shows the the calculated spectrum for the 12C(y,K f ) i 2 B at E7 = 1.3 GeV. This is the update of the former prediction by using here the NSC97f AN interaction and the smaller smearing width. This prediction has been confirmed in very good agreement with the recent 12C(e,e'Kf)i2B measurement '. In the case of pshell hypernuclear production, the involving particles in the low-lying state are in the s- and porbits, so that the 'high-spin' selectivity mentioned above is realized as the transitions with A J = AL A S = 2-, 2+, and 3+. It is worthwhile t o remark that in Fig. 6 there appear side peaks at EA N -16 and -14 MeV in i8Al as confirmed in i2C (12 and 13 ). They might be based on the excited states (3/2+ and 7 / 2 + ) in 27Al coupled with an s-state A particle.

+

230 300

250 200 150 100

250

L

0

5

0

10

15

20

25

30

EXCITATION ENERGY Ex (MeV) Figure 7. Calculated spectrum for the "C(y, K+)A2B reaction at E-, = 1.3 GeV and = 3 deg.

Elkb

4. Photoproduction with the 40Ca and 52Cr targets The next sample target is 40Ca which is doubly LS-closed up to the Qd312 shell, so that the situation is different from the 2sSi case because 40Ca has the uppermost proton orbit of the jmultiplet ]~ is Jh,, = j , j t = 1~ I A = L,, with a natural 2]~ the highest spin is parity. On the other hand, in a [ ~ i ? ; , ~ jmultiplet JZ,, = j < j 2 = 1~ - 1 = L,, - 1, so that this restriction of the angular momentum transfer makes the latter cross sections much smaller. This situation of the j -3 MeV, on a polynomial fit to the averaged accidental background. The excitation function was obtained by

249

t

I

5

0 I

-10

,

,

,

,

Ex Energy (MeV)

10 I

-5

,

I

I

I

I

0

I

I

I

I

I

BAWV)

Figure 6. The A’B spectrum. The curve is a theoretical calculation, spread by 0.9 MeV and overlayed on the data.

Millener from an effective p-shell A-nucleus interaction previously matched to (n+,K+) data8. The energy resolution of the ground state peak is 0.9 MeV (FWHM) which is better than the best one (1.5 MeV) obtained in SKS hypernuclear experiments. Both of the SA and PA doublets, (1-;2-) and (2+;3+), are unresolved. Absolute scale of missing mass was calibrated using the p(e,e’K+)A/Co reaction on the CH, target. Therefore, the binding energy of the ground state of i2B was determined within the present data. The binding energy of the i2B ground state was obtained to be 11.4 f 0.5 MeV, which was consistent to the emulsion data, 11.37 f 0.06 MeVg. The differential cross section can be calculated as if it were photoproduction, by assuming the virtual photons are massless. The cross section of the i2B ground state was derived to be 147 f 17 (statistic) f 18 (systematic) nb/sr. The theoretical prediction of the cross section (152 nb/sr) by Motoba was consistent with the present result and therefore it was found that

250

a DWIA calculation for the (e,e’Kf) reaction adopting a phenomenological potential for AN interaction described reasonably well the hypernuclear production process as in the case of the (r+,K+) reaction. The global structure of the A2B spectrum was similar to that of the mirror hypernucleus, A2C1which was measured with the (r+,K+) reaction. A A’B spectrum with higher statistics and higher resolution is expected to give information on hypernuclear structure and AN interaction in the future. 5 . Summary

The A2B spectrum was observed in the first (e,e’K+) hypernuclear spectroscopy. The energy resolution of hypernuclear states is 0.9 MeV(FWHM), which is better than the existing measurements in reaction spectroscopy. The binding energy and the cross section of the ground state doublet are consistent with previous emulsion data and the theoretical prediction, respectively. It can be said that a calculation based on the DWIA for the (e,e’K+) reaction adopting a phenomenological potential for AN interaction described reasonably well the hypernuclear production process as in the case of the (r+,K+) reaction. The present experiment proved the effectiveness of A hypernuclear spectroscopy via the (e,e’K+) reaction for the first time, and paved the way to the precision spectroscopy of hypernuclei. References 1. 2. 3. 4. 5.

6. 7.

8. 9.

R. E. Chrien, Nucl. Phys. A , 478, 705c (1988). T. Hasegawa et al., Phys. Rev. Lett.,74,224,(1995). T. Miyoshi et al., Phys. Rev. Lett. 90, 13 (2003). T. Miyoshi et al., Nucl. Instrum. Methods A 496, 362 (2003). H. Yamazaki et al.,Phys. Rev. C 52, R1157 (1995). T. Motoba, M. Sotona and K. Itonaga, Prog. Theor. Phys. Suppl. 117, 123 (1994) T. Motoba, Proceedings of the 8th Conference on Mesons and Light Nuclei, edited by J. Adams (AIP, New York, 2001), Vol. 603, p. 125 D. J. Millener, Proceedings of the Jlab Workshop on Hypernucler Physics with Electromagnetic Probes, Hampton University, Hampton, VA, edited by L. Tang and 0. Hashimoto, 1999. M. JuriE et al., Nucl. Phys. B 52 (1972).

RECENT PROGRESS IN T-RAY SPECTROSCOPY OF HYPERNUCLEI

H. TAMURA,l’*S. AJIMURA,’ H. AKIKAWA,3’t D.E. ALBURGER,4 K. AOKI,5 A. BANU,‘ R.E. CHRIEN,4 G.B. FRANKLIN,7 J. FRANZ,8 Y. FUJI1,l Y. FUKA0,3 T. FUKUDA,’ 0. HASHIMOT0,l T. HAYAKAWA,’ E. HIYAMA,5 H. HOTCHI,git K. IMAI,3 W. IMOTO,’ Y. KAKIGUCHI,~ M. K A M E O K A , ~ T. KISHIMOTO,’ A. KRUTENKOVA,1° T. MARUTA,5 A. MATSUMURA,l M. MAY,4 S. MINAMI,2 Y. MIURA,l K. MIWA,3 T. MIYOSHI,l>SK. MIZUNUMA,l T. NAGAE,5 S.N. NAKAMURA,l K. NAKAZAWA,ll M. NIIYAMA,3 H. NOMURA,l H. NOUMI,5 Y. OKAYASU,l S. OTA,3 T. OHTAKI,’ H. OUTA,5>sP. PILE,4 B.P. QUINN,7 A. RUSEK? P.K. SAHA,’ Y. SAT0,5 T. SAITOH,‘ M. SEKIMOT0,5 R. SUTTER,4 H. TAKAHASHI,39qT.TAKAHASH1,l L. TANG,l’ K. TANIDA,13 S. TERASHIMA,3 M. TOGAWA,3 A. TOYODA,5 M. UKA1,l H. YAMAUCHI,~ L. YUAN,~’ S.H. Z H O U , ~ ~ Department of Physics, Tohoku University, Sendai 980-8578, Japan Department of Physics, Osaka University, Toyonaka 560-0043, Japan Department of Physics, Kyoto University, Kyoto 606-8502, Japan Brookhaven National Laboratory, N Y 11973, USA Institute of Particle and Nuclear Studies, KEK, Tsukuba 305-0801, Japan GSI, Darmstadt 0-64291, Germany Carnegie Mellon University, Pittsburgh, PA 15213, USA Department of Physics, University of Reiburg, Freiburg 79104, Germany Osaka Electro-Communication University, Neyagawa, 572-8530 Japan lo Institute for Theoretical and Experimental Physics, MOSCOW, 117218 Russia l1 Department of Physics, Gifu University, Gifu 501-1193, Japan Department of Physics, Hampton University, Harnpton, VA 23668, USA l3 RIKEN, Wako 351-0198, Japan l 4 China Institute of Atomic Energy, Beijing 102413, China (E930(’01), E509, E518 collaborations)

’

‘

’

’’

251

252 A recent progress of hypernuclear y-ray spectroscopy with Hyperball is described. In E930 at BNL, we observed two y transitions pf i60from the 6.5 MeV 1- state to the ground-state doublet (1- , 0-) and derived the strength of the AN tensor force for the first time. At KEK, westudied i l B with the ( r + , K + )reaction and observed six y transitions. We also attempted an experiment of in-beam y spectroscopy with stopped K - reaction and observed a y ray from LLi hyperfragments.

1. Introduction

We have been investigating precise structure of light A hypernuclei by yray spectroscopy technique employing a germanium (Ge) detector array (Hyperball). This new experimental approach revealed precise structure of i L i 1,2 and from which we experimentally determined the strengths of the spin-dependent forces between a A and a nucleon. After a brief review on the LLi and ;Be experiments, we report on three new experiments of hypernuclear y spectroscopy carried out with Hyperball after 2001, namely, BNL E930('01) for i60,KEK E518 for i l B and KEK E509 for hyperfragments.

1.1. A N spin-dependent interactions One of the most important motivations of hypernuclear y spectroscopy is to study hyperon-nucleon interactions. From precise level structure of A hypernuclei, we can extract information on AN interaction, including its spin dependence and the EN-AN coupling force. The potential of the two-body effective interaction between a A and a nucleon can be written as: Vef f AN

( r ) = V O ( ~+)Vu(r)~

+ VA(T)~ A N ~+AV N ( T~) A N ~ + vT(r) [ 3(aAf)(aNf) - a A a N ]

A V N

N

While the strength of the spin-averaged central force, VO,is well known, the other four spin-dependent terms, namely, the spin-spin term Vu,the Aspin-dependent spin-orbit term VA, the nucleon-spin-dependent spin-orbit term V N ,and the tensor term VT,were not well known before. *E-mail: tamuraOlambda.phys.tohoku.ac.jp

t Present address: Japan Atomic Energy Research Institute, Tokai 319-1195, Japan. $Present address: University of Houston, Houston, TX 77204-5506, USA. §Present address: RIKEN, Wako 351-0198, Japan. (Present address: KEK, Tsukuba 305-0801, Japan.

253

Level structure of hypernuclei allows us to obtain the strengths of the spin-dependent terms of the AN interaction. The radial integrals of the four terms (Vo, VA,V N ,VT)with the ~ N S wavefunction A in p-shell hypernuclei are denoted as A, SA,S N , and T, respectively. These effective-interaction parameters can be experimentally determined from low-lying level energies of p-shell hypern~clei>>~ In a hypernucleus, each level of the core nucleus is split into a doublet ( J - 3 , J+a) when a A in the 0s orbit is coupled to the core nucleus with spin J (# 0). Such spin doublets, often with small energy spacings, are called “hypernuclear fine structure”. Since the spacings are expected to be of the order of 100 keV or less, high-resolution 7ray spectroscopy with Ge detectors is almost the only method to investigate them.

1.2. Hyperball Hyperball is a large Ge detector array dedicated to hypernuclear y spectroscopy. As shown in Fig. 1, it consists of fourteen sets of coaxial N-type Ge detectors and holds a photo-peak efficiency of 2.5%at 1 MeV. The most important feature of Hyperball is the fast readout electronics for Ge detectors, which enabled the first successful observation of hypernuclear y rays with Ge detectors under severe background from intense pion beams. Each Ge detector is surrounded by BGO counters which axe used not only for Compton suppression but for rejection of high-energy photons from ?yo and high-energy charged particles. More descriptions on Hyperball are found e1sewhere.l y6

1.3. i L i and !Be

In the first experiment with Hyperball (KEK E419), we observed four y transitions in KLi and established its level scheme as shown in Fig. 2 (topleft). The spin-flip M1 transition in the ground state double (3/2+ + 1/2+) gives the doublet spacing energy of 692 keV, from which the strength of the spin-spin term was derived to be A= 0.5 MeV. In addition, the E2(5/2+ -+ 1/2+) energy (2050 keV) gives SN= -0.4 MeV. We also obtained the B(E2) value of this E2 transition with Doppler shift attenuation method and confirmed the hypernuclear shrinking effect for the first time.2 In the next experiment with Hyperball, we studied :Be employing the (K-,T-) reaction at 0.93 GeV/c at BNL AGS (E930).3 We successfully observed a fine structure, twin peaks at around 3.05 MeV. The two peaks are assigned as the E2($++;+, :++$+) transitions shown in Fig. 2 (top-

254

Figure 1. Schematic view of Hyperball. It consists of fourteen Ge detectors and BGO counters. Right figure shows the side view of Hyperball in the E930(’01) setup around the target.

right). Our result of about 43 keV spacing indicates a very small spin-orbit term, l S ~ l 0.01 MeV. It is to be noted that the :Be result is consistent with the recent observation of the spin-orbit splitting of the A single particle states ( h p ) A 7 @3/2)A) in i3Ce8 N

2. Spectroscopy of i e O and A N tensor force (E930(’01))

Among the four spin-dependent terms of AN interaction, only the tensor term (parameter T) has been unknown. Since the one-pion exchange is forbidden in AN interaction, the tensor term is expected to be small, but the kaon and two-pion exchanges give some contribution to the tensor term. The effect of the AN tensor force significantly appears in energy spacings of the doublets in plp-shell hypernuclei. The expected level structures of i60and i5N are shown in Fig. 2 (bottom). The spacing of the ground-state is written as:7 doublet (O-,l-) of

i60

E(l-)

- E(O-) = -0.38A + 1 . 3 8 s ~- 0.03,s”

+ 7.85T (MeV).

(1)

It has a large contribution of the tensor term. By the 160(K-,.n-) reaction, we can populate the i60[(p3l2);l (.slp)A]l- state at Ez=6 MeV and detect M1 transitions from this state to each member of the ground-state doublet. The Doppler broadening is not serious due to a small momentum transfer

255

€930

Already ObseNed (E419,ESSO)

Important transhione to be observed

Figure 2. Level schemes and y transitions of p-shell hypernuclei which have been investigated in E419 and E930 for determination of all the spin-dependent interaction parameters (A, SA,S N ,T). The shell model descriptions of the energy spacings in terms of the four parameters are shown together. The level schemes of i L i and !Be were already determined from the observed y rays, and that of i60will be discussed in the following section based on our new data.

in the ( K - J T - ) reaction, and the Doppler-shift correction enables us to resolve twin peaks if they are split by more than 20 keV. The 11 MeV-excited [(p1/2);1 (p1p),1]0+state of i60is expected to decay to excited states of i5N with sizable branching ratios and to emit y rays. The ground-state doublet spacing of i5N, which also has a large contribution of the AN tensor force, can be measured simultaneously. In order to investigate the tensor term T , we have taken i60and i5N data with l 6 0 target in 2001 at BNL AGS in the second beam cycle of

256

m

b

fit

20

6' 1100

6200

6300

6400

6500

6600

6700

6800

6900

1100

6200

6300

6400

6500

6600

6700

6800

6900

6200

6300

6400

6500

6600

6700

6800

6900

?

B 100 m

3

Ei

50 '6100

E,

0

Figure 3. Preliminary y-ray spectrum of AGO.(a) Highly unbound region is gated. (b) Bound state region is gated. (c) Same as (b) but Doppler shift correction is applied.

E930. Detailed description of this experiment is found in Ref. g. The experimental method and setup are almost identical to that in the previous E930 run for !Be. The setup around the target is shown in Fig. 1 (right). Using high-intensity and pure K - beams at 0.93 GeV/c provided by the D6 beam line, i60was produced by the 1 6 0 ( K - , ~ -reaction ) with a water target of 20 cm thick. Momenta of K - and scattered T - were measured with magnetic spectrometers to obtain the excitation spectrum of i60.y rays were detected with Hyperball in coincidence. Figure 3 shows preliminary y-ray spectra for i60.Figure 3 (a) shows the spectrum when events in the highly unbound region (-BA > 50 MeV) are selected. Several beam-induced y rays from l6O target are observed. The width of the l60peak at 6130 keV demonstrates the resolution in this energy region. Figure 3 (b) shows the spectrum when events in the bound state region of the i60mass spectrum are selected. A broad bump

257

is observed at around 6.55 MeV. When the event-by-event Doppler shift correction was applied using the recoiling hypernuclear momentum vector, the (K-,n-) reaction point, and the Ge detector position, this broad bump turns narrower peaks as shown in (c). Therefore, they are attributed to the Ml(1- + 1- and 1- -+ 0 - ) transitions in i60. The structure was fitted with the expected Doppler-corrected peak shape which was calculated from a simulation for Doppler shift correction. The width of the calculated peak is determined by accuracy of the measured reaction point and the Ge detector size. The spectrum was fitted well with two peaks as shown in Fig. 4. The energies (and the counts) of these peaks were obtained as 6534.1f1.5 keV (149f18 counts) and 6560.2f1.3 keV (226f30 counts). By comparing the ratio of the peak counts with the expected branching ratios, the 6534 keV and 6560 peaks were assigned as 1, + 1; and 1; + 0- transitions, respectively. Then we obtained the energy spacing of the ground state doublet:

E(1-) - E(O-) = 26.1 f 2.0 keV (preliminary). The ground state doublet (1-, 0-) is a typical hypernuclear fine structure similar to the one in :Be. But the very small spacing here is resulted from a cancellation of the spin-spin force (A term) and the tensor force (T term) contributions. It gives the tensor term strength of T = +30 keV (preliminary) from Eq. 1. This is the first experimental information on the AN tensor force. The tensor force in the meson exchange baryon-baryon interaction models (ND, NF, NSC89, NSC97f) corresponds to T = 18 - 54 keV through a G-matrix calculation." They are consistent with our observation.

6500

6600

'6400

6500

6600

6700

Figure 4. (a) Simulated peak shape for a fast y transition after Doppler shift correction. (b) The structure around 6.55 MeV in the i60y-ray spectrum (Fig. 3 (b)) was fitted with two peaks of the simulated peak shape.

