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Simon Capstick Volker Crede Paul Eugenio Proceedings of the Workshop on the

Physics of Excited Nucleons

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editors Simon Capstick

Volker Crede Paul Eugenio Florida State University

Proceedings of the Workshop on the

Physics of Excited INucleons

Florida State University, Tallahassee, USA

1 2 - 1 5 October 2005

\[p World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONGKONG • TAIPEI • CHENNAI

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NSTAR 2005 Proceedings of the Workshop on the Physics of Excited Nucleons Copyright © 2006 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, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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V

The 10th workshop on The Physics of Excited Nucleons was hosted by the Florida State University in Tallahassee, Florida, October 12-15, 2005. This workshop was the latest of a series of successful conferences, which started at Florida State University in 1994, followed by Jefferson Lab (1995), the INT in Seattle (1996), George Washington University (1997), ECT* in Trento (1998), Jefferson Lab (2000), University of Mainz (2001), University of Pittsburgh (2002), and the LPSC in Grenoble (2004). A summary of the Baryon Resonance Analysis Group (BRAG) premeeting, held on October 11, is also included in this volume. The workshop was attended by about 90 scientists from about 15 countries. The goal of the meeeting was to bring together theoretical and experimental experts on all areas of physics relevant to baryon spectroscopy. The participants presented new experimental results in their talks, from facilities such as BES, BNL, ELSA, GRAAL, JLab, MAMI, and LEPS located all around the world. This unprecedented quality of the data produced by experiments at these facilities is enabling rapid advances in the field. Special emphasis was made on experimental programs designed to measure polarization observables. The participants shared their latest findings in plenary focus sessions on topics such as coupled-channel analysis, strange particle production, doubly-strange baryons (Cascades), polarization experiments and observables, and recent developments in the theoretical description of the spectrum and properties of baryons using lattice QCD, chiral symmetry restoration, coupled-channel unitarized chiral models, and the large Nc approach. A similar emphasis was made in 36 detailed and interesting talks given in two parallel sessions. Each focus session ended with a critical discussion of important issues involving that sessions' speakers and the rest of the participants. The valuable contributions to the success of the workshop of all of the speakers is gratefully acknowledged. We wish to thank all of our institutional sponsors: the Department of Physics, the College of Arts and Sciences, and the Office of Research at the Florida State University; Thomas Jefferson National Accelerator Facility and the US Department of Energy; the International Society of Technical Environmental Professionals (INSTEP); and the Tallahassee Convention and Visitors Bureau. We are grateful for the advice provided by the International Advisory Committee and the invaluable help of the Organizing Committee. We would like to give special thanks to: Loreen Kollar, for helping make this meeting happen; Eva Crowdis, who tirelessly resolved problems ranging from financial to culinary; Lorena Barahona, Sandy Heath, Nick Nguyen, and Son Nguyen

vi

for their hard work with logistics and shuttle services; Ken Ford for his invaluable help with graphics and photographs; Wlodzimierz Blaszczyk and David Caussyn for their expert help with our computing services; and our graduate students Lucasz Blasczyk, Shifeng Chen, Charles Hanretty, Mica Lyczek-Way, and Blake Sharin, who collected talks, prepared presentations, and provided shuttle services to and from the hotel, along with countless other duties. Without the efforts of every one of these people this meeting would not have been successful. Tallahassee, March, 2006 Simon Capstick, Volker Crede, Paul Eugenio

vii

NSTAR 2005 Workshop on the Physics of Excited Nucleons October 12-15, 2005 Florida State University, Tallahassee - USA

ORGANIZATION

LOCAL ORGANIZING COMMITTEE S. Capstick, V. Crede, and P. Eugenio Florida State University, USA

ORGANIZING COMMITTEE V. Burkert (JLab), D. Carman (Ohio), S. Dytman (Pittsburgh), M. Manley (Kent State), W. Roberts (JLab/Old Dominion/DOE), S. Schadmand (Jiilich), H. Schmieden (Bonn), R. Schumacher (CMU), E. Swanson (Pittsburgh), U. Thoma (Giessen), A. Thomas (JLab), L. Tiator (Mainz)