258

3. Spectroscopy of i l B (E518)

In 2002, we carried out a y spectroscopy experiment of i1E3with the ( T + , K+) reaction at 1.05 GeV/c employing Hyperball and the SKS spectrometer at KEK-PS. One of the purposes of this experiment is to measure the transition probability B(M1) of the A spin-flip M 1 transition i1B(3/2+ + 1/2+) and to extract information on the magnetic moment of a A inside a nucleus by the method described in Ref. l l . The other purpose is to cross-check the AN spin-dependent interaction parameters which have been already determined from our KLi, :Be, and i60data. The experimental setup is almost identical to the one in E419.1>2We used a 10 cm-thick 98%-enriched loB metal target. When the bound state region is gated in the i l B mass spectrum, the y-ray spectrum exhibited six peaks as shown in Fig. 5. They are transitions from ilB. One of them is identified in the Doppler-shift-corrected spectrum. The assignment of all the observed y rays and the reconstruction of the level scheme seem difficult due to a low statistics which does not allow yy coincidence measurements. The most prominent peak at 1482 keV is assigned to the E2(1/2+ + 5/2+) transition. It is likely to be an E2 transition because its narrow width indicates the lifetime of the transition longer than 10 ps, which corresponds to a very small B(M1) value if it is an M1 transition. The 1/2+ + 5/2+ transition is the only E2 transition expected in ilB, and the observed largest y-ray yield is also consistent with this assignment. This E2 energy is predicted to be 1020 keV in the shell model calculation by Millener with the experimentally determined spin-dependent AN interaction parameter^.^ This difference suggests more experimental and theoretical studies are necessary to understand AN interaction and hypernuclear structure. 4. Hyperfragments (E509)

In the KEK-PS E509, we attempted an in-beam y-spectroscopy type experiment using stopped K - absorption reaction, which is known to produce various hyperfragments with large production probabilities. See Ref. l 2 for details. We stopped K - from the K5 beam line on several light targets (7Li, 9Be, 1°B, llB, and 12C) and measured y rays with Hyperball. From 1°B, llB, and 12C targets, we observed the iLi(5/2+ + 1/2+) transition at 2050 keV. The yield of this y ray for loB target is very large, 500 counts in 3.5 days, suggesting an effectiveness of this method. The production rate of iLi(5/2+) is derived to be 0.075 f 0.016% per stopped K - on loB target.

2 59

(a-1) Bound region (-20 < -BA1.5 GeV The scattered electron (e’) and K+ are separated by the dipole magnet (Splitter) located just behind the target. The scattered electron is measured by the Enge split-pole spectrometer which was used also for the E89-009 experiment and K+ by the newly developed high resolution kaon spectrometer (HKS). The two key experimental conditions which were improved from the previous experiment are:

’.

0

0

The HKS was newly designed to have 3 times greater solid angle than the previous kaon spectrometer and simultaneously to achieve a momentum resolution of 2 x A new experimental configuration, “Tilt method”, that will max-

275

imize hypernuclear production rates has been proposed. In this configuration, the Enge electron spectrometer is tilted vertically t o the splitter dispersive plane so as to choose electron scattering angles of 4-5degrees. This avoids the intense 0-degree bremsstrahlung electrons but still allows detection of the scattered electrons at a sufficiently forward angle. Therefore, the “Tilt method” inherits the advantageous aspects of the “0 degree tagging method” employed in the E89-009 experiments, but it is relatively free from the huge background rate of bremsstrahlung electrons at the focal plane of the electron spectrometer. This will allow us to use beam currents as high as a few tens p A . The new configuration makes it possible to measure hypernuclear spectra even with higher Z targets. Employing the proposed new experimental configuration and with the high-resolution kaon spectrometer (HKS), we expect t o achieve hypernuclear yields more than one order of magnitude higher and the signal-toaccidental ratio one order of magnitude better compared to the previous E89-009 experiment. The proposal of the new experiment with the HKS and the tilt method was accepted by JLab PAC19 3 . Table 1. Specification of the HKS Configuration

QQD and horizontal 70’ bend

Central momentum

1.2 GeV/c

Dispersion

4.7 cm/%

Momentum acceptance

I 12.5 % (1.05 - 1.35 GeV/c)

Momentum resolution (Aplp)

2 x

Solid angle

30 msr without Splitter 16 msr with a splitter

Kaon detection angle

Horizontal : 7 degrees (0 - 14’)

Flight Path Length Maximum Magnetic Field

10 m 1.6 T (normal)

2. Spectrometer Design 2.1. High resolution Kaon Spectrometer ( H K S )

The HKS consists of two quadrupole magnets (Q1and Q2) and one dipole magnet (D). Due to two degrees of freedom of the quadrupole doublet, the horizontal and vertical focusing can be adjusted simultaneously. The HKS

276

Schematic Top view of New Hypernuclear Spectronieter at Jab

- .-.

-

0

1

2m 2003.7 17

Figure 1. Experimental setup of the E01-011 experiment.

is designed to achieve both 2 x lop4 momentum resolution and 16 msr solid angle acceptance at the same time when it is used with the Splitter. The HKS is positioned at an angle of 7", covering from 0 to 14 degrees, with respect to 1.2 GeV/c zero degrees scattered particle to avoid scattered positively charged particles at 0 degrees, mostly positrons. The basic specification of the HKS spectrometer is given in table 1. The construction and field mapping of the HKS magnets ( Q l , Q2 and D) were finished in Japan (Kobe, Mitsubishi). They are ready for shipping to USA.

277

Figure 2. The assembled HKS magnets. From left t o right, Q1 (8.2 ton), Q2 (10.5 ton) and D (210 ton) magnets are shown.

2.2. Enge split-pole spectrometer and the tilt method

In the pilot (e,e’K) hypernuclear experiment, E89-009, the electrons associated with bremsstrahlung dominated the background in the scattered electron spectrometer (Enge). The idea to suppress the bremsstrahlung background is to use the difference of the angular distributions between bremsstrahlung electrons and scattered electrons associated with the virtual photons which contributes to kaon production. The tilt of the Enge spectrometer off the bending plane of the Splitter magnet allows us to avoid the extremely high rate electrons originating from bremsstrahlung and M4ller scattering. However, increasing the tilt angle, the number of the accepted virtual photons will decrease. Therefore, we need to take following rates into account to optimize the tilt angle: (1) virtual photons associated with hypernuclear production, (2) electrons associated with bremsstrahlung, and (3) M4ller scattering electrons.

Figure 3 shows the electron scattering angle distributions at the target. The electron distributions associated with Bremsstrahlung, virtual photons and M4ller scattering are plotted. Since the beam energy is fixed, the scattering angle and momentum for M4ller scattering electrons have one to one correspondence, and thus a ring shaped distribution results from the M4ller scattering within momentum acceptance of the Enge spectrometer.

278

Using a RAYTRACE Monte Carlo simulation, the events which passed through the tilted Enge spectrometer without hitting the pole or collimators were selected. Figure 3 shows that the acceptance of the tilted Enge spectrometer locates just out side of the M$ller ring, and thus hyper-forward Bremsstrahlung background and M$ller electrons are blocked while the electrons associated with virtual photons passed through the Enge spectrometer. Electron Scattering Angle Q Target (316 MeV+40%),Tilt 7.75 deg

-200

0

-100

x

100

200

( l o 3 PJP,)

Figure 3. The scattering angle of the electrons (p = 3161t40% MeV/c) at the target calculated by RAYTRACE optics code. The very forward Bremsstrahlung electrons and Mdller electron rings are observed. The acceptance of the tilted Enge spectrometer locates just outside of the Mdller ring.

This tilt configuration of the Enge spectrometer drastically suppress the electron background at the electron detector. In the E89-009 experiment, the electron rate was over 200 MHz and it limited the beam intensity and the target thickness. The virtual photon yield will be reduced by the tilt method, however, it can be easily got back by increasing the beam intensity and target thickness. Tilt method will reduce the electron rate from 200 MHz to a few MHz even with 5 times thicker target and -50 times stronger beam.

279

3. Detectors Development Table 2.

Detectors for HKS spectrometer

Size

Comments

HDCl

30H x 12OW x 2Tcm

HDC2

30H x 12OW x 2Tcm

xx’uu’(+30 deg)vv’(-30 deg) 5 mm drift distance xx’uu’(f30 deg)vv’(-30 deg) 5 mm drift distance

Nomenclature

Drift chamber

Time of flight wall 30H x 125w x 2Tcm 30H x 125w x 2Tcm 35H x 17OW x 2Tcm

7.5w cm x 17-segments, H1949 3.5w cm x 9-segments, H1949 9.5w cm x 18-segments, H1949

HACl

46H x 16gW x 31”cm

HAC2

46H x 16gW x 31Tcm

HAC3

46H x 16gW x 31Tcm

HWCl

35H x 187.2w x 8Tcm

HWC2

35H x 187.2w x 8Tcm

n = 1.055 hydrophobic aerogel 14 x 5” PMT (7 seg.) n = 1.055 hydrophobic aerogel 14 x 5” PMT n = 1.055 hydrophobic aerogel 14 x 5” PMT 15.6w cm x 12-segments, H7195 Water with wavelength shifter 15.6w cm x 12-segments, H7195 Water with wavelength shifter

HTFlX HTFlY HTF2X

cerenkov counter

3.1. Summary of the H K S and Enge detector packages

The HKS detector package is designed to identify K+s from p, d,e+ backgrounds and to measure their momentum with a resolution of 2 x In order to realize the requirements, the HKS detector package consists of one pair of drift chambers, three planes of time-of-flight counters, two planes of water Cerenkov counters, and three planes of aerogel Cerenkov counters. The geometry of these detectors and some of their general parameters are summarized in table 2. Table 3. Nomenclature Drift chamber EDC Hodoswpe EHODl EHOD2 EHOD3

I

Detectors for the Enge spectrometer

I

Size

I

Comments

I 12H x

loow

x 30Tcm

xx’uu’xx’vv’xx’ 5mm drift (uu’,vv’ *30 deg)

x 12H x 12H x

loow loow

x lTcm x lTcm x 2Tcm

4w cm x 25-segments, H6612 4w cm x 25-segments, H6612 12w cm x 1-segment. H1949

12”

loow

The Enge detector package is designed to achieve (dp/p) = 4 x

280

(FWHM) and it consists of a drift chamber for tracking and two planes of hodoscope arrays for TOF measurement. Table 3 summarizes the size of each detectors. 3.2. Counter beam test

Prototype and the final version of the counter systems (HKS TOF, aerogel Cerenkov, water Cerenkov, Enge Hodoscope) were tested with 1.2 GeV/c unseparated p, K+, T + , e+ beam at KEK-PS (PS-T494, 500, 530). The Enge honeycomb drift chamber was also beam-tested with electrons of a few 100 MeV at the internal tagged photon facility of Laboratory of Nuclear Science (LNS) of Tohoku University. Most of the detectors have been constructed and shipped to Jlab in March 2003. 4. Expected performance 4.1. Eneqy resolution

In the proposed experiment, the hypernuclear mass resolution is governed by the following items. The contributions to the energy resolution are summarized in table 4. The proposed spectrometer system is expected t o achieve an energy resolution of 300-400 keV (FWHM), depending on the choice of targets. Table 4. The energy resolution of the HKS system

Item Target HKS momentum Beam momentum Enge momentum K+ angle Target (100 mg/cm2) Overall

Contribution to the mass resolution (keV, FWHM) C Si V Y 230 5 180 120 32 18 56 134 5 171 5 148 5 138 5 180 5 350 5 345 5 390 5 360

(1) HKS momentum resolution With a Monte Carlo simulation, the momentum resolution of the HKS was estimated to be 110 keV/c (rms) for a spatial resolution of 200pm of the wire chambers. This corresponds to a missing mass resolution of 230 keV. (2) B e a m momentum resolution Beam momentum resolution is required to be better than 1xlOP4. This corresponds to 180 keV/c (FWHM) for 1.8 GeV/c beam. It is

28 1

also necessary to monitor long term fluctuation of the beam central momentum. If these fluctuation should turn out to be significant, they will be corrected in the off-line analysis. Enge momentum resolution Assuming a spatial resolution of 6Opm (rms) and an angular resolution of 2 mr (rms), the momentum resolution of the Enge spectrometer is estimated to be 120 keV/c (FWHM). Kinematical broadening due to uncertainty of the K+ scattering angle The uncertainty of the K+ emission angle is dominated by the multiple scattering through the materials between the target and the drift chambers (uncertainty due to the spatial resolution of the chambers are less than 0.2 mrad). Contribution of the following materials are taken into account: the target (100 mg/cm2), vacuum windows (Kevlar 216pm, Mylar 127pm), helium bag (100 cm) and chambers STP). I (mylar 0.0045”, argon 5.08 cm @ The total uncertainty of the K+ angle was estimated to be 2.9 mrad (rms) for the carbon target. This angular uncertainty corresponds to 134 keV (FWHM) ambiguity to the i2B mass. Similarly, this effect t o i8Al (Si target) will be 56 keV (FWHM). Momentum loss in the target Assuming a Vavilov distribution, the average momentum loss and spread of 1.2 GeV/c K+ in 100 mg/cm2 carbon were calculated.The corresponding contribution to the energy resolution is 180 keV (FWHM). 4.2. Yield estimation Table 5. The hypernuclear yield comparison between E01-011 and E89-009

Virtual y flux/lOOOO eTarget Thickness (mg/cm2) e’ acceptance, e’-Kf momentum matching K+ survival rate Solid angle of K arm (msr) Beam current (FA) Estimated yield (!2Bor/hour)

I I

E01-011

E89-009

Gain Factor

0.2 100 200 0.35

0.05 4.5

16

4 22 120 0.4 5

30 45

0.66 0.9

1.7 0.9 3.2 45 50

The expected yield of the hypernuclear states are evaluated based on the E89-009 result for the i 2 B ground state in the 12C(e,e7K+)i2B reaction,

282

comparing the beam intensity, acceptance ratio of the virtual photons, kaon detection efficiency and so on. The E01-011 experiment is expected to increase hypernuclear yields by a factor of 50, and to improve the signal to accidental ratio by a factor of 10 (Table 5 ) . 5 . Summary

The first successful (e,e’K+) hypernuclear experiment (JLab E89-009) proves the (e,e’K+) reaction is a promising way for the high resolution hypernuclear spectroscopy, but the kaon spectrometer and extremely high background rate in the electron arm limited the resolution and yield. In order to overcome the problems, we proposed a new experiment with the newly developed High resolution Kaon Spectrometer (HKS) and new configuration of the electron spectrometer (tilt method). The new experiment aims t o improve the energy resolution by a factor of 2, the hypernuclear yield by a factor of 50 and the signal to noise ration by a factor of 10. The development of the detector package were almost finished and the final tuning at JLab is in progress. We will be ready for the first experiment with the HKS in 2004. Lots of hot hypernuclear data will spring out from the Jlab Hall-C in the near future. References 1. T. Miyoshi, et al., Phys. Rev. Lett., 90, 232502 (2003); T. Miyoshi, ibid. 2. SAPHIR collaboration, Phys. Lett., B 445, 20 (1998). 3. 0. Hashimoto, L. Tang, J. Reinhold, S.N. Nakamura, et al., E01-011 Proposal submitted to JLab PAC19 (2001); S.N. Nakamura et al., Physics with GeV Electrons and Gamma-rays (Eds. T.Tamae et aZ.), Universal Academy Press, (2001) 113; Y. Fujii et al., ibid.

FINUDA: READY TO START PHYSICS

S . MARCELLO Dipartimento di Fasica Spen’mentale Universitci da Torino and INFN, Sezione di Torino via P. Giuria 1 , 10125 Torino,ITALY E-mail:[email protected]

The FINUDA experiment is ready to start physics at the DABNE q5 factory in Frascati. There the K - of low energy can be used to produce A-hypernuclei through the Ka& + A 2 +: 2 + 7r- reaction. The FINUDA apparatus has been designed to reach high momentum resolution (0.3%) and acceptance (27r sr) for the 7r- coming from hypernucleus formation, moreover it has excellent detection capabilty for the products coming from hypernucleus decay. Therefore it is possible to perform high statistics measurements, either on high resolution spectroscopy, either on hypernucleus decay modes. Expected performances and physics programme are here summarid.

1. Introduction 1.1. The Experiment

The FINUDA192 experiment on hypernuclear physics is going to start data taking at the DA@NE3q5 factory in Frascati. The machine has been in operation up to December 2002 with luminosity between 3 and 7x 1031cm-2s-1 providing about 10 millions of $/day. After some upgrades it has started to run again and e+ - e- collisions with a higher luminosity are expected to come very soon. The $’s, produced in the collisions of e+ and e-, circulating in opposite directions at an energy of 510 MeV each, decays at rest into K+K- (49%), K z K z (34%), p (13%), r+m-mO (2.5%) and qy (1.3%). Thus DA@NE can be considered as a source of monochromatic, collinear, quantum-defined and tagged pairs of neutral and charged kaons. The clever idea4 to perform a fixed target experiment, such as FINUDA, at a collider was the possibility to stop the K - from the $-decay in a very thin target (- 0.3 gcm-2), due to its low energy (- 16 MeV), in order to 283

284

produce A-hypernuclei through the reaction:

Then K-’s can be stopped with minimal straggling very close to the target surface, allowing to achieve a very good resolution on the measurement of the outgoing T - momentum, which is directly related to the energy levels of the produced hypernucleus. On the contrary, in the past experiments at hadron machines, in spite of the good resolution of the spectrometers, the major limitation using KS& was due to the thickness of the nuclear target. At DA@NE a further advantage is given by the presence of the tagging particle: the K+, the detection of which is very useful to define the K--beam. The K - ’ S momenta are measured by a high resolution magnetic spectrometer, shown in Fig. 1, with a large acceptance, typical of collider experiments, optimized for momenta ranging between 250+280 MeV/c, with an energy resolution of 750 keV. Since the best resolution obtained up to now in hypernuclear spectroscopy is 1.45 keV with SKS5 spectrometer at KEK, a resolution of 750 keV is in competition only with the experiment planned at Jefferson L a b ~ r a t o r y ~ ? ~ .

interactionkarget region .end cap straw tube5

\

LMDC beam pipe external TOF :oil superconducting ( ~

Y

compensating magnets

-

magnet yoke

I m

z @

Figure 1. Pictorial view of FINUDA apparatus.

Using stopped K - to produce hypernuclei the large momentum transferred to the A-hyperon is of the same order of magnitude (- 250 MeV/c)

285

of the Fermi momentum of nucleons inside the nuclei, therefore several hypernuclear states may be produced, from the ground state up to the excited ones. Indeed the A particle embedded in a nucleus is not affected by Pauli blocking, then it can populate all the single states. Moreover the A - N interaction is appreciably weaker than the N - N one. Therefore in the hypernuclear ground state the A resides in the Isshell and can explore very deeply the nuclear structure. Furthermore high resolution experiments might reveal effects due to partial deconfinement of the A in the nuclear matter. A-hypernucleus spectroscopy with high resolution, extended over the full nuclear mass range, constitutes a top priority of the physics programme. In particular a step forward is expected in the medium-high mass region, because the existent data are still scarce and FINUDA can use any kind of nuclear target, which can be machined in thin foils. For all the nuclei but the lightest ones, when the A is embedded in the nuclear medium, the mesonic decay modes are strongly suppressed due to a reduction of the phase space combined with the Pauli blocking of the recoil nucleon ( p ~ ~ 100~MeV/c). [ ~ So ~the non-mesonic ~ modes: N

i, +~ ( A - 2 ) ( ~ - 1+ ) n + p 22 + ( A - 2 ) ~+ n + n

(2)

(3) are dominant8, since phase space is wider and the nucleons in the final state are not affected by Pauli blocking ( p ~ ~ 417~MeV/c). l ~ ~ ~ A comprehensive study of the partial decay widths r, and r,, of the p induced and n-induced processes (2) and (3) respectively, and mean lifetime of the hypernucleus, N

= ti/ riot = ~ r , -+ rn0+ rp + r, + rNN], (4) leads to a close investigation of the validity of the well-known AI = 1/2 rule, which gives information on the structure of the weak Hamiltonian. In &. (4) r N N concerns the two-nucleon induced process, which cannot be neglectedQJO,since its contribution is 15% of the non-mesonic width T~~~

rnm

.

-

Up to now a theoretical explanation of the large experimental values of Fn/rpratio is still unclear. I',/r, ratio is directly connected to the isospin structure of the basic weak interaction, whether it were < 0.3, AI = 1/2 rule would hold, on the contrary whether it were > 0.3, A1 = 3/2 terms (of unknown nature) would be needed in the weak Hamiltonian.

286

New analysis of measurements at KEK on i2C non-mesonic decays'' and on :He non-mesonic decays12J3 and new theoretical calculation^'^ sound to shed some light in the understanding of a long standing puzzle. But it is still missing a theoretical complete picture, which can explain the differences among the partial non-mesonic decay widths and the Fn/rPratio. So it turns out that FINUDA measurements can still give an important contribution. So extensive investigation of A-hypernuclei are needed because they can give improvements not only in the exploration of nuclear structure in presence of a strange quark, but also in solving open problems in the A - N weak interaction, especially on the parity-conserving part8. Finally, I just mention that the production of neutron-rich hypern~clei'~ can be also investigated in FINUDA through the reaction

K-

+

AZ

+

R(z-2)

+ 7r+.

(5)

1.2. The Apparatus

A detailed description of the FINUDA detectors can be found elsewhere2, only general features are given here. The apparatus is a magnetic spectrometer with cylindrical geometry covering a large solid angle of 2 ?T sr. Since the most important goals are: to measure the energy levels of the hypernuclear states with high resolution and to detect the n's and p's, produced in the non-mesonic decays of Eqs. (3) and (2), which have kinetic energies centred at 80 MeV, the apparatus has been designed to fulfill the following main tasks:

-

(1) to measure the momentum of 7 ~ - coming from the hypernucleus formation, with an accuracy Ap/p 0.3 %. (2) to detect neutrons with an efficiency of 10% (3) to select hypernuclear events from the huge machine background (Touschek effect) and other backgrounds by means of an efficient trigger. N

In the spectrometer three main regions can be distinguished: (i) The interaction/target region is shown in Fig. 2. Here the highly ionizing K+K - pairs are detected by a scintillator barrel (Tofino) of 12 thin strips around the beam pipe with a time resolution 250 ps. The barrel is surrounded by an octagonal array of D Si-pstrips (ISIM) with a spatial resolution D 30pm and energy N

N

287

resolution of 20% FWHM. A thin nuclear target module is positioned on the external side of each element of the octagon. The task of this pstrip detector is the reconstruction of the K - interaction 250 pm. point in the nuclear target with an accuracy of (ii) The external tracking device is composed by four different position detectors immersed in a He atmosphere to reduce the effects of the multiple Coulomb scattering. Therefore four points are measured to reconstruct the track of particles crossing this region (e.g. the T - of the hypernucleus formation). The first element of the device is an array of 10 Si-pstrip modules (OSIM) placed close to the target array. Then two layers of planar low mass drift chambers, with a spatial resolution of op,+ 150 pm. Finally, a straw tube detector, composed by three super-layer, giving a spatial resolution 150 pm and oZ 500 pm. In this volume the of up,g tracking of the p from the non-mesonic decay can be done with an acceptance of 30%and an energy resolution of 1.3 MeV at 80 MeV. (iii) The external Time of Flight barrel is composed by 72 scintillator slabs, 10 cm thick, with time resolution of -500 ps FWHM. The neutrons from non-mesonic decays have an acceptance of 70% and can be detected with an efficiency of 10% and energy resolution of 8 MeV at 80 MeV.

-

N

-

N

OSIM

target

Figure 2.

Schematical view of the interaction/target region.

So FINUDA is a very complex apparatus, able to detect and reconstruct the T - coming from the hypernucleus formation process in coincidence with the particles emitted in the following decay as shown in Figs. 3 and 4. Moreover the good performances of the time of flight detectors allow to

288

measure directly the lifetime of A in various hypernuclei.

Figure 3. MC simulation for pinduced decay of ''17.

Figure 4. MC simulation for n-induced decay of "C.

Concerning the trigger, a description of performances is given elsewhere16, here it is worth to remind that the rejection power for Touschek background (intra-beam scattering in the same bunch) is of the order of 10-6. 2. Physics Programme of next Data Taking

One of the main features of FINUDA experiment is that it allows to study simultaneously hypernuclear spectroscopy and hypernuclear decays. In the data taking, which is approaching, five different types of targets will be used at the same time. Indeed eight slots are available for the targets in the interaction region, as shown in Fig. 2, considering that K--bearn is coming isotropically in 4 direction. The set of the eight installed targets is the following: two modules of 6Li, one of 7Li, three of 12C,one of 27Al, one of 51V. Since the low-lying excited states of hypernuclei are stable for nucleon emission, they can be explored with high resolution (- 3 keV) by means of y-spectro~copyl~. On the contrary such a technique cannot be used for the high region of excitation energy, because hypernuclei can have nucleon deexcitation. This region can be explored by FINUDA with a resolution of 750 keV.

289

We expect to collect a bulk of data corresponding to an integrated luminosity Lint N 250 pb-l, therefore high statistics measurements can be done with error down to 3% for the spectroscopy and 10% or less for the non-mesonic decays, which is still very good compared to the present mesurements. The most deeply studied pshell hypernucleus is i2C, so the existing measurements can be taken as a reference to check the response of our apparatus. Furthermore, statistical accuracy can be improved for the nonmesonic decays of "C. The hypernuclear excitation spectra of such a hypernucleus will be studied detecting states produced down to capture rates of 10-5Hyp/K;op. The use of ' L i target allows the study of some light hypernuclear systems, described in details elsewhere18,such as those produced in the reactions:

+ ' L i + 7 ~ - + :He + p

KK-

+

K-

+ 'Li

' L i -+ x-+ K-

(6)

+ :He + p + n

(7)

+iH +p +p

(8)

In the Eq. (6),the :He in the ground state is produced with a quite high capture rate ( 5 i 7 ~ l O - ~ H y p / Kand ~ ~it~decays ~) through the non-mesonic mode as follows:

:He -+ 3 H

+p +n

and

:He -+ 3 H e

+ n + n.

(9)

Therefore measurements of the decay widths rp and r,, separately, and mean lifetime Thyp for the non-mesonic decays of Eq. (9) can be done with a very good statistical error as shown in Table 1, where the expected events for H e using two modules of Li target are summarised. :He in Eq. (7) is copiously produced through the Coulomb assisted mechanism. The two rare decays of ;He:

'

:He

-b

d

+d

and

:He -+ d

+

3H

(10)

can be easily studied, because the event for each decay can be fully reconstructed in the apparatus. Concerning the non-mesonic decay a very peculiar measurement can be done using the 'Li target. In fact, considering the reaction:

K-

+ 'Li

-+ no

+ :He

(11)

290

Table 1. Expected events for ;He using two 6Li targets with an integrated luminosity Lint ~250pb-'. BR(%)"

Expected events 9.53~10~

%p

Stat. error(%)

N 1

r,- /rA

0.44

13.75~10~

- 1

rp/I'A (only p detected)

0.21

9.53~10~

- 1

0.21

8.20~10~

N 4

rp/rA (both p

0nd n detected) detected)

rn/rA (60th n's

0.20

205

rnPP

- 7 N

11

and the following decay of :He:

:He

+

n

+ n + 4He

(12)

such an exclusive process can be recognised by kinematic constraints, taking advantage of the very large particle emission threshold of 4 H e (19.8 MeV), in spite of the limited energy resolution (12 MeV) on the detection of both the two n's.

3. Expected Rates for i2C High resolution spectroscopy can be done selecting the r ' s of hypernucleus formation which don't cross back the interaction region (in order to not degrade the momentum), for such events the trigger and reconstruction efficiency is 13%. An integreted luminosity Lint 2 pb-' per day, means the average rate of K+K- is 54 Hz. Taking into account a capture rate of 10-3HypJ KZop the expected rate for high resolution spectroscopy is 25 events/hour, for hypernuclei produced in the eigths targets. Therefore a first data set corresponding to Lint 50 pb-' can already provide a good survey of high resolution spectroscopy with a statistical error of 3% for i2C,as shown in Table 2, and 5% for other hypernuclei,. Considering non-mesonic decays we can loose the constraint on the reconstruction of T - , getting a reconstruction efficiency of 27%, which lead to a rate of 52 events/hour for the hypernuclei which can be used for such an analysis. However it still needs to take into account the branching ratio for the non-mesonic decay rn,/rtot,which was evaluated to be 0.71 for p-induced and n-induced decays20. Moreover the fraction of reconstructed non-mesonic events over the triggered ones (with a K- in coincidence) is: 9 . 6 ~ 1 0 -and ~ 2.4x1W3 for pn and nn respectively21. Therefore the rate of expected events, for the targets all together, gets to be: 0.3 events/hour

-

N

-

-

29 1

-

and 0.09 events/hour for the p-induced and the n-induced decays respec250 pb-' are needed to perform tively. This means that at least Lint measurements with competitive statistics. Such a statistics can be collected in about 2 months of data taking. In Table 2 are summarised the expected rates and statistical errors using three 12Ctargets. Table 2. Expected events for high resolution hypernuclear spectroscopy and non-mesonic decay using three 12C targets with different data taking time (Lint).Capture rates of 10-3Hyp/K,21. However it is extremely important to better define these systems in order to extract the strength of the A l l interaction. The most recent observation of :*He indicates the interaction is much weaker20 (by a factor of 4) than the previously accepted valuez1. This needs to be confirmed as this parameter is crucial to our understanding of multi-strange, nuclear systems. Hypernuclear systems also provide information beyond spectroscopy. Their mesonic weak decay is sensitive to the high momentum, and configuration mixing components of the nuclear wave function. The non-mesonic decay process can be used to tag not only the parity violating, PV, but also the parity conserving, PC, components of the AN interaction within the nuclear medium. There has been a persistent puzzle as to, experimentally, why the neutron to proton stimulated non-mesonic decay (AN + NN) is so large, x 1, as the dominant 13S1 -+13 D1 tensor transition is only open to the proton channel23. New, coincidence data for the decay process were presented at this symposium, and these suggest that the neutron stimulated enhancement is due to final state neutron emission from the residual

321

60 50

.. ..... ............... ........... . _ . _ . _ / .......-.-. . "........

40

30 20

10 n 3400

6500

6600

6700

Figure 4. The experimental gamma spectrum from the 1- to the ground state doublet, (0-,11) of i60,showing the level splitting. This splitting determines the tensor component of the AN effective interaction.

nucleus24. However there still remains a problem that the measured decay asymmetry seems too large and of the wrong sign. Although not presented, more recent data indicates that the earlier asymmetry measurements were incorrect. In summary, the investigation of strangeness in nuclear systems is not merely an extension of conventional nuclear physics. Certainly one cannot, nor would one want to, reproduce the wealth of information that has been accumulated on conventional nuclei. The hypernucleus, however, offers a selective probe of the hadronic many-body problem, providing insight in areas that cannot be easily addressed by other techniques. Such questions as isobar mixing, charge symmetry breaking, and quark confinement are more important, and thus more evident, in strange hadronic matter. What is now needed is a series of precision studies with high resolution where level positions and weak decay dynamics can be compared to theory.

4. Facilities

The premikre facility in this field is located at the Jefferson Laboratory, CEBAF. The CLAS detector, located in Hall B at CEBAF reported on

322

electroproduction experiments as well as those with real, tagged photons. Polarization studies are now beginning, and hopefully will be more emphasized in the future. The initial hypernuclear production experiment discussed above was undertaken in Hall C, and will be followed by a more advanced setup, increasing production rate and resolution. Another hypernuclear experiment in Hall A is scheduled to begin in late 2003. The SAPHIR detector at Else is still analyzing data, some of which was presented at this symposium. However, a new set-up combining the CRYSTAL BARREL from CERN with the TAPS detector has begun work using a tagged photon beam at this facility. The experimental program will emphasize neutral, exotic meson production, and the predicted statistical error and data quality should surpass that of SAPHIR. Linear polarization is available. The first observation of the O+ pentaquark occurred at the LEPS facility at Spring 8. Similar studies continue. The GRAAL facility at the European Synchrotron Facility also provides photons from Compton backscattering, and this work is just beginning. Finally, the FINUDA facility at Daphne will begin studies of hypernuclear spectroscopy with unprecedented resolution and rates. FINUDA may also be able to study coincident nucleon emission from the hypernuclear non-mesonic weak decay from a few hypernuclear species. 5. Conclusions

The full power of electromagnetic facilities is just beginning to be appreciated. While energies are still a little below what one would need to address many physics topics, the present machines are tapping a rich field. As with any new tool, one needs to learn how best to use it, and how it can be applied to the most pertinent problems. Given the amount and quality of the data that can be produced, all activities require close cooperation between experimentalists and theorists to optimize the results.

Acknowledgments The administration of any conference of this size is a major undertaking. The organizers were diligent in their task to secure interesting and well prepared presentations and poster sessions, and the surroundings were hospitable and conducive to fruitful discussions and cultural explorations. It is my pleasure, to warmly thank all those who were responsible for making this symposium a success, and I extend especial thanks to Professor

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Hashimoto and his staff. References 1. K. Glander, see presentation this symposium; arXiv:nucl-ex/0308025. 2. R. Schumacher, see presentation this symposium; arXiv:nucl-ex/0108013. 3. C. Bennhold, see presentation this symposium; T. Mark, see presentation this symposium; T. Mart and C. Bennhold, Phys. Rev. C61, 012201 (2000) 4. B. Saghai, see presentation this symposium; B. Saghai, et al, Phys. Lett., B517, lOl(2001) 5. See for reference Proceedings of the Workshop on the Physics of Excited Nucleons, S.A. Dytman and E.S. Swanson, eds, World Scientific, 2002 6. M. D. Mestayer, see presentation this symposium. 7. T. Nakano, see presentation this symposium; T. Nakano, et al, Phys. Rev. Lett. 91, 012002(2003) 8. Robert JafTe and Frank Wilczek, arXiv:hep-th/0307341. 9. S. Stepanyan, et al, arXivhep-ex/0307018. 10. D. Diakonov, et al 2. Phys., A359, 305(1997); V. Kopeliovich, see presentation this symposium. 11. J. Pniewski and M. Danysz, Phil. Mag. , 44, 348(1952). 12. N. K. Glendenning, Phys. Rev., C64, 025801(2001). 13. J. Schafher-Bielich and A. Gal, Phys. Rev. C62, 034311(2000). 14. D. J . Millener, A. Gal, and C. B. Dover, Phys. Rev., C38,2700(1988). 15. E. V. Hungerford, Prog. Theor. Phys. Sup., 117, 135(1994). 16. T. Miyoshi, see presentation this symposium; T. Miyoshi, et al, Phys. Rev. Lett., 90, 232502(2003). 17. T. Motoba, M. Sotona, and K. Itonga, Prog. Theor. Phys. Sup., 117, 123(1994); D. J. Millener, Proceedings of the Workshop of Hypernuclear Physics with Electromagnetic Probes, Hampton, Va., (1999). 18. H. Tamura, see presentation this symposium; Proceedings of the 16th Conference on Particles in Nuclei, Osaka, Japan, (2002) 19. K. Tanida, et al, Phys. Rev. Lett., 86, 1982(2001). 20. H. Takahashi, et al, Phys. Rev. Lett. 86, 212502(2001) 21. D. J. Prowse, Phys. Rev. Lett., 17, 782(1996) 22. M. Danysz, et al, Nucl. Phys., 49,121(1963); S . Aoki, et al, Prog. Theor. Phys., 85, 1287(1991); J. K. Ahn, et al, Phys. Rev. Lett., 87, 132504(2001). 23. J. Cohen, Progress an Part. and Nucl. Phys., 25, 139(1990) 24. B. H. Bang, see presentation this conference.

THEORETICAL PERSPECTIVE

B. F. GIBSON Theoretical Division, Los Alamos National Laboratory, Los Alamos, N M , U S A E-mail: [email protected] This is a personal perspective regarding the bright outlook for the future of photoand electroproduction of strangeness based upon the inspirational presentations made at SENDAI03. These remarks are focused upon the theoretical apsects of the symposium.