I N T E R N A T I O N A L ADVISORY C O M M I T T E E R. Beck (Bonn), C. Bennhold (GWU), B. Briscoe (GWU), J.-P. Chen (JLab), M. Giannini (Genova), L.-Y. Glozman (Graz), R. Gothe (South Carolina), K. Hicks (Ohio), F. Klein (Catholic), S. Krewald (COSY Jiilich), B. Krusche (Basel), T.-S.H. Lee (Argonne), V. Metag (Giessen), C. Meyer (CMU), V. Mokeev (Moscow State), T. Nakano (Osaka), B. Nefkens (UCLA), E. Oset (Valencia), M. Ripani (Genova), D.-O. Riska (Helsinki), D. Richards (JLab), M. Sadler (ACU), B. Saghai (Saclay), A. Sandorfi (BNL), S. Strauch (South Carolina), P. Stoler (RPI), T. Walcher (Mainz), D. P. Weygand (JLab), B. S. Zou (Beijing)

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CONTENTS

Foreword Organization

v vii

Plenary Talks Focus Session on Coupled-Channel Analysis Models for Extracting N* Parameters from Meson-Baryon Reactions T.-S. H. Lee

1

MAID Analysis Techniques L. Tiator

16

Meson Production on the Nucleon in the Giessen K-Matrix Approach H. Lenske

26

The Importance of Inelastic Channels in Eliminating Continuum Ambiguities in Pion-Nucleon Partial Wave Analyses A. Svarc

37

Phenomenological Analysis of the CLAS Data on DoubleCharged Pion Photo- and Electroproduction off Protons V. I. Mokeev

47

Gauge-Invariant Approach to Meson Photoproduction Including the Final-State Interaction H. Haberzettl

57

Session on Pentaquarks and Exotics, Recent Experimental Results, G D H Sum Rule The Status of Pentaquark Baryons V. D. Burkert

67

Recent BES Results from J/ip Decays Z. Guo for the BES Collaboration

80

Results from the GDH Experiment at Mainz and Bonn A. Braghieri

90

The Strangeness Physics Program at CLAS D. Carman for the CLAS Collaboration

98

Recent Results from the Crystal Barrel Experiment at ELS A U. Thoma

108

KK. and KT, Photoproduction in a Coupled Channels Framework 0. Scholten

118

Cascade Physics: A New Window on Baryon Spectroscopy J. Price

128

Focus Session on Polarization Polarization Observables in the Photoproduction of Two Pseudoscalar Mesons W. Roberts The Polarisation Programme at ELSA H. Schmieden Experiments with Frozen-Spin Target and Polarized Photon Beams at CLAS F. Klein The Crystal Ball at MAMI D. Watts

138

148

159

165

The GRAAL Collaboration: Results and Prospects C. Schaerf

176

CLAS: Double-Pion Beam Asymmetry S. Strauch

185

Focus session on developments in theoretical description of baryon spectrum, including lattice QCD and coupled-channel unitarised chiral models Dynamically Generated Baryon Resonances M. Lutz

195

Describing the Baryon Spectrum with \/Nc QCD R. Lebed

205

Towards a Determination of the Spectrum of QCD Using a Space-Time Lattice C. Morningstar Dynamical Generation of Jp A(1520) Resonance

= §

215

Resonances and the 225

S. Sarkar Parallel Talks Parallel Session P l - A Coupled-Channel Fit to 7rN Elastic and r\ Production Data W. Briscoe The Carnegie-Mellon University Program for Studying Baryon Resonance Photoproduction using Partial Wave Analysis M. Williams Multichannel Partial-Wave Analysis of KN Scattering H. Y. Zhang

236

240

244

Helicity Amplitudes and Electromagnetic Decays of Strange Baryon Resonances T. Van Cauteren

248

Progress Report for a New Karlsruhe-Helsinki Type PionNucleon Partial Wave Analysis S. Watson