1. Background

Heinz Barshall, the first editor of Physical Review C has been quoted as saying that the world of physicists is partitioned into two camps: (1) measurers (2) guessers

We heard first where the measurers are headed. We must now ask what the guessers can do to further the investigation of photo- and electroproduction of strangeness. The emphasis a t this symposium has been on the physics of strangeness. As C. Bennhold suggested in his introductory talk, strangeness has a unique role to play. At one end of the quark specture, we have the u,d current quarks, which are very light (masses of the order of 5 MeV). Chrial symmetry and effective field theories appear to be our best means of connecting S U ( 2 ) light quark QCD to the everyday world of hadrons and nuclei in which we live. At the other extreme, we have the heavy c,b,t quarks (masses greater than 1500 MeV). Heavy quark theories appear to provide an adequate description of such phenomena. This leaves the s quark as an orphan. It is neither light nor heavy. We know not whether an SU(3) chiral perturbation theory treatment is valid. Perhaps lattice QCD, which has difficulty in the light quark sector because of the light masses, will be 324

325

more applicable to strange quarks. One anticipates that there will be a significant role for strangeness to play in helping us to understand the nature of matter and the forces with which the constituents of matter interact. We must identify that role. We have seen a physics focus at this symposium which can be separated into two areas: 0

0

The “resonance” structure of the elementary (baryon-meson observables) amplitudes., The precision structure information that pertains to nuclear systems.

In what follows I will address the physics covered in this symposium as belonging t o one of those two general headings. 2. N* Resonances

The goal of experiments in this area is to test models of and approximations to QCD. QCD is thought to be the theory of nuclear forces. QCD in itself cannot be tested; it cannot be wrong. Measurements are a manifestation of QCD. Unfortunately, QCD is not calculable. Therefore, we build models of QCD, make approximations to QCD. We can use our measurements to test those models of and the approximations we make to the theory of QCD. After examining the nucleon resonance data, an immediate question comes t o mind. Are our models, which predict many more states than have been observed, too naive? Is a bound-state, valence quark picture too simple when multi-meson decay channels open as the energy of the system increases. One is drawn closer t o agreement with the observation, “If a number of additional resonances are not found soon, then the missing resonances are unlikely to exist.” Such an outcome would appear to confirm that current models are too naive, too simple. In this vein, one should heed the warning, “Beware single-channel analysis”. Most (y, q ) , (y, K), (y, mr)models which have been employed are of the single-channel variety. To truly confirm that a missing N’ resonance has been found, one should observe its effect in several channels. That strongly implies that one must use a multi-channel framework in analyzing or modeling data. This leads one t o the question of what is required of an adequate model. It is importnat t o realize that a proper analysis of basic amplitudes is not

326

easy. Included should be: (1) Lorentz invariance - considered essential for higher energy. Nonetheless, it should be recognized that 2H(e,e)d and 2H(e,e'p)n data show only limited evidence of large relativistic effects. (2) Gauge invariance - large effects were incorrectly predicted in the past due to lack of gauge invariance in a given model calculation. (3) Analyticity - essential in locating resonance poles in the complex energy plane. (4) Unitarity - crucial where multi-particle states play a significant role. The 3H(y,d)n and 3H(y,p)nn channels are so strongly coupled that the isospin 1/2 d n 2-body channel absorbs 90% of the isospin 1/2 3-body photodisintegration strength and modifies the shape of the spectrum.

+

+

The differential cross sections for y p + K+ A as a function of W(Gev) which were shown by R. Schumacher in his JLab talk illustrate this. The high W peak is shifted in position and shape as a function of angle, which can only be said to be a possible sign of interference phenomena, that multiple resonances in the data are possible. B. Saghai discussed a new constitutent quark model analysis (improved in that it requires only 12 parameters versus the 19 required in a meson exchange picture) of the electromagnetic production data. The reproduction of the CLAS data for y p + K+A was indeed impressive, when S-, P-, D-, and F-waves were included. Saghai emphasized that one must limit the number of parameters as one goes to higher energy, where additional resonances exist, in order to extract physics from the data. He noted the need to incorporate multi-step processes and a couple-channel treatment of the data. Where do we go from here? It is imperative that theorists build models, take them seriously, and push them to the limit of failure. It is in the failure of our models that we learn something about the missing physics.

3. The O+ The most exciting report at the symposium was that of the strangeness +1 exotic resonance which decays into a KN system. First reports from Frascati by the Diana collaboration comprised of ITEP and Frascati gave the initial indication of this exotic resonance in an experiment involving K+Xe scattering. The reported width was 5 9 MeV. The Spring-8 collabo-

327

ration then reported a sharp resonance peak in photoproduction of K+K-n from 12C with a width of less than 25 MeV. Finally, as we have heard at SENDAIO3, the JLab CLAS collaboration has reported such an exotic resonance in yd + pK+K-(n) and in y p + n+K-K+(n) with a width of 21 MeV, the invariant mass resolution. The robustnes of the mass predictions of several model calculations, as summarized by Kopeliovich, is impressive. It has been labeled as an exotic pentaquark (uudds) object, which could be the lightest member of an antidecuplet. However, the small width is difficult to explain in such a simple quark configuration. Moreover, one would expect that the width should be less than 5 MeV, given the quality of the KN scattering data which was taken years ago, in part, in an effort to search for such exotic objects. One awaits a revised look at the KN scattering data and a limit on the width from that analysis. One also awaits a determination of the isospin of this exotic as well as its parity. Many a model of the “pentaquark” will fall as the remaining unknown quantum numbers are specified. This is truly an exciting time, assuming that the resonance is verified. If the resonance is as narrow as I expect the KN data to show, it seems unlikely that a simple valence quark model can provide the explantion. It would seem that one would need a complex quark/gluon configuration to achieve such a narrow width - as we have narrow resonances in complex nuclei where many constituents can combine to form low-lying collective states. Alternatively, a narrow width could result from a resonance with high angular momentum (L i 3) to produce the required barrier for a narrow resonance or from the pentaquark having an isospin of 2, so that isospin violation would be required to lead to a decay into an isospin 0 or 1 KN system. 4. Hypernuclear Structure

Our goal is to understand the (precision) nuclear structure information that experiments continue to bring forth. The strangeness (or flavor) degree of freedom adds a third dimension to nuclear physics. It takes us out of the isospin plane of conventional nuclei defined by protons and neutrons. Hypernuclear structure has already exhibited a number of novel features and dynamical symmetries: 0 0

0

sizeable charge symmetry breaking the the A=4 isodoublet anomalously small binding of the A=5 A hypernucleus A=4 C hypernuclear states

328

AR hypernuclear bound states non-mesonic weak decays 7r+ weak decay of ;He Hypernuclear physics provides a significant test of our models: DO our sophisticated models of conventional non strange nuclei - developed painstakingly over the past -75 years - extrapolate beyond the realm of zero strangeness where they were constructed or are the merely exquisite interpolation tools? As we have seen from Bennhold’s opening talk, the hyperon-nucleon scattering data are very sparse. The experiments are difficult due to the low beam intensities and short lifetimes of the hyperons. Production and scattering within the same target is almost automatically required. Angular distributions and polarizations have been measured at a few energies. However, the data are too few and the precision insufficient to permit a phase shift analysis, as we have for the N N system where thousands of excellent data exist for p p and n p scattering. There are some 600 scattering events in the low energy region - momenta ranging from 200 - 300 MeV/c. Another 250 events exist in the momentum range of 300 - 1500 MeV/c. The low energy data fail t o define the relative sizes of the s-wave (spin-singlet and spin-triplet) AN scattering lengths and effective ranges. Comparing those parameters from a number of Y N potentials - the diversity of values - indicates just how poorly the low energy scattering parameters are determined. Nonetheless, it is clear that no bound AN state exists. The hypertriton is the “deuteron” of the hypernuclear sector. From Schumacher’s review of JLab experiments we observed that the final-state interaction in the 2H(e,e’ K+)YN reaction is sensitive t o the An interaction. In particular, data in the missing mass range of 2.05 2.08 GeV clearly show an enhancement over the quasifree simulation, due to the Y N final-state interaction. Somewhat greater precision in future measurements will be required to extract limits upon the An scattering lengths and effective ranges. H. Loehner also discussed work at ELSA to look at final-state interactions in the 2H + y -+ KO + C+ n reaction. Channel coupling to Co p must be included in the analysis before a definitive result can be obtained. Shumacher also discussed what can be done in terms of exploring hypernuclear states by using the 4He(e,e’ K + ) i H example where quasifree production is dominant but does not hid the bound state peak at -2 MeV.

+

+

329

Similarly, one has observed in 12C(e,e’ K+)izB the excitation of the ground state doublet and the A in a p-shell. The precision of the data are impressive in comparison with the calculation of T. Motoba and J. Millener, as was shown by Schumacher. Again, calculations by Motoba demonstrated the complementarity of the (r,K+) and (n+,K+) reactions. In particular, the former reaction em2-, 3+) from an l60target leading phasizes yjr unnatural parity states (l+, to i 6 N , whereas the latter reaction emphasizes the natural parity states (1-, 2+, 3-) from the same l60target leading to i60in the final state. We also saw that in the photon reaction 28Si(y,K+)i8A1that a series of pronounced peak is predicted to persist, yielding doublets of (2+, 3+), (4-, 3-), (5+,4+), when a full shell model calculation based upon (1s Od)n is employed. That is, we were told that the full model cross section is about 65% of the lp - l h estimate. Hypernuclear spectroscopy is indeed an interesting field of study to pursue. Finally, E. Hiyama discussed the interesting aspect of adding a A to a neutron rich conventional nucleus (e.g., 6He) to form a hypernucleus (in this case, ;He). Unbound levels in the conventional nucleus become bound in the hypernucleus; y transitions can be observed. The 2+ continuum excited state of the A+6 core becomes a bound doublet in the A=7 hypernucleus. Moreover, the A=6 core (conventional nucleus) shrinks in size within the hypernucleus due to the attractive nature of the AN interaction; that is, the core nucleus is compressed. Hiyama suggested that J-PARC should provide many more examples of such neutron-rich hypernuclear systems. 5 . Thank you

I would like to extend a warm thank you to the organizers of this inspirational symposium: 0. Hashimoto (Chair), N. Kawamura (Secretary), H. Tamura, S.N. Nakamura, K. Maeda, T. Tamae, T. Takahashi, Y. Fuji, M. Kanada, and H. Yamazaki, as well as to the staff and students who made the sessions function so smoothly. To close this session I would like to say to Hashimoto san, “Domo arigato, Sensi”. 6. Acknowledgments

The research of the author is supported by the U. S. Department of Energy.


331

Pre-symposium (15 July)

At the Aobayama campus of the Tohoku University

332

New physics building was completed just in time for SENDAIO3

333

Post symposium at the Sakunami hot-springs (19 July)

Japanese style dinner, discussion with Sake

334

Excursion (20 July) Yamadera

335

Pre-symposium at Aobayama campus, Tohoku University

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338

Excursion, YAMA-DERA

Pre-symposium Recent Progress of Hypernuclear Physics


1. Y-N Interactions


INTERACTION IN THE SUe QUARK MODEL AND ITS APPLICATIONS TO FEW-BODY SYSTEMS*

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Y. FUJIWARA,' K. MIYAGAWA' M. KOHN03 Y. SUZUK14 AND C . NAKAMOT0,5 'Department of Physics, Kyoto University, Kyoto 6064502, Japan E-mail: [email protected]. ac.jp Department of Applied Physics, Okayama Science University, Okayama 700-0005, Japan Physics Division, Kyushu Dental College, Kitakyushu 80,5'-858U, Japan Department of Physics, Niigata University, Niigata 950-2181, Japan 5Suzuka National College of Technology, Suzuka 510-0294, Japan

The recent QCD-inspired spin-flavor SUB quark model for the baryon-baryon interaction, proposed by the Kyoto-Niigata group, is a unified model for the complete baryon octet (I38 = N,A, C and E), which has achieved very accurate description of the NN and Y N interactions. These quark-model interactions are now applied to realistic calculations of few-body systems in a new three-cluster Faddeev formalism which uses the 2-cluster resonating-group method kernel explicitly. We review the essential features of the most recent models, fss2 and FSS, and their predictions to few-body systems in confrontation with the available experimental data. As the few-body systems, we discuss the three-nucleon bound states, 2aA system for :Be, and 2Aa system for ,&He.

1. Introduction

An important purpose of studying baryon-baryon interactions in the quark model (QM) is to obtain the most accurate understanding of the fundarnental strong interaction in a natural picture, in which the short-range part of the interaction is relevantly described by the quark-gluon degree of freedom and the medium- and long-range parts by dominated meson-exchange processes. In the spin-flavor SUs QM, the baryon-baryon interactions for all the octet baryons (B8 = N , A, C and Z) are treated ent,irely equivalently with the well-known nucleon-nucleon ( N N ) interaction. We have recently *This work is supported by a Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (JSPS) (No. 15540270).

343

344

proposed a comprehensive QM description of general baryon-octet baryonoctet (BsBs) interactions, which is formulated in the (3q)-(3q)resonatinggroup method (RGM) using the spin-flavor SUs QM wave functions, a colored version of the one-gluon exchange Fermi-Breit interaction, and effective meson-exchange potentials (EMEP’s) acting between q ~ a r k s . l The - ~ early version, the model FSS,1-3 includes only the scalar (S) and pseudoscalar (PS) meson-exchange potentials as the EMEP’s, while the renovated one fss2 introduces also the vector (V) meson-exchange potentials and the momentum-dependent Bryan-Scott terms for the S and V mesons. Owing to these improvements, the model fss2 in the nucleon-nucleon ( N N ) sector has attained the accuracy comparable to that of one-boson exchange potentials (OBEP’s). 415

80

80

60

60

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-

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s

40 h

“P

40

0,

“ 2 0

“

20

0

0

-20

(b)

-*O 0

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100 T!ab

40

20 h

m

a

E?

0

300

(MeV)

0

-F 3

- 10

-20

la

v)

-20

- 30

Figure 1. Comparison of n p phase shifts for J 5 2 with the phase-shift analysis SP99 by Arndt et al.” The solid curves are the results by fss2 and the dotted curves by FSS.

345 5

5

B3

-

0

mm ??.

O

yo

yo

-5

FSS

--

-5

:e) sp99 50

100 150 200 250 300 3 Tm (MeV)

10,

h

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s yo

,

,

,

,

,

,

50

I

100 150 200 250 300 3b0 Tlab (MeV)

,

FSS

B 9

______

yo

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50

100 150 200 250 300 350

Figure 2. The same as Fig. 1 but for higher partial waves with J 5 4.

These QM potentials can now be used for various types of many-body calculations, which include the G-matrix calculations of baryonic matter and the Faddeev calculations of few-baryon ~ y s t e m sFor . ~ this purpose, we have recently developed a new 3-cluster formalism which uses two-cluster RGM kernel explicitly.8The proposed equation entirely eliminates 3-cluster redundant components by the orthogonality of the total wave function to the pairwise two-cluster Pauli-forbidden states. The explicit energy dependence inherent in the exchange RGM kernel is self-consistently determined. This equation is entirely equivalent to the Faddeev equation which uses a modified singularity-free T-matrix (which we call the RGM T-matrix) constructed from the two-cluster RGM kernel. We first applied this formalism to a 3-dineutron system and the 3cy system, and obtained a complete agreement between the Faddeev calculation and the variational calculation which

‘

346 150 Z p elastic

100 zE

........

E

-

v

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0 p~ (MeV/c)

150

15

r p elastic ........

E

5-

........

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8

5

50

isoSPi"

Figure 3. data.

........

Calculated Y N total cross sections compared with the available experimental

uses the translationally invariant harmonic-oscillator (h.0.) basis8>' Here we apply the formalism to the Faddeev calculations of the 3-nucleon (3N) bound state,7 as well as 2aA and 2Aa systems.

2. BsB8 interactions by fss2

Figures 1 and 2 display some iniportant low-partial wave N N phase-shift parameters predicted by the model fss2, in comparison wit,h the phase shift analysis SP99.l0 The previous results by FSS are also shown with t>hedotted curves. Due to the inclusion of V mesons, the N N phase shifts of the fss2 n t t h o nnn-rnlatixridir minrrrioc r r n tn

T,

I

-

2 5 0 MQV nro rrrnatlxr imnrnmd

347

and now have attained the accuracy almost comparable to that of oneboson exchange potentials. The good reproduct.ion of the N N phase-shift 600 MeV,4 where the inelasticity parameters in fss2 continues up to of the S-matrix becomes appreciable. The total cross sections of the Y N scattering predicted by fss2 are compared with the available experimental data in Fig. 3. The “total,’ cross sections for the scattering of charged particles (i.e., pp, C+p and C - p systems) are calculated by integrating the differential cross sections over cosO,im = 0.5 N cosOrmax= -0.5. The solid curves indicate the result, in the particle basis, while the dashed curves in the isospin basis. In the latter case, the effects of the charge symmetry breaking, such as the Coulomb effect and the small difference of the threshold energies for C - p and Con channels, are neglected. New experimental data for C - p elastic total cross sections at the intermediate energies, pc = 400-700 MeV/c, measured at, KEK,ll are consistent with the fss2 predictions. The C+p differential cross sections at the intermediate energy p c = 450 MeV/c are compared with the KEK experiment l2 in the left panel of Fig. 4. We need more experimental data to increase the statist,ics, in order to see which model is the most appropriate. In the right panel, the polarization observables for the C+p elastic scattering at pc = 800 MeV/c are shown for the models fss2 and FSS. The recent experimental data from KEK-PS 457 l3 imply the asymmetry parameter aexP = 0.44 f 0.2 at p c = 800 f 200 MeV/c, which is not inconsistent with our quark-model predictions although the specific scattering angle is not possible to be identified. N

20 I t

0.6

Pr = 450 MeVk

Q

’

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MeV/c

0.4

I

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a

0.2

I

.: .* -

-

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0

‘1.0

0.6

0.2 -0.2 -0.6 cosecm

- 1.0

-0.2

’

0

’

30

60

90

120

150

I

180

ec.rn.(dd

Figure 4. Left: C + p differential cross sections a t pc = 450 MeV/c predicted by various models. The experimental data are from RRf. 12. Right: C + p poralization a t p c = 800 MeV/c, predicted by fss2 and FSS. For the experiment, see the text.

348 50

50

40

40

g30

=30 E

v

Y

g 20

g m

10

10

0

~

0

~~

200

400

ai O p elastic --->%' A

o5

800

lo00

0

- ---

--->z z+ ........

30

a 5

600

20

,-------10 n "

0

200

400

600

Plab (MeV/c)

800

lo00

0

200

400

600

800

1000

Plab (MeW

Figure 5 . S - p and S o p total crooss sections predicted by FSS (left) ans f s 2 (right). For 2 - p cross sections both of the isospin I = 0 and 1 channels contribute, while for &-n (or Z o p ) only I = 1 channel contributes. The Coulomb force is neglected.

We show some comparison of the Z - N total cross sections which are recently obtained from the BNL-E906 experiment.14 The in-medium E - N total cross sections around the momentum region Plab 550 MeV/c are estimated as ozrJ(in medium) = 30&6.7?3,;7,mb. More detailed analysis using mb. the Eikonal approximation l5 gives o:N(in medium) = 20.9 f 4.5:::; They have also estimated the cross section ratio ~ g - ~ / = o l.l+1.4+0.7 ~ -0.7-0.4' - ~ If we compare these experimental data with the FSS and fss2 predictions depicted in Fig. 5, we find that the FSS predictions in the left panels seem to be more favorable. However, we definately need more experimental data with higher statistics. We summarize the characteristics of the BsB8 interactions predicted by the model fss2 as follows. 0 There is no bound state in the BsB8 system, except for the deuteron. 0 GC total cross sections are not so large as the N N total cross sections. 0 Z N interaction has a strong isospin dependence like the C N interaction. 0 Z-C(namely, E:C(I = 3/2)) interaction is fairly attractive. N

--

349

Some of these features are very much different from the Nijmegen predictions given by Stoks and R.ijken.16 3. Faddeev calculation for the three-nucleon bound state

The 3-cluster Faddeev formalism using the 2-cluster RGM kernel was applied to the 3-nucleon bound state, where the off-shell T-matrices derived from the non-local and energy-dependent RGM kernel for our quark-model N N interactions, fss2 and FSS, are ernpl~yed.~ The model fss2 yields the ground-state energy E(3H) = -8.519 MeV in the 50 channel c a l c ~ l a t i o n , ~ ~ which seems to be overbound in comparison with the experimental value J T , ~ P ( ~ H= ) -8.48 MeV. In fact, this is not the case, since the present calculation uses the n p interaction for each nucleon pair, which is more attractive than the nn interaction. The effect of the charge dependence is estimated to be 0.19 MeV.18 If we take this into account, our result is still 150 keV less bound. The charge rms radii for 'H and 3He are also correctly reproduced. These results are the closest to the experiments among many results obtained by Faddeev calculations, employing modern realistic N N interactions. A non-local description of the short range correlations in the quark model is essential to reproduce the large binding energy and the correct size of the three-nucleon bound state without reducing the D-state probability of the deuteron. 4. 2 a A Faddeev calculation for :Be

As a typical example of three-cluster systems composed of two identical clusters, we apply the present formalism to the 2 a A Faddeev calculation

(4

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I

I 200

400

600

800

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0

200

400

600

800

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Figure 6. AN 1so phase shifts by fs (solid curve) and by SB

350

for :Be, using the 2 a R.GM kernel and the ha folding potential constructed from a simple A N effective interaction. For the 2 a RGM kernel, we use the the 3-range Minnesota force l9 with the exchange mixture u = 0.946869, and the h.0. width parameter, u = 0.257 h-', assumed for the ( O S ) ~ a-clusters. The 2 a phase shifts are nicely reproduced in the 2a RGM calculation, using this effective N N interaction. For the 3 a system, we find that the 3 a ground-state energy obatined by solving the present 3 a Faddeev equation is only about 1.5 MeV higher than that of the full microscopic 3a RGM calc~lation.~ The effective AN interaction, denoted by SB (Sparenberg-Baye potential) in Table 1, is constructed from the l S 0 and 3S1phase shifts predicted by the Y N sector of the model fss2, by using an inversion method based on supersymmetric quantum mechanics.20 These are simple 2-range Gaussian potentials which reproduce the lowenergy behaviour of the A N phase shifts in Figs. 6 and 7, obtained in the full coupled-channel calculations:

+ + 1072 exp(-13.74

K,,(T) = -128.0 exp(-0.8908 r 2 ) 1015 exp(-5.383 r 2 )

V3s1(r)= -56.31 f exp(-0.7517

T ~ )

T')

, ,

where V ( T )in MeV and T in fm. In the 3S1state, the phase-shift behavior < 600 MeV/c is fitted, since only in the low-momentum region with tthe cusp structure is never reproduced in the single-channel calculation. Since any central and single-channel effective A N force leads to the wellTable 1. The ground-state energy Egr(O+) and the 2+ excitation energy Ex(2+) in MeV, calculated by solving the Faddeev equation for the 2aA system. For the effective N N force for the 2a RGM kernel, the 3-range Minnesota force is used. The AN force, SB, stands for the Sparenberg-Baye potential and NS - JB are the G-matrix based effective forces used by Hiyama et al.23 The experimental values are from Ref. 2 4 . (MeV) Hiyama diff.

Ex(2')

E g r (0')

ours

Exp't

(MeV)

-6.837

-

-

-6.742

-6.81

0.07

2.916

-7.483

-7.57

0.09

2.935 2.930

2.915

-6.906

-7.00

0.09

-6.677

-6.76

0.08

2.919

-6.474

-6.55

0.08

2.911

-6.62 f0.04

I

3.029(3//3.060(3)

351

known overbinding problem of :He by about 2 MeV (in the present case, it is 1.63 MeV), the attractive part of the 3S1AN potential is modified to reproduce the correct binding energy, E""p(;He) = -3.12 f 0.02 MeV, with an adjustable parameter f = 0.8923. This overbinding problem is mainly attributed to the Brueckner rearrangement effect of the a-cluster, originating from the starting energy dependence of the bare two-nucleon interaction due to the addition of an extra A particle.22 The odd-state A N int,eraction is assumed to be zero. The partial waves up to AM^ = elMax= 6 are included both in the 2 a and Aa channels. The direct and exchange Coulomb kernel between two a-clusters is introduced at the nucleon level with the cut-off radius, Rc = 14 fm. Table 1 shows the ground-state (O+) and the 2+ excitat.ion energies of :Be, predicted by the SB and the other various AN potentials used by Hiyama et aZ.23. In the present calculations using only the central force, the SB potential with the pure Serber character can reproduce the the ground-state and the excitation energies within the accuracy of 100 - 200 keV. 5. 2Aa Faddeev calculation for ,.&He Next, we use the ha T-matrix, used in the 2 a A Faddeev calculation, to calculate the ground-state energy of :AHe. The full coupledchannel T-mat,rices of fss2 and FSS with the strangeness S = -2 and the isospin I = 0 are employed for the AA RGM T-matrix. Table2 shows the ABAAvalues (in MeV) defined by ABAA= BAA(A\He) 2BA(iHe)' VAA(Hiyama) the 3range Gaussian potential in Ref. 23.

p O0

0

200

400

600

800

lo00

Plab ( k v / c )

Figure 8. AA lS0 phase shifts by fss2 (solid curve) and by SB potential (Ckcles).

We find that the Hiyama's 3-range Gaussian AA potential 23 and our Faddeev calculation using FSS yield very similar results with the large ABAA values about 3.6 MeV, since the AA phases shifts predicted by these interactions increase upto about 40". The improved quark model fss2 yields ABAA= 1.41 MeV. (If we use the AA single-channel T-matrix, this number is reduced to ABAA= 1.14 MeV.) In Table2, the result denoted by VAA(SB)is by the 2-range Gaiissian potential generated from the fss2 AA phase shift (Fig. 8) in the full-channel calculation, using the supersym-

352

metric inversion method.20 This potential is explicitly given by

VAA(SB)= -103.9 exp(-1.176 r 2 )+ 658.2 exp(-5.936 r 2 ) , where Vnn(SB) in MeV and r in fm. We think that the 0.5 MeV difference between our fss2 result and the VAA(SB)result is probably because we neglected the full coupled-channel effect of the A A a channel to the S N a and CCa channels. We should also keep in mind that in all of these 3cluster calculations the Brueckner rearrangement effect of the a-cluster with the magnitude of about -1 MeV (repulsive) is very i m p ~ r t a n t . 'It ~ is also reported in Ref. that the quark Pauli effect between the a cluster and the A hyperon plays as a non-negligible repulsive contribution of the order of 0.1 - 0.2 MeV for the A separation energy of ,&He, even when we assume a rather compact (3q) size of b = 0.6 frn. Taking all of these effects into consideration, we can conclude that the present results by fss2 are in good agreement with the recent experimental value, ABrf = 1.01 f 0.20 MeV,27deduced from the Nagara event.

6. Summary

We have extended the (3q)-(3q)RGM study of the the N N and Y N interactions to the strangeness S = -2, -3 and -4 sectors without introducing any extra parameters, and have clarified some characteristic features of the && interaction^.^ The results seem to be reasonable, if we consider i) the spin-flavor SU, symmetry, ii) the weak pion effect in the strangeness sector, Table 2. Comparison of ABAA values in MeV, predicted by various AA interactions and VAN potentials. VAA (Hiyama) is the 3-range Gaussian potential used by Hiyama et al.23 The difference between our calculation and Hiyama's calculation is also shown. FSS and fss2 use the AA RGM T-matrix in the free space. E2A is the 2 h expectation value determined self-consistently. V,A(SB) is the two-range Gaussian potential given in the text. In VAA(SB)only the S-wave is used, while in the others converged results with enough partial waves are given.

VAN SB

3.618

-

FSS

fss2

E

E2A

E

c2A

VAA(SB) (S-wave)

-

3.650

5.131

1.411

5.942

1.902

0.04

3.623

5.159

1.364

5.951

1.917

3.231

4.482

1.288

5.231

1.636

1.270

5.410

1.719

V,~(Hiyama) Hiyama diff ours

NS

3.548

3.59

ND

3.181

3.10

NF

3.208

3.22

0.01

3.301

4.626

JA

3.370

3.44

0.07

3.468

4.908

1.306

5.705

1.833

JB

3.486

3.56

0.07

3.592

5.150

1.325

5.956

1.924

-0.08

353

and iii) the effect of the flavor symmetry breaking. These B& interactions are now used for t,he detailed study of the few-body systems, as well as baryonic matter problems, in various ways. Here we reported applications of the N N , Y N and Y Y interactions to the Faddeev calculations of the three-nucleon bound state, the 2 a A system for :Be, and the 2 A a system for ,&He. We find that our most recent model fss2 gives the triton binding energy large enough to compare with the experiment, without reducing the deuteron D-state probability. The charge root-mean-square radii of 3H and 3He are also correctly reproduced. In the application to the 2 a A system, the 2 a RGM kernel with t,he effective Minnesota force l9 and some appropriate AN force generated from the low-energy phase-shift behavior of fss2 yield the the ground-state and excitation energies of :Be within the accuracy of 100 - 200 keV. The weak AA force ABi:p = 1.01 f0.20 MeV by the Nagara event 27 for ,&He is reasonably reproduced by the Faddeev calculation of the 2 a h system, using the present ha T-matrix and the full coupled-channel AA-ZN-CC ?-matrix of fss2. It is important to note that the newly developed 3-cluster Faddeev formalism using the 2-cluster RGM kernel opens a way to solve few-baryon systems interacting by the quark-model baryon-baryon interaction without spoiling the essential features of the RGM kernel; i.e., the non-locality, the energy dependence and the existence of the pairwise Pauli-forbidden state. It can also be used for the 3-cluster systems involving a-clusters, like the :Be and ,&He systems. A nice point of this formalism is that the underlying N N and Y N interactions are more directly related to the structure of the hypernuclei than the models assuming simple 2-cluster potentials. In particular, we have found that the most recent quark-model interaction, the model fss2, yields a realistic description of many systems including the 3-nucleon bound state, :Be and ,6,He. References 1. Y. Fujiwara, C. Nakamoto and Y. Suzuki, Phys. Rev. Lett. 76, 2242 (1996). 2. Y. Fujiwara, C. Nakamoto and Y. Suzuki, Phys. Rev. C 54, 2180 (1996). 3. T. Fujita, Y. Fujiwara, C. Nakamoto and Y. Suzuki, Prog. Theor. Phys. 100, 931 (1998). 4. Y. Fujiwara, T. Fujita, M. Kohno, C. Nakamoto and Y. Suzuki, Phys. Rev. C 65. 014002 (2002). 5. Y. Fujiwara, M. Kohno, C. Nakamoto and Y. Suzuki, Phys. Rev. C 64, 054001 (2001). 6. M. Kohno, Y. Fujiwara, T. Fujita, C. Nakamoto and Y. Suzuki, N I L C Phys. ~. A674, 229 (2000).

354 7. Y. Fujiwara, K. Miyagawa, M. Kohno, Y. Suzuki and H. Nemura, Phys. Rev. C 66, 021001 (R) (2002). 8. Y. Fujiwara, H. Nemura, Y. Suzuki, K. Miyagawa and M. Kohno, Prog. Theor. Phys. 107, 745 (2002). 9. Y. Fujiwara, Y. Suzuki, K. Miyagawa. M. Kohno arid H. Nemura, Prog. Theor. Phys. 107, 993 (2002). 10. Scattering Analysis Interactive Dial-up (SAID), Virginia Polytechnic Institute, Blacksburg, Virginia R. A. Arndt: Private Communication. 11. Y. Kondo e t al. (KEK-PS E289 collaboration), Nucl. Phys. A676,371 (2000). 12. J. K. Ahn et al. (KEK-PS E251 collaboration), Nucl. Phys. A648, 263 (1999). 13. T. Kadowaki et al. (KEK-PS E452 collaboration), Eur. Phys. J . A l 5 , 295 (2002). 14. T. Tamagawa et al. (BNL-E906 collaboration), Nucl. Phys. A691, 234c (2001). 15. Y. Yamamaoto, T . Tamagawa, T. Fukuda and T. Motoba, Prog. Theor. Phys. 106, 363 (2001). 16. V. G. J. Stoks and Th. A. Rijken, Phys. Rev. C 59, 3009 (1999). 17. Y. Fujiwara, K. Miyagawa, Y. Suzuki, M. Kohno and H. Nemura, Nucl. Phys. A721, 983c (2003). 18. R. Machleidt, Adv. Nucl. Part. Phys. 19, 189 (1989). 19. D. R. Thompson, M. LeMere and Y. C. Tang, Nucl. Phys. A286, 53 (1977). 20. J.-M. Sparenberg and D. Baye, Phys. Rev. C 55, 2175 (1997). 21. R. H. Dalitz, R. C. Herndon and Y. C. Tang, Nucl. Phys. B47, 109 (1972). 22. H. Bando and I. Shimodaya, Prog. Theor. Phys. 63, 1812 (1980). 23. E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Prog. Theor. Phys. 97, 881 (1997). 24. H. Akikawa et al. (BNL-E93O collaboration), Phys. Rev. Lett. 88, 082501 (2002). 25. M. Kohno, Y. Fujiwara and Y. Akaishi, Phys. Rev. C 68, 034302 (2003). 26. Y. Suzuki and H. Nemura, Prog. Theor. Phys. 102, 203 (1999). 27. H. Takahashi et al. (KEK-PS E373 collaboration), Phys. Rev. Lett. 87, 212502 (2001).

X + P SCATTERING EXPERIMENTS WITH A SCINTILLATING FIBER ACTIVE TARGET

H. KANDA Physics Department, Graduate School of Science, Tohoku University, 980-8578,Sendai Japan E-mail: [email protected] KEK PS E289 COLLABORATION Hyperon-proton scattering experiments, KEK-PS E251 and E289 had been carried out at KEK-PS K2 beamline and the analyses for deriving scattering cross sections are under way. With use of a scintillating fiber active target, we had performed the direct observation of hyperon tracks and their scattering vertex which had never been done after bubble chamber experiments in 1960’s and 1970’s. Pion beam of 1.64 GeV/c is incidented on the active target and C + is produced via ( r + , K f ) reaction. The C+ travels through the target and scatters on a proton inside the target. E251 resulted 11 C + p elastic scattering events from 3 x 10 events of (nt,K t ) reactions’. E289 collected a few times more scattering events than E251. These statistics are larger than the result from past bubble chamber experiments for the C + momentum region from 400 MeV/c to 600 MeV/c.

1. Introduction

The interaction between nucleons (NN interaction) have long been investigated both experimentally and theoretically. Many kind of observables with high accuracy have been obtained from many experiments. And many kind of theories have been presented for interpreting the experimental results. These theories are based on the one pion exchange (OPE) or the one boson exchange (OBE) and well describe the NN interaction. Nowadays the interaction between a hyperon and a nucleon (YN interaction) and also the interaction between hyperons (YY interaction) have been investigated through both their scattering and hypernuclear structures. Theories are extended to describe the NN and YN interactions in the same framework aiming at description of the general interactions between baryons. Elaborated experiments attempt to overcome hyperons and hypernuclei’s short life time which had made difficult to obtain precise experimental results.

355

356 One of those attempts is using an active target with good spatial resolution for a hyperon scattering experiment. In KEK-PS E251 and E289, we employed an active target system consisted of fine scintillating fibers, image intensifier tubes(IIT’s), and CCD cameras. It enabled the detection of short tracks of produced and scattered hyperons. And the further advantage is that the system works synchronously with other particle detectors. It accepts an intelligent trigger issued by the counter informations to acquire the image data. In E251, image digitizer was a VME module and recorded in the other data structure. In E289, we used a CAMAC CCD controlling and image digitizing module for recording CCD image data altogether with the other ADC and TDC data. It enabled us a simpler event reconstruction. With this technique, we attempted to acquire higher statistics in the hyperon-nucleon scattering experiment.