252

Baryon Excitation Through Meson Hadro- and Photoproduction in A Coupled-Channels Framework: Chiral-SymmetryInspired Model A. Waluyo

256

Parallel Session P l - B Double-Polarization Observables in Pion-Photoproduction from Polarized HD at LEGS A. Sandorfi

260

Electroexcitation of the Pu(1440), £>i3(1520), 5 U (1535), and Fi 5 (1680) up to 4 (GeV/c)2 from CLAS Data /. G. Aznauryan

265

A Genetic Algorithm Analysis of N* Resonances D. G. Ireland Measurement of the N -> A+(1232) Transition at High Momentum Transfer by TT° Electroproduction M. Ungaro Measurement of Cross Section and Electron Asymmetry of the p(e,e'7r+)n Reaction in the A(1232) and higher resonances for Q2 < 4.9 {GeV/c)2 K. Park Pion-Nucleon Charge Exchange in the N*(1440) Resonance Region M. Sadler Parallel Session P l - C

271

277

281

286

Nucleon Resonance Decay by the K0I1+ R. Castelijns

Channel

292

Coupled Channel Study of K+A Photoproduction T.-S.H. Lee

298

Measurements of Cz, Cx for K+A and K+H° Photoproduction R. Bradford

302

Photoproduction of K*+A and K+Y±(1385) in the Reaction 7P -> K+An° at Jefferson Lab L. Guo K*° Photoproduction off the Proton at CLAS /. Hleiqawi Inclusive £~ Photoproduction on the Neutron via the Reaction 7 n (p) -•• K+ S - (p) J. Langheinrich

306

310

314

Parallel Session P 2 - A 5 = 0 Pseudoscalar Meson Photoproduction from the Proton M. Bugger

318

Photoproduction of Neutral Pion Pairs off the Proton with the Crystal Barrel Detector at ELSA M. Fuchs

324

Analyzing r]' Photoproduction Data on the Proton at Energies of 1.5-2.3 GeV K. Nakayama

330

Eta Photoproduction off the Neutron at GRAAL V. Kuznetsov T] Photoproduction off Deuterium /. Jaegle

336

340

XIV

A and S Photoproduction on the Neutron P. Nadel-Turonski

345

Parallel Session P2-B The Problem of Exotic States: View from Complex Angular. Momenta 349 Ya. Azimov Search for 6 + at CLAS in 771 -* @+K~ N. A. Baltzell

355

E+(1189) Photoproduction off the Proton M. Nanova

359

Photo-Excitation of Hyperons and Exotic Baryons in 7JV —> KKN Y. Oh

364

On the Nature of the A(1405) as a Superposition of Two States E. Oset

368

Channel Coupling Effects in Photo-Induced p — N Production 0. Scholten

372

Parallel Session P2-C The Influence of Inelastic Channels upon the Pole Structure of Partial Waves in the Coupled Channel Pion-Nucleon Partial Wave Analysis S. Ceci The Importance of TTN —> KK Process for the Pole Structure of the P l l Partial Wave T-matrix in the Coupled-Channel Pion-Nucleon Partial Wave Analysis B. Zauner S Spectroscopy in Photoproduction on a Proton Target at Jefferson Lab L. Guo

376

380

384

XV

Structure of the a-Meson and Diamagnetism of the Nucleon M. Schumacher

389

Excited Baryons in the 1/NC Expansion N. Matagne

393

Surprises in 2n° Production by ir~ and K~ at Intermediate Energies 397 B. M. K. Nefkens Brag Meeting Summary of the Baryon Resonance Analysis Group Meeting

406

S. Capstick Program of the Workshop

412

List of Participants

421

Author Index

429

1

MODELS FOR E X T R A C T I N G N* P A R A M E T E R S FROM M E S O N - B A R Y O N REACTIONS T.-S. H. LEE Physics Division, Argonne National Laboratory Argonne, IL 60439, USA Models for extracting the nucleon resonance parameters from the data of meson-baryon reactions are reviewed. The development of a dynamical coupledchannel model with 7r7riV unitarity is briefly reported.