2. Experiment

The Experimental setup for E289 experiment is shown in Fig. 1. We used & beam of 1.64 GeV/c for production of hyperon via p(.ir+,K+)C+ reaction. Momentum analyzed and particle identified T + is incident on the scintillating fiber (SCIFI) active target. The SCIFI target works as the production target of C+ and also as the scattering target. Scintillating fibers of 300 x 300pm square cross sections are stacked in 2 perpendicular directions and viewed by 2 sets of image intensifiers (Fig.2) so that three-dimensional track information can be reconstructed from two images. Tracks of charged particles inside the SCIFI target are recorded as CCD image data’. Outgoing particles are momentum and mass analyzed by the spectrometer “KURAMA.” Its momentum resolution is A p / p = 0.9% (RMS) and mass resolution is 32 MeV/c2 (RMS) for proton. In 100 days of data taking period, 3.1 x 106 triggers were issued. After spectrometer analysis for ( T + , K + ) reaction and computational image analysis for a thick bright track of C+ to select C+ produced events, 6.8 x lo5 events were scanned by human scanners. The scanners looked into the image data and categorized the events by track topologies in the image data. One of the C+ scattering candidates is shown in Fig. 3. Star marks in the image are some kinematically significant points input by the human scanners. With aid of these points, track informations of relevant charged particles are reconstructed and kinematics of the events were analyzed.

357

Figure 1. Setup of K2 beamline.

Figure 2.

Schematics of the scintillating fiber active target

3. Preliminary result We applied visibility cuts (requirements on track lengths) and kinematic cuts to select incident C+ beam produced from a free proton (a hydrogen nucleus). We further applied visibility cuts and kinematic cuts for the secondary C+p scattering vertex and selected 34 events as e p elastic scattering. The detection and analysis efficiency were estimated with use of a Monte Carlo simulation with a image data generator. Simulated Cip scattering images were mixed in the experimental image data and scanned by human scanners for the evaluation of the scanners’ categorization efficiency and

358

Run 1334

Event 2

Spill 886

.i

-40

Figure 3.

-20

0

20

40

Example of the image data for C +-p scattering event.

......-..’ -1

-0.8 -0.6 -0.4 -0.2

0

0.2

0.4 0.6

0.8

1

case 0 E251 result Figure 4. Preliminary result of differential cross section for C +-p elastic scattering comparing with the result from E251 and the theoretical predictions.

359

accuracy. We estimated that our analysis method had finite efficiency in the center of mass angle from 40 to 140 degree (0.8 < c o s Q ~ 300 MeV/c Large spin-flip amplitude Better energy resolution of sub-MeV (FWHM)

However, the hypernuclear study using the reaction had been hampered by experimental difficulties such as much smaller cross section than those of mesonic reactions, huge background from electrons associated with bremsstrahlung, and necessity to measure both electrons and kaons at very forward angles. By overcoming these difficulties the first hypernuclear spectroscopy using the (e,e’K+) reaction was successfully carried out at Jefferson Lab Hall C (Jlab E89-009 experiment132). The experiment demonstrated the feasibility of the ( e ,e’K+) reaction for the A hypernuclear spectroscopy. 387

388

Encouraged by the first successful experiment, a new (e,e’K+) hypernuclear spectroscopy was proposed at Jlab (Jlab E01-011 e ~ p e r i m e n t ~ ? ~ ) . It is expected t o realize much higher yield rate and hypernuclear mass resolution than those of the first one by employing a high resolution large solid angle kaon spectrometer (HKS) and a method to avoid 0-degree peaked background from bremsstrahlung. This article summarizes consideration to experimental conditions of the ( e ,e’K+) hypernuclear spectroscopy, introduces two hypernuclear experiments at Hall C, and shows what can be extracted from experimental result of Jlab Eo1-011 experiment. 2. Consideration to experimental conditions

To tag the hypernuclear production via the (e,e’K+) reaction, both scattered electron and kaon must be measured in coincidence at very forward angles. Thus in principle there should be a dipole magnet in front of an elec-

Schematic Top View of

/

21.5

JBeani

-

0

1

af dab

2m 2C43.2 3

Figure 1. Schematic top view of E01-011 experiment

tron arm and a kaon arm to separate unscattered beam, scattered electrons and scattered kaons. As an example, the experimental setup of E01-011 experiment is shown in Figure 1. This section describes choice of experimental conditions suitable for hypernuclear production experiment.

389

2.1. Detection angle of scattered electrons

Ee=1850beV

-6

I

10

0

50

,

.

,

.

i

100

.

,

.

.

i

150

.

.

.

.

200

Electron Polar Angle (mr)

Figure 2. Calculated virtual photon flux for beam energy of 1.85 GeV and photon energy of 1.494 GeV.

Figure 2 shows an angular distribution of calculated virtual photon flux for beam energy of 1.85 GeV and photon energy of 1.494 GeV. It is clearly seen that virtual photon flux is extremely forward peaked. Thus tagging efficiency of virtual photon is maximized at zero degree. E89-009 experiment adopted this configuration (so called “zero-degree tagging method”) to obtain maximum tagging rate of virtual photons. On the other hand, E01-011 experiment adopted so-called “tilt method” , which tilts the electron arm vertically to avoid zero-degree particles as well as electrons from Mprller scattering.

390

2.2. Energy of virtual photons and kaons Virtual photon energy, E-,, is given as E-, = E, -Eel where E, and E,, are energies of incident and scattered electron. Total cross section of elementary process, p ( y , K + ) A , is maximum from 1.1 to 1.5 GeV. In this regard, Ey should be within this energy range. Momentum of scattered kaon is calculated by using energy of virtual photon and assumed hypernuclear mass. For example, E-, of 1.8 GeV gives p~ of about 1.2 GeV/c. Lower p~ gives better momentum resolution and better particle identification (PID) but smaller kaon survival factor. Choice of kaon momentum depends on the other experimental conditions such as path length, momentum range, and momentum resolution of a kaon arm. Two Hall C experiments chose similar virtual photon energy of 1.4 to 1.5 GeV t o take advantage of good resolution and good PID. 2.3. Detection angle of kaons

Since angular distribution of the kaons is forward peaked as shown in Figure 3, kaons should be detected ils forward as possible to maximize hypernuclear yield. Again zero degree should be avoided to exclude positrons from pair creation. 2.4. Energy of electron beam

Choice of beam energy depends on two factors, hypernuclear yield and number of background kaons. Hypernuclear yield increases with beam energy. However, background kaons also increase with beam energy since kaon production channels other than A production open at higher beam energy. In addition, higher beam energy requires better momentum resolution to the electron arm. Thus it is better to keep beam energy as low as possible to minimize background. 3. Hypernuclear experiments at Jlab Hall C

Taking into account the conditions described in the previous section, the experimental conditions are determined. Table 1shows comparison between two hypernuclear experiments, E89-009 and EOl-011, at Jlab Hall C. Major differences between them are detection angle of electrons and kaons, and use of new spectrometer for the kaon arm. E89-009 experiment placed electron arm at zero-degree to maximize tagging efficiency of virtual photons. Though it employed fine-segmented

391

hodoscopes and silicon strip detectors for the electron arm to accept singles rate of up to 200 MHz at the entire focal plane, beam current was limited due to bremsstrahlung associated electrons, and resulted in low yield rate and low signal to accidental ratio. E01-011 experiment employs the kinematical setup which exclude zerodegree for both arms to avoid bremsstrahlung associated electrons and electrons from Mdler scattering, and also positrons from pair-creation. Moreover, the existing kaon arm, SOS, is replaced by the newly constructed HKS spectrometer, which has large solid angle of 16 msr and 2 ~ 1 O -(FWHM) ~ momentum resolution. ,4s a result, better than 390 keV (FWHM) energy resolution and yield of 45/h for i2B,.,. are expected. The energy resolution is more than two times better than E89-009 experiment and the yield is comparable to that of mesonic reactions. Table 1.

Comparison between two hypernuclear experiments at Jlab Hall C

Beam energy (GeV) Beam energy spread 6 E / E (FWHM) Beam current (PA) Target thickness (mg/cm2) K + arm: Central momentum (GeV/c) Scattering angle (deg.) Momentum bite (%) Momentum resolution 6 p / p (FWHM) Solid angle (msr) Singles rate (MHz) e' arm: Central momentum (MeV/c) Scattering angle (deg.) Momentum bite (%) Momentum resolution 6 p / p (FWHM) Singles rate (MHz) Yield for y B g . s .(/h) Energy resolution for i2Bg.s.(keV, FWHM)

E 89-009 1.865

5 0.1

E01-011 1.845 10-4 30 100 HKS 1.20 7.0 f12.5 2~ 10-4 16 2(Estimation)

285 0 f20

316 4.5 (vertical) &30

5 0.66 22

sos 1.24 1.9 f23 5x

200 0.9 900

5x 3 (Estimation) 45(Estimation) 5390

4. Information on hypernucleus we can extract

In E89-009, only peak position and cross section of several hypernuclear states are extracted since limited statistics and low signal to accidental ratio. In E01-011, on the other hand, it is possible to obtain angular distri-

392 2.25

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Figure 3. Left panel shows angular distributions of kaons from 12C(e,e'K+)i2Bat beam energy of 1.8 GeV, virtual photon energy of 1.48 GeV, and electron detection angle of 4.5 deg. Right panel shows yield ratios to that of ground state production. By taking yield ratio to that of ground state production, one may be able to distinguish spin-parity of each state.

bution and excitation function of hypernuclear states, since much higher yield is expected and the kaon arm has large angular acceptance and the electron arm has large momentum acceptance. Moreover, since missing mass resolution is improved, intrinsic width of hypernuclear states may be obtained. As an example, angular distribution of kaons is calculated with a code by M. Sotona 6 , for several states produced via 12C(e,e'K+)i2B reaction at beam energy of 1.8 GeV, virtual photon energy of 1.48 GeV, and electron detection angle of 4.5 deg. Left panel of Figure 3 shows angular distribution of kaons. Each line corresponds to the following states; : b 3 / 2 ) - 1 ( ~ 1 / 2 ) A J" = 2- ground state, Solid : (P3/2)-1(P3/2)A J" = 2- 9.5 MeV state, Dashed : (P3/2)-'(~1/2)* J" = 2- 10.5 MeV state, Dotted Dot-dashed : (s112)-l (s1/2)A J" = 1+ 20.0 MeV state. Right panel shows yield ratios to that of ground state production. By taking yield ratio to that of ground state production, one may be able to distinguish spin-parity of each state. Error bars shown in the panel axe estimated statistical error for EO1-011 experiment.

393

5. Summary Firstly, the experimental conditions which enable us to perform hypernuclear spectroscopy using the ( e ,e’K+) reaction are summarized. One of the most essential condition is to detect both electrons and kaons at as forward as possible but exclude zero degrees. Secondly, two hypernuclear experiments at Jlab Hall C are introduced. The first one, E89-009 experiment demonstrated the feasibility of the ( e ,e’Kf) hypernuclear spectroscopy. However, due to huge background from bremsstrahlung statistics are limited. The second one, E01-011 experiment is expected to realize 350 keV (FWHM) energy resolution and yield rate of 45/h for i2Bg,s,by employing “tilt method” and replacing the existing kaon arm with the HKS, which has large solid angle of 16 msr and momentum resolution of 2 ~ 1 0 - ~ . Thirdly, by using expected statistics for E01-011 experiment and theoretical angular distribution of a DWIA calculation, possibility to extract information on spin-parity is shown. References 1. T. Miyoshi et al., Phys. Rev. Lett. 90 232502 (2003). 2. T. Miyoshi, Talk in this symposium. 3. 0. Hashimoto, L. Tang, J. Reinhold, and S. N. Nakamura, E01-011 proposal to Jlab PAC19, 2001. 4. S. N. Nakamura, talk in this symposium. 5. M. Q. Tran et al., Phys. Lett. B 445, 20 (1998) 6. M. Sotona, private communication.


3. Hypernuclear Weak Decay


NONMESONIC DECAY RATES AND ASYMMETRY PARAMETERS OF LIGHT A-HYPERNUCLEI

K. ITONAGA Laboratory of Physics, Miyazaki Medical College Kiyotake, Miyazaki 889-1 692, Japan E-mail: itonagaOphysics.med.miyazaki-u.ac.jp* T. MOTOBA

Laboratory of Physics, Osaka Electro-communication University Neyagawa, Osaka 572-8530, Japan E-mail: motobaOisc.osakac.ac.jp T. UEDA Arida 1891, Chiyoda-cho, Hiroshima 731-1533, Japan E-mail: uedatamOthemis.ocn.ne.jp

First the nonmesonic decay rates and rn/rPratios of light A-hypernuclei are calculated in the meson exchange interaction model. The potential features and the roles of the K-meson exchange on the decay rates and the n / p ratios are discussed. We show that the '&-induced channel interaction is not well constrained in view of the n / p ratio comparison between calculations and experimental data, especially of :He. Second, the asymmetry parameter a1 of ;He is evaluated and is found to be negative in our model, which contradicts the data. It is, however, demonstrated that it may be possible to explain the asymmetry parameter data of ;He if we can constrain the central force of the decay interaction more properly.

1. Introduction

With the advent of new techniques, high resolution and high statistics, the following observables and high quality data are newly reported in the nonmesonic weak decays. First the energy spectra of a nucleon in the light and medium-heavy hypernuclei are measured, i.e., the proton energy spectra have been presented1>' for ;He, ,:"Cand i8Si, while the neutron *New E-mail address after October 1. 2003

397

398

+

+

spectra are presented3 for ;He and i2C. Second, the n n and n p pair double coincidence measurement is performed and the deduced data of Fn/rpwith small error bar is presented4 for ;He. The central value of n / p ratio data is reported to be small which differs from the previous data around ~ n i t y . ~Third 9 ~ the asymmetry parameters of a proton emitted in the decay of ;He and i2C are remeasured at KEK with high statistics7 since the pioneering works of Osaka group? These data are helpful in elucidating hyperon-nucleon weak interactions and the weak decay mechanism. The aim of this report is twofold. One is to evaluate the observables such as the nonmesonic decay rates, the decay rate n / p ratios and the asymmetry parameter of a proton in the light hypernuclear weak decays in our meson exchange interaction model which includes the K-meson exchange. Another is to discuss the properties of the meson exchange interactions such as the scalar, tensor and parity-violating vector forces based on the experiment-calculation comparisons, and also discuss the weak decay mechanism that affects the observables.

2. Meson exchange interactions and nonmesonic decay rates

In the previous work, we evaluated the nonmesonic decay rates and the decay n / p ratios by adopting the meson exchange interaction model. We employed In, 27r/p, 2nlo and lw as the exchange mesons for the AN -+ N N p r o c e ~ sThe . ~ nonmesonic decay rates are consistent with the data and the n / p ratios are calculated as large as 0.3 - 0.4 for light hypernuclei though they are still not enough to explain the data. Since the K-meson exchange is known to be important to obtain the large n / p ratios observed in experiments,10J1212we introduce the K-meson exchange interaction in our m0de1.l~The strong coupling constant at the vertex A N K is taken from the work of Ueda et a1.14 while the weak coupling constant at the vertex N N K is adopted from the work of Parrelio et a1.15 Table 1 shows the calculated decay rates and rn/FP ratios of :He and ;He which are compared with the experimental data.16i5,6JJ7 When the Kexchange interaction is introduced, the decay rate Fnm is a little increased and the Fn/rP is enhanced by 70 % for ;He. The calculated n / p ratio overshoots the recent experimental data of Ref. 4. The similar situation is found for i2C. In the case of $He, the total decay rate is a little decreased and the n / p ratio is calculated to the reduced value, althogh its value seems to overestimate the recent data of Outa et a1.l

399

The calculations are understandable from the potential behavior of the K-meson exchange interaction VK. The central and the tensor forces of VK have opposite signs to and have similar strengths as those of the one-n exchange V,. On the other hand, the parity-violating vector force has the same sign as that of V, for the 3S1-induced decay channels while it has the opposite sign as that of V, for the 'So-induced channel. Due to those behaviors of the K-exchange interaction, the r,, are almost unchanged when VK is introduced. The n / p ratios are much enhanced for :He and i z C due to the strong additive interference of VK and V, in the neutronstimulated 3S1+ 3P1channel. The n / p ratio of :He is, on the contrary, reduced because the 3S1-induced channels are missing for the A n + nn decay and the 'So + 'POchannel contributes destructively. Nevertheless, the calculated n / p ratio is still large and does not agree with the recent data.' This may suggest the insufficiency of the interactions of lS0-induced decay channels. It is noted that the meson exchange interactions including the Kexchange have favourable properties in accounting for the nonmesonic decay rates of light A-hypernuclei. As regards to the n / p ratio problems, certain discrepancies exist between calculations and experiments. It may be related to the asymmetry parameter problem to be discussed in $3, and improvements and refinements of the decay interaction are still necessary. 3. Asymmetry parameter of a proton in the decay of :He

The angular distribution of a proton emitted in the decay of a polarized ;He is expressed as

a1 = rl/ro. The al is called the asymmetry parameter. The as

r0 and rl

(2) are expressed

400

x 2fiRe[-ae*

+ b(c - h d ) * / & + f ( h c + d)*] .

(4)

The a, b, c, d, e and f are widely adopted notations for the decay channel matrix elements.18 It is notable that ro in Eq. 3 which is proportional to F p is expressed as the sum of the absolute-squared decay amplitudes while Fl in Eq. 4 is represented as the sum of three terms which are products of the parity-conserving and parity-violating decay amplitudes. Thus the asymmetry parameter a1 gives us information on the signs and magnitudes of the decay amplitudes. The recent report of the experiment of :He at KEK shows a1 = 0.09 f 0.08 which is small and positive7 and is consistent with the previous datas of al = 0.24 f 0.22 done at KEK. When we adopt the full interactions in our model, we obtain a1 = -0.33 whose sign is contrary to the experimental data. The sign of the asymmetry parameter is determined by rl in Eq. 4. The negative a1 in our calculation comes from negatively large (-ae*) term in which a > 0 and e* > 0. The f ( f i c + d ) * is calculated to be positive but the manitude is moderate. The other term is small. As a result, the negative a1 is turned out. We recall that our central interaction due to the 2n/a exchange is not well constrained and may be insufficient in view of the n / p ratio of ;He in calculation as mentioned in $2. The effect of the central force on the sign and the magnitude of a1 is examined here. As a trial, we use the which is weaker than V,,,, by about 50 % in magnitude. modified LiV2n,(r” In the case of the weaker 2n/a exchange interaction, a1 is calculated to be 0.12 whose sign is consistent with the experiment. In this calculation, the positive sign of a1 comes from the dominant f (&+ d)* term where f < 0 and ( d c d) < 0. It is notable that the amplitudes c and d are evaluated by taking into account of initial and final state correlations. The final state tensor correlation is specially important and c becomes negative. It is also noted in the present case that the (-ae*) < 0 term contribution is reduced due to the weakened central force or the reduced a-channel amplitude. This demonstrates that the central force has a certain role for the sign and magnitude of al provided that other force parameters are held. These calculational study encourage us that we may have a possibility to get the correct sign and magnitude of the asymmetry parameter a1 of :He. Through our model calculations for the decay observables, we may say the followings concerning on the interactions and amplitudes. i) The parity-

+

40 1

violating amplitudes have definite signs for the most interaction model and b < 0, e > 0 and f < 0. ii) The central force of our model is repulsive but the strength is not well constraint. iii) The tensor force of our model seems to be attractive but the ambiguity exists in strength. In summary, it is important t,o study the nonmesonic decay rates, the n l p ratios and the asymmetry parameters simultaneously and consistently in understanding the weak decay interactions and the weak decay mechanism such as the initial and the final correlations. References 1. H. Outa et al., Nucl. Phys. A639, 251c (1998). 2. 0. Hashimoto et al., Phys. Rev. Lett. 88, 042503 (2002). 3. S. Okada et al., in these Proceedings. 4. S. Kang et d.,in these Proceedings. 5. J. J. Szymanski et al., Phys. Rev. C 4 3 , 849 (1991). 6. H.Noumi et al., Proc. IV Int. Symp. on Weak and Electromagnetic Interactions in Nulei, Osaka, (World Scientific, 1995), p.550. 7. T. Maruta et al., in these Proceedings. 8. S. Ajimura et al., Phys. Rev. Lett. 84, 4025 (2000). 9. K. Itonaga, T. Ueda and T. Motoba, Phys. Rev. C 6 5 , 034617 (2002). 10. K. Sasaki, T. Inoue and M. Oka, Nucl. Phys. A669, 331 (2000); A678, 445 (2000). 11. D. Jido, E. Oset and J. E. Palomer, Nucl. Phys. A694, 525 (2001) 12. A. Parrexio and A. Ramos, Phys. Rev. C 65, 015204 (2002). 13. K. Itonaga, T. Motoba and T. Ueda, Mod. Phys. Lett. A 18, 135 (2003). 14. T. Ueda, F. E. Riewe and A. E. S. Green, Phys. Rev. C 17, 1763 (1978). 15. A. Paxrexio, A. Ramos and C. Bennhold, Phys. Rev. (756, 339 (1997). 16. M.M.Block et al., Proc. Int. Conf. on Hyperfragments, St. Cerge, 1963, CERN Report No. 64-1, p.63. 17. V. J. Zeps et aE., Nucl. Phys. A639, 281c (1998). 18. M. M. Block and D. H. Dalitz, Phys. Rev. Lett. 11, 96 (1963).

402

Table 1. Nonmesonic decay rates and are given in units of I'A.

rn/rPratios of ;He

and :He. The decay rates

;He V? Vr

+ Vzr/p+ V2,/, + V w

0.252

0.027

0.279

0.107

0.305

0.118

0.422

0.386

0.227

0.185

0.451

0.669

vr + VZr/p+ VZ,,, + vu +VK Exp.

0.41 f 0.13

EXP.~

0.21f0.07

Exp.

0.17 f 0.04

0.20f0.11

0.41f0.14

0.93f0.55

0.50 f 0.07

I .97 f0.67

He V?

0.204

0.010

0.214

0.048

0.223

0.081

0.303

0.361

0.215

0.071

0.286

0.333

0.14 f 0.03

0.432::fi

Exp.'

0.16 f 0.02

0.01 f 0.05

0.17 f 0.05

0.06+)20:

Exp.l7

0.16 f 0.02

0.04 f 0.02

0.20 f 0.03

+

+

VT Vz=/p V2,/,

V?

+ Vw

+ v 2 7 r / p + VZ,,, + vu +VK

Exp.l6

THE MESONIC AND NONMESONIC WEAK DECAY WIDTHS OF MEDIUM-HEAVY A HYPERNUCLEI

Y . SAT0 AND E307 COLLABORATION High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan E-mail: yoshinori. satoQkek.jp KEK-PS E307 experiment measured the lifetimes and mesonic and nonmesonic decay widths of medium-heavy A hypernuclei. The results of x- mesonic decay widths confirmed an enhancement of mesonic decay width due to the distorted wave function by pion-nucleus optical potential for the first time. The nonmesonic decay widths saturate around A-50, and the local density approximation holds well in the nonmesonic decay of A hypernuclei. The Fn/rP ratios were evaluated by the direct comparison of the proton energy spectra with the simulated ones. ratios are smaller than unity and close to the calculated The results of the rn/rp ones by the conventional meson exchange model and the direct quark exchange model. However, no theoretical calculation proposed so far can explain both of ratios. nonmesonic decay widths and rn/rp

1. Introduction

Weak decay of A hypernucleus has two dominant decay modes. One is mesonic decay, in which a A hyperon in a nucleus decays into a nucleon with pion emission. (A + N n ) . The other is nonmesonic decay, in which a A hyperon in a nucleus interacts with other nucleon(s) and finally decay into nucleons (AN + N N ) . Due to the difference of the released energy of Qf,.,, 40 MeV in mesonic decay and the one of Qf,,, 176 MeV in nonmesonic decay, mesonic decay tends to be suppresed by Pauli blocking, and nonmesonic decay becomes dominant in heavy A hypernuclei. It has been indicated that the mesonic decay widths calculated by the distorted wave function are different from the ones calculated by the simple plane wave function 1,2, but there is no experimental data which can discreminate the theoretical models. ratio In nonmesonic decay, there are large discripancies of the between the experimental data and the calculated ones. The calculated

-

-

403

404

ones based on the conventional meson exchange models 1 3 J 4 and the direct quark exchange model give the smaller rn/rpratios than unity, but the existing experimental data are close to unity or larger with large error bars 3i4. The more precise data are seriously needed in order to understand the mechanism of nonmesonic decay. 2. KEK-PS E307 experiment

In KEK-PS E307 experiment, the lifetimes, T - mesonic decay branching ratios, and proton energy spectra of izC, i8Si, and nFe hypernuclei were measured with the (wf,Kf) reaction. The 1.05 GeVlc pion beam transfered by K6 beam line in KEK-PS was irradiated onto the experimental target of natural carbon, sillicon, and iron. The momenta of the outgoing kaons were analyzed by Superconducting Kaon Spectrometer (SKS)5, and the production of A hypernuclei was explicitly identified in the hypernuclear mass spectra. The decay particles emitted from the target were simultaneously detected by the decay counter systems located above and below the target. The decay counter system is comprised of scintillation counters for time measurement, a drift chamber with six planes for particle tracking, and thin slabs of scintillators for range measurement. The details of the present experimental setup and the lifetime measurement are described in Refs. 6 and 7. The T - mesonic decay branching ratios of A hypernuclei were obtained by the number of decay pions detected by the decay counter system with the correction of its detection efficiency (ex. (84 f 2)% for the carbon target) and acceptance (m. (27 f 1)%for the carbon target). The energy spectra of decay protons in the range from 40 MeV to 150 MeV were measured by the decay counter system.

3. Experimental results 3.1. Hypernuclear mass spectra Figure 1 shows the hypernuclear mass spectra and same ones with coincident pions and protons on A'C, i8Si, and AFe hypernuclei respectively. The hypernuclear mass spectra of i 2 C and i8Si were fitted by the combined function of the four or five gaussian functions for the dominant peaks and the polinomial function in the quasi-free region. The previous experiment (KEK-PS E140a) measured the hypernuclear mass spectra of i z C and i8Si with good energy resolution of 2 MeV in the Full Width at Half Maximum (FWHM) by the same condition using SKS '. In the present analysis,

405

each peak position and its relative intensity are assumed to be same as the ones measured by the previous experiment. The free parameters in the fitting are the intensity of the SA state and the parameters in the quasi-free region. The peak widths of the SA state are 4.8 MeV for the i 2 C hypernucleus, and 6.3 MeV for the i8Si hypernucleus in (FWHM). The branching ratios of r- mesonic decay were evaluated by the equation of b,- = Y,-/YHY(EDRD)-', where Y,- and YHYare the numbers of decay pion and identified hypernucleus obtained by the fitting. The symbols of E D and RD are the detection efficiency and acceptance of the decay counter, respectively. For AFe hypernucleus, each hypernuclear state is not separated, so the number of event in the gated window was used to evaluate the upper limit of the r- decay branching raio. 3.2. Results of 7

~ -

mesonic decay widths

Figure 2 shows the r- mesonic decay widths of i 2 C and A'B hypernuclei, which were converted to the decay widths by combining the results of the lifetime measurement published in Ref. 7 and the present results. Motoba et al. and Nieves et ad. calculated the r- mesonic decay width with the wave function obtained by the pion-nucleus optical potentials The calculated results with the distorted wave function agree with the present data, and it differs from the one with the plane wave ('Free'). The present data confirmed an enhancement of the mesonic decay width due to the distortion of the pion wave function for the first time. Other results are summarized in Table 1. ' I ~ .

Table 1. The T - mesonic decay branching ratios ( b W - ) obtained in the present analysis and the (total) mesonic decay branching ratios ( 6 , = b,- + b , o ) . The quoted errors are statistical and systematic, respectively. b-0 bm r,h ,, .i r .. ( x 10-2) (x10-2) i2C 9.9 f 1.1 f0.4 17.4 f5 . 7 f 0.8 27.3 f 1.1 f 5.8 0.113 f 0.014 f 0.005 FB 17.0f2.7f3.6 14.0f3.9f2.5 31.0f2.7f5.9 0.212f0.036f0.045 i8Si 3.6 f 0.8 f 0.2 8.3 f 8.3a) 11.9 f0.8 f 8.3a) 0.046 f0.011 f0.002 i7Al 3.2 f 0.8 f 1.5 2.0 f 2.0a) 5.2 f 0.8 f2.5O) 0.041 f 0.010 f 0.019 AFe < 1.2 (90% CL) 1.5 f 1.5 < 0.015 (90% CL) a) The ratios of rWopWwere assumed to be 2.30 for i8Si and 0.65 for i7Al with 100% errors, according to the theoretical calculations by Motoba et al. 2 .

b,

-

(xio-2)

406

Figure 1. Hypernuclear mass spectra by the " C ( d , K + ) , 28Si(s+,K+), and Fe(T+,K+) reaction. (a) inclusive, (b) with coincident protons ( E p > 40 MeV), and (c) with coincident pions ( E , > 12.5 MeV).

3.3. Nonmesonic decau widths and

rn/rpratios

Table 2 summarizes the results of nonmesonic decay widths and I',/rp ratios. The nonmesonic decay widths were evaluated by the branching ratios of mesonic decay and the total decay width as follows;

brim = 1 - (bx- +b,o), r n m = rtotbnrnr

where b,, b,- , and b,o are the branching ratios of mesonic decay, and b,, is the branching ratio of nonmesonic decay. The symbol of riotis the total decay width obtained by the lifetime measurement. Figure 3 illustrates the present results of nonmesonic decay widths with the previous experimental data and the calculated ones. It shows that the

407

nonmesonic decay width saturates around A-50. It means that the local density approximation holds well in nonmesonic weak decay. Figure 4 shows the measured proton energy spectra with the calculated ones. The proton energy spectra measured by the decay counter, RYP(EizP),are normalized to the number of measured proton per hypernuclear decay. On the other hand, Fbmos et al. calculated the number of proton emitted after weak decay in the unit of nonmesonic decay 'OJ1. A Monte-Carlo simulation for the decay counter is applied in order to obtain the calculated proton energy spectra, which can be compared with the experimental data. In the simulation, the decay protons are generated in the target according to the calculated energy spectra. Finally, the simulated spectrum is obtained by the correction of the detection efficiency and the nonmesonic decay branching ratio. It can be summarized as RFP(E7P) =< f2ZcoinNp(Ep) > &gbnm,where, the sym> means the proton energy spectra obtained by the bol < RcoinNp(Ep) simulation. The rn/rpratios were obtained by the fitting of the experimental data with the calculated ones, changing the rn/rPratio as a free parameter. The systematic errors were also evaluated by taking into account of the errors of the detection efficiency and the systematic error in the nonmesonic decay branching ratios. The present results of rn/rpratios are smaller than the ones previously published in Ref. 12 since the original proton energy spectra reported in Ref. 10 were updated by the authors l l . The error bars of the present ratios are smaller than the ones previously measured in BNL and KEK '. The present rn/rPratios are smaller than unity and close to the ones calculated by the conventional meson exchange potential I 3 J 4 and the direct quark exchange model l5

4. Summary

KEK-PS E307 experiment obtained the lifetimes, T - mesonic decay widths, and the rn/rpratios of medium-heavy A hypernuclei. The results of 7rmesonic decay confirmed an enhancement due to the distortion of the wave function by pion-nucleus optical potential for the first time. The nonmesonic decay widths saturate around A-50, and the local density approximation holds well. The rn/rPratios were obtained by the direct comparison of the experimental data with the simulated ones. Further theoretical and experimental study are needed to explain both of the nonmesonic decay widths and the rn/rpratios, simultaneously.

408

rn/rpratios

Table 2. Nonmesonic decay widths and experiment.

rnm/ rA i2C

ilB

0.828 f0.056 f0.066 0.89 f 0.15f 0.034 1.14 f 0.20~ 0.861 f 0.063f0.073 0.95 f 0.13f 0.044

rn/rp

“1N only” 0.87f0.09 f0.21 1.87 f 0.5927:$4 1.33+1.123

-

in the present

“1N and 2N” 0.602~:&2~:~~

-0.81

2.16 f 0.581E:iz4 1,04+0.593 -0.48

i*Si i’A1 A Fe

R

1.125f 0.067f0.106 1.230f 0.062f0.032 1.21 f 0.08

- mesonic decay widths of A hypernuclei

0.79+0.’3+0.25 -0.11-0.24

0.53+0.’3+0.25 -0.12-0.24

1,13+0.18+0.23

0.87+0.18+0.23

-0.15-0.22

%or

-0.15-0.21

,

Non-mesonic decay widths 01 A hypernuclei I , I , , ,,, I ,

. . ..

.

B

1.0

0.0 0.6

6

10

00

w

1

w

m

Mass number (A)

Figure 2. Comparison of the existing and Figure 3. Total nonmesonic decay widths present data with theoretical calculations of A hypernuclei. The close circles are the and Nieves et al. ’. present results. The open circles are preby Motoba et al. ‘Szym’ and ‘Noumi’ are the previous ex- vious experimental data in which the hyperimental data by Szymanski et al. and pernuclear production wag explicitly idenNoumi et al. 4 , respectively. The closed cir- tified. The open diamonds are experimencles are the present results. tal data by the p Bi and p U reactions 1611’. The plotted lines are the calculations by Itonaga et al.(solid) la, Ramos et al.(dashe-dotted) 19, and Alberico et al.(dashed) ’O. The open square shows a result with the direct quark exchange model in nuclear medium by Sasakiet al. 15.

+

+

References 1. J. Nieves and E. Oset, Phys. Rev. (347, 1478 (1993). 2. T.Motoba and K Itonaga, Prog. Theo. Phys. Suppl. No.117, 477 (1994). 3. J. J. Szymanski et al., Phys. Rev. C43,849 (1991). 4. H.Noumi et al., Phys. Rev. (352, 2936 (1995).

409 Proton Energy Spectra from A hypernuclear weak decay

(1N pmcm only) 0.020

0.10

EPw (MeV)

Figure 4. Comparison of the simulated energy spectra with the experimental data. The horizontal axis is the observed energy by the decay counter. The vertical axis is normalized to the number of protons per weak decay whose energy is higher than 40 MeV.

5. T. Fukuda et al., Nucl. Instr. and Meth. -4361, 485-496 (1995). 6. H. Bhang et al., Phys. Rev. Lett. 81, 4321 (1998). 7. H. Park et aE., Phys. Rev. (361, 054004 (2000). 8. T. Hasegawa et al., Phys. Rev. C53, 1210 (1996). 9. A. Sakaguchi et al., Phys. Rev. C43, 73 (1991). 10. A. Ramos et al., Phys. Rev. C55, 735 (1997). 11. A. Ramos et al., Preprint in nucl-th/0206036. 12. 0. Hashimoto et al., Phys. Rev. Lett. 88, 042503 (2000). 13. A. Parreno, A Ramos and C. Bennhold, Phys. Rev. C56, 339 (1997). 14. A. Parreno and A Ramos, Phys. Rev. C65, 015204 (2001). 15. K. Sasaki et al., Nucl. Phys. A669, 331-350 (2000). K. Sasaki et al., Nucl. Phys. A678, 455-456 (2000). 16. H. Ohm et al., Phys. Rev. C55, 3062 (1997). 17. P Kulessa et aE., Nucl. Phys. A639. 283c (1998). 18. K. Itonaga et al. Phys. Rev. C65, 034617 (2002). 19. A. Ramos et al., Phys. Rev. C50, 2314 (1994). 20. W. M. Alberico e t al., Phys. Rev. C61, 044314 (2000).

Weak decay of light s-shell hypernuclei i H , ;He and :He

H. OUTA for KEK-PS E167/E462 COLLABORATION Muon Science Lab., RIKEN, Wako, Japan E-mail: [email protected] Results of old hypernuclear weak decay experiment for AH and :He (E167) are summarized from a renewed interest. From the accurate measurements of the pi-masonic weak decay widths, we found an evidence for the existence of an inner repulsion core in A-nucleus interaction. Old values of mon-mesonic weak decay(NMWD) widths are also updated. Recently we are carrying out n+p and n+n coincidence measurement of :He produced via the 6Li(7r+, K + ) reaction to settle a long standing puzzle on the ratio of partial decay widths, rn/rp r(hn -+ n n ) / r ( A p + n p ) in the NMWD of A hypernuclei. Although results are still preliminary, we found that the ratio is significantly smaller than unity, as theory suggests. Preliminary results of this new experiment are summarized.

1. Introduction

The dominant weak decay modes of A hypernucleus are as follows: one is the A decay into a pair of a nucleon and a pion (A + p T - or A + n TO ), and the other is the A decay with a neighboring nucleon into two nucleons (A p + n p or A n -+ n n). The former process is called mesonic decay and the latter one is called non-mesonic weak decay(NMWD). We will denote the partial rate of each process as follows:

+

+

+

+

A-+n+no

+

+

rno

A + n + n + n rn

rtota1

1 =THY

(1)

where T H Y is the lifetime of A hypernucleus. Thus the detector system of the complete weak decay measurement must have sensitivity to all the decay products: p / n / r / y from T O . 1.1 Test of the A-nucleus potential In recent works, the existence of a central repulsion in the hyperon-nucleus potential has been discussed by many authors. The strength of long-range 410

41 1

attraction of the YN interaction is much weaker than that of the N N interaction and it is almost counterbalanced by the short-range repulsion. Reflecting this situation, there remains inner repulsion also in the hyperonnucleus potential which is constructed from the YN effective interaction using the folding procedure. This effect can be detected most distinctly in the case of very light ( A = 4,5) hypernuclear systems. A hyperon is pushed outward from a core nucleus due to this repulsion. Consequently, the overlap of the wave function of the hyperon with the nucleus is reduced. no

40

,.-

0.0

.*

-Isle

-.--

V

%H

+P %e+n

h

,'

V

-

2-20

%e+p

,I

-40

o a -0.2

-Isle

pot ---SGpot

-0.4 -0.6

4

'He Figure 1. Decay scheme of the s-mesonic decay of i H and ;He. Charge symmetric features can be observed by comparing the mesonic decay of AH and iHe.

wf

r (fm)

Figure 2. Comparison of A radial wave functions, and a - A folding potentials, for ;€I calculated with single-gaussian (SG) and Isle interactions taken from l .

Fig. 1 represents the mesonic weak-decay scheme of $2H and :He. When we use a A-nucleus potential with an inner repulsive core, as shown by the solid line in Fig. 2, the two-body decay widths of A=4 A hypernuclei become smaller due to the quenching of the overlap of the wave functions of the A and the final nucleon, which must be inside of 4He. When we pay attention to the ratio of widths for two-body decay to three-body decay, we see a large effect coming from the difference in the A-nucleus potentials. In order to measure the .rr-mesonic decay widths, not only a lifetime measurement but also branching ratio measurements are required. 1.2 Spin/isospin dependence of the non-mesonic decay process Since both AH and :He are known to have J"=O+, they form a unique system to test the spin/isospin dependence of the non-mesonic decay process. Their non-mesonic decay widths can be expressed as follows 2;

rnm($2H) = ( 3%i+

2Rpo) XP4/6

%o+

&Wn(",e) = ( 2%0+ 3Rp1-k Rpo) xp4/6 rnpn (i He) = ( 3Rn1+ %of 3Rp1 Rpo) x p 5 / 8

+

(2)

412

In these equations, p4 and p5 denote the mean nucleon density at the A position for A=4 and A=5 A hypernuclear systems, respectively. Partial decay rates are given as R N S ,where subscript N means a neutron or proton stimulated process and S is the spin of the initial state. If the AI=1/2 rule holds in the non-mesonic decay process, R,o can be replaced by 2RP0 '. Here, we want to stress several important points required for a total understanding of the non-mesonic decay process in s-shell hypernuclei: (1) Precise measurement of the non-mesonic decay widths of all the s-shell hypernuclei will reveal the spin/isospin-dependence of the decay process. (2) The total decay width is naively considered to be proportional to the overlap of A and nucleon wave functions. Thus it is very sensitive to the A-nucleus potential; whereas p4 and p 5 calculated from the single-range gaussian (SG) potential are respectively 0 . 2 3 ~ and 0 0 . 4 2 ~ 0(PO is the nuclear saturation density), they are reduced to 0 . 1 4 ~ 0and 0 . 2 1 ~for~ the the Anucleus potential with an inner repulsive core (Isle potential) ll4. (3) There is no direct measurement of the non-mesonic decay width of i H . It is estimated by theoretical calculation of the mesonic process from the =0.36*0.13 for i H It missing-number measurement of (I'nm+I'no)/l?Tis very sensitive to theoretical assumptions about the mesonic decay widths. 'i5.

2. E167: i H and :He mesonic decay and NMWD widths In the experiment E167, we measured the weak decay widths of i H and :He formed via 4He(stopped K-,s-)iHe and 4He(stopped K-,so)iH reactions, respectively. We measured (1) the lifetime of iH and :He and (2) the branching ratios of s-,TO and proton emission from the decay of :He with high accuracy. For example, Fig. 3 shows the ;He peak formation region of 4He(stopped K - , s - ) spectra with decay s- and no coincidence. The ;He peak is cleanly separated not only in the inclusive spectrum but also in n-decay coincidence spectra, which facilitate the precise determination of the pionic decay branching ratio analysis. Since the details of the experimental method and analysis are given elsewhere6, here we will summarize only the results of the experiment in Table.l.

2.1 Mesonic decay widths of i H and ;He From a naive consideration of Fig. 1, the following relations are expected to hold: rno(A)/rn(A) = 0.56 l?no(iHe)/I'n- (;H) (3) rn-( i H ; three body). r n - (:He> N

Our results in Table 1 are consistent with these expectations.

413

Table 1: Various weak decay widths of ;He and iH in units of the free-A decay width (FA). For the ;He decay, results of Zeps et al. lo are also listed. Other experimental results are utilized for quantities marked with '*'. 7i'

Decay widths of ;He Decay Results ZepslO rtotal/rA 1.03::;: 1.07f0.11

Figure 3. Both A- (open circles) and T O tagged(c1osed circles) (Ks&,ped,~-) spectra are overlaid on the inclusive spectrum (histogram)

Decay widths of i H Decay Results rtotal/I'A 1.36?::::

Figure 4. Comparison of the mesonic decay widths with theoretical calculations The ordinate is the deviation of experimental minus calculated value in units of the present experimental error.

'lg.

The mesonic decay widths of s-shell A hypernuclei were first calculated by Dalitz l l . Recently Motoba et al. and Kumagai-Fuse et al. independently calculated the mesonic decay widths. Both calculations were carried out for two-types of A-nucleus potential; one has the simple onerange-gaussian (ORG) shape and the other (Isle 13~1or YNG 9, has an inner repulsive core and an outer attractive pocket in the potential, as shown in Fig. 2. Results of the calculations for A=4 nuclei are given in Fig. 4. In the figure, the ordinate is the difference of the experimental and calculated values in units of the experimental error of the present experiment. A l2l9

414

dashed line represents the result for the ORG A-nucleus potential whereas a solid line corresponds to the potential with an inner repulsive core. The calculation by Motoba et al. tends to underestimate the decay widths for the two-body decay channel. Kumagai et al. claim that the disagreement between the two theoretical results arises from the requirement of antisymmetrization of the wave functions in the final state. Only the calculation by Kumagai et al. for a central repulsion can reproduce all the results within fla error. The existence of an inner repulsive core in the A-nucleus interaction is experimentally established for the first time. 2.2 Spin/isospin dependence of NMWD width Concerning the NMWD width of ;H, the only available data

is

Up to now, very old experimental data and theoretical calculations were used t o estimate the mesonic decay widths. From Eq. (4),rnm(;H) can be written as:

For this estimate, we utilized Kumagai's calculation of r,o with the Isle potential. This is very reasonable because we naively consider from Fig. 1 that PTo(;H)/rT- (;He) rTo(A)/rT(A) = 0.56. In the old estimation, Dalitz assumed very small F T o / r T - for i H based on the old bubble chamber data for the same ratio in ;He decay. It has been misbelieved for a long time that Fnm(;H) 2Fnm(;He). As shown in Table 1, the upda.ted nonmesonic decay widths of i H and ;He have become close t o one another. We have found that the non-mesonic weak decay of i H e predominantly takes place from Ap -+ np process. In the recent counter experiments for :He and i2C, fairly large (-1) rn/rpratios were reported 3!14 for these spin/isospin-saturated nuclei. The present result for ;He, rn/rP < 0.34, is small compared t o these values even when we take into account the difference in nucleon numbers (two protons and one neutron in :He) which can be involved in the decay process. When we consider the partial decay widths in Eq. (2), R,o must be very small in order to consistently explain the NMWD widths of both ;He and :He. This means that the neutronstimulated decay process (An -+ nn) must take place predominantly from a spin-triplet An initial state.

-

-

415

3. E462: Exclusive measurement of the NMWD of :He Concerning the rn/rpratio of NMWD, most of the previous experiment reports the larger ratio of close or larger than unity whereas the theoretical calculations predict much smaller ratio. It is known as “puzzle of np-ratio” for a long time. In the experimental side, most of the experiments measured only protons and the widths of An + nn were deduced by the subtraction of the all the other decay processes. Thus the result might be much affected by the missing of proton caused by the re-scattering process of protons inside the nucleus(FS1) and/or the existence of the two-nucleon induced decay modes(ANN + NNN). Recently we are carrying out n+p and n f n coincidence measurement of :He produced via the 6Li(n+,K+) reaction (E462) to settle this long standing puzzle. Back-to-back two nucleon detection of n+p and n+n from -the NMWD of light hypernucleus and measuring those number ratio enables us to directly measure the rn/rpratio without suffering from the FSI effect. Figure. 5 shows the decay arm detector setup of E462. This is the first experiment which is sensitive to the all major decay product of hypernuclei(p,.rr-,n,y) and lifetime of :He is also measured. 3214315

Figure 5. Setup of the decay-coincidencecounter system. It consists of three coincidence arm placed for top/bottom/side of the 6Li target. Beam incoming timing is measured by T1. The T2 and T3 are high-resolution TOF counters which measures the timing of charged particles. Three 30cm thick neutron counter array(T4) were used to measure neutral particles.

Data taking is finished in 2002 and we are now analyzing the data. Preliminary results of this experiment are given in 5 contributions in this

416

proceedings16. See detail for them. Here their results are summarized: (1) Neutron spectrum from :He shows no peaking at the half of decay Qvalue, suggesting strong FSI and/or A N N + N N N contribution (Okada). (2) We succeeded both of n+p/n+n back-to-back coincidence measurement. The rn/rpratio is directly obtained as 0.44f0.11 (Kang). (3) Asymmetry of decay proton from the NMWD of polarized :He was measured with improved accuracy as anm = 0.09f0.08 (Maruta). (4) Lifetime and 7 ~ - mesonic decay width of :He are measured as 1/~=0.947fO.O37r~and rn- =0.350fO.O17r~ . Measured rlF-again suggest central repulsion in A - a potential but weaker than theoretical expectation (Kameoka) (5) The 7ro mesonic decay width of ;He was accurately measured for the first time as rTo =0.197*0.012r~ From the subtraction of r X - and r,o from the total decay rate, the total NMWD width is accurately measured as rnm=0.400f0.018~~(Ym). All of these results are 2-20 times accurate over the previous experiments. r,,(:He)Q and From eqn. 2, one can deduce the relation of F,,(:H)/ E ,O of ;He17. If Q > /3 then l&o/R@ in eqn. 2 must be smaller the rn/rp than l / ~Improved . accuracy future measurement of the NMWD width of A=4 hypernuclei will open a door to test the violation of AI=1/2 rule.

References 1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

I. Kumagai-Fuse, S. Okabe and Y. Akaishi, Phys. Lett. B 345 (1995) 386. R.H. Dalitz, Proc. of Int. Conf. on Hypernuclei Physics (1964), 147. J.J. Szymanski et al., Phys. Rev. C 43 (1991) 849. I. Kumagai-he, private communication M.M. Bloch et al., Proc. of Int. Conf. on Hypernuclei (1964), 63. H. Outa et al., Nucl. Phys. A547 (1992) 109c.; A585 (1995) 109c.; A639 (1998) 251. D. Bertrand et al., Nuc. Phys. B 16 (1970) 77. H. Outa, Hyperfine Interactions 103 (1996) 227. T. Motoba, Nucl. Phys. A 547 (1992) 115c. V. J. Zeps et al., Nucl. Phys. A639 (1998) 261. R. H. Dalitz and L. Liu, Phys. Rev. 116 (1959) 1312. T. Motoba et al., Nucl. Phys. A 534 (1991) 597. Y. Kurihaxa et al., Prog. Theor. Phys. 67 (1982) 1483. H. Noumi et al., Phys. Rev. C 52 (1995) 2936. 0. Hashimoto et d.,Phys. Rev. Lett. 88 (2002) 042502. S. Okada; B.H. Kang; T. Maruta; S. Kameoka; H. Yim, Five E462 experimental preliminary reports in these proceedings M. O h , Talk at HYP2003 conference

NEUTRON ENERGY SPECTRA FROM NON-MESONIC WEAK DECAY OF :He AND izC HYPERNUCLEI

S. OKADA Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan K.AOK1, T. FUKUDA, T. NAGAE, H. NOUMI, H. OUTA, P. K. SAHA, Y. SATO, M. SEKIMOTO AND A. TOYODA High Energy Accelerator Research Organization (KEK), Ibaraki 305-0801, Japan H. C. BHANG, J. I. HWANG, B. H. KANG, E. H. KIM, J. H. KIM, M. J. KIM, H. PARK AND H. J. YIM Department of Physics, Seoul National University, Seoul 151-742, Korea

0. HASHIMOTO, S. KAMEOKA, Y. MIURA, S. N. NAKAMURA, Y. OKAYASU, T. TAKAHASHI, H. TAMURA, K. TSUKADA AND T. WATANABE Department of Physics, Tohoku University, Sendai 980-8578, Japan T. MARUTA, M. NAKAMURA AND K. TANIDA Department of Physics, University of Tokyo, Tokyo 113-0033, Japan

S. AJIMURA AND Y. MIYAKE Department of Physics, Osaka University, Osaka 560-0043, Japan A. BANU GSI, Darmstadt D-64291, Germany We have measured neutron energy spectra emitted from the weak decay of :He and i z C produced via (n+,K+) reaction. The most serious problem in such a nucleon measurement is energy distortion due to the final state interaction (FSI). Furthermore, recently the 2N induced decay process, ANN + n N N , have been predicted in theoretical calculation. Both processes tend to enhance low energy region. While proton energy measurement suffers from energy loss in the target, the neutron energy measurement is advantageous to observe the shape of low energy part. The neutron energy spectrum from the lightest hypernucleus of ;He, which is most suitable for minimizing FSI effect, is measured for the first time. 417

418

1. Introduction Generally it is difficult to study weak interaction between two nucleons because its parity conserving part is masked by the strong interaction. The non-mesonic weak decay (NMWD) process of A hypernucleus, A'""+ n N , is unique tool to study weak interaction between baryons, because this strangeness non-conserving process is purely caused by weak interaction. Most simply, AN + n N reaction can be expressed as a pion re-absorption from A + NT decay inside nuclei called one-pion exchange model (OPE). According to the OPE model, it is expected that the ratio between partial decay widths of An 3 nn and Ap + n p , I'n/l?p, is close to 0. However, experimental results so far reported seem to indicate much larger rn/rF ratio, close to unity or even largerzi3. This discrepancy has stimulated much theoretical work: the heavy meson exchange model4, the two-pion exchange model5, and the direct quark model6. However, the experimental results have been suspected because they had too large uncertainties. This uncertainties mainly come from that the neutron wyas not observed directly, so as the rn had been deduced by the total decay width (I'tot = l / ~ ~ inverse y ; of the hypernuclear life time) and other partial decay widths as rn = Ftot - rF- rmesonic. There are two processes which caused difficulties of the nucleon measurement from hypernuclear weak decay. One is the final state interaction (FSI) between the emitted nucleons from NMWD and its residual nucleus. The other is the 2N induced decay process, ANN + n N N , which had been recently predicted in theoretical calculation'. Both processes tend to enhance low energy region in nucleon energy spectra. Since the decay proton is insensitive for low energy region (below about 30MeV) due to the energy loss in the thick target used to enhance statistics, rn must be overestimated in such a indirect estimation. While the importance of nucleon measurement for low energy region is pointed out because of FSI and 2N induced process, the measurement of neutron energy spectrum is attracted attention. Because neutron is sensitive for low energy part since neutron suffer no energy loss in the target. Recently the neutron energy spectra of i z C and igY is measured (KEK-PS E369)7. These had a large low energy component due to FSI and/or 2N induced process. Unfortunately it is difficult to distinguish between these two processes. For the most minimizing FSI effect available, we measured the neutron energy spectrum from NMWD of the lightest hypernucleus of :He for the first time (KEK-PS E462). In addition, that for i z C is also measured with high statistics using same setup (E508).

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2. Experimental Setup The present experiments (E462/E508) were performed at the K6 beam line of the KEK 12-GeV proton synchrotron (KEK-PS). The ;He and i2C hypernuclei were produced by the (7rr+,K+) reaction at 1.05 GeV/c on 6Li and 12C (active) target. The hypernuclear mass spectra was calculated by reconstructing momenta of incoming 7r+ and outgoing K + using the beam line spectrometer (QQDQQ) and the SKS spectrometer respectively. The neutral particles were determined by the neutron counter arrays which have 30cm thickness and charged particle veto counters installed before the neutron counters. The neutral particle identification (y and neutron) and the determination of neutron energy are performed by the timeof-flight(T0F) technique between start timing counter of incident beam and the neutron counter.

3. Analysis and Results The hypernuclear events are selected by gating the ground sttate region in the hypernuclear mass spectra for ;He and i2C 8 . In this gate region (for i2C), the 1/@ spectra of neutral particles with 2 MeVee a threshold is shown in Fig.1, where the neutron gate is corresponding to 5< En

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