1. Introduction In the past few years, very extensive data of electromagnetic meson production reactions have been accumulated at several electron and photon facilities. We now have a great opportunity to learn about the properties of nucleon resonances (AT*) from these data. The advance in this direction is an important step toward understanding the non-perturbative QCD. For example, the extracted N-N* transition form factors could shed lights on the dynamical origins of the confinement of constituent quarks and the meson cloud associated with baryons. Furthermore, it is important to resolve the long-standing "missing" resonance problem. To make progress, we need to perform amplitude analyses of the data to extract the A''* parameters. More importantly, we need to develop dynamical reaction models to interpret the extracted AT* parameters in terms of QCD. At the present time, the achievable goal is to test the predictions from various QCD-based hadron models such as the well-developed constituent quark model 1 and the covariant model based on Dyson-Schwinger Equations 2 . In the near future, we hope to understand the N* parameters in terms of Lattice QCD (LQCD). In the A region, both the amplitude analyses and reaction models have been well developed. We find that these two efforts are complementary. For example, all amplitude analyses 3 gave the result that the A^-A Ml transition strength is G M ( 0 ) = 3.18 ± 0.04. This value is about 40 % larger than the constituent quark model predictions G M ( 0 ) = \\r^gGp(Q) ~ 2.30.

2

This problem is resolved by developing dynamical models 4 ' 5 within which one can show that the discrepancy is due to the pion cloud which is not included in the constituent quark model calculations. The meson cloud effect on the N-A transitions has been further revealed in the study of pion electroproduction reactions. Some of the recent developments are : • Sixteen reponse functions oip(e, ep) at Q2 = 1 (GeV/c) 2 have been measured 6 at JLab. These data allow for the first time an almost model independent amplitude analysis. • LQCD calculations of the 7./V —> A form factors are becoming available7. • High precision data for exploring the meson cloud effects in the low Q2 region have been obtained at JLab and Mainz. • Double polarization data of d{^, TTN)N have been obtained at LEGS of BNL for improving our understanding of the pion photoproduction amplitudes on the neutron target. In the higher mass N* region, the situation is much more complicated because of many open channels. Any reliable analysis of the meson production data in this higher energy region must be based on a coupled-channel approach. The main objective of this contribution is to report the development in this direction. In section 2, we review most of the models of meson production reactions and also assess the recent coupled-channel analyses. In section 3, the development of a dynamical coupled-channel model with 7T7T./V unitarity will be reported. A summary is given in section 4. 2. Models of Meson Production Reactions Most of the models for meson production reactions can be derived by considering the following coupled-channel equations

Ta,b(E) = Va,b + J2 Va,c9c(E)Tc>b(E) ,

(1)

c

where a,b,c = 7AT, irN, r)N, uN, KY, nA, pN aN, ••. The interaction term is denned by Va,b = < a\V\b > with V = vb9 + vR.

(2)

Here vbg represents the non-resonant(background) mechanisms such as the tree diagrams illustrated in Figs. l(a)-(d), and vR describes the N* excitation shown in Fig. 1(e). Schematically, the resonant term can be written

3

\

T

s

I

(a)

\

\

(c)

(b)

N

*

(d)

Baryons Mesons

(e)

Fig. 1.

Tree-diagram mechanisms of meson-baryon interactions.

as

rjr,^ ) = NTE^f E-M?

(3)

'

where Tj defines the decay of the z'-th TV* state into meson-baryon states, and M° is a mass parameter related to the resonance position. The meson-baryon propagator in Eq.(l) is gc(E) = < c | g(E)

\c>,

with 9(E)

E-Ho =

+ ie p

g (E)-i7T6(E-H0),

(4)

where Ho is the free Hamiltonian and 9P(E)

(5)

E-HQ

Here P denotes taking the principal-value part of any integration over the propagator. If g(E) is replaced by gp(E) and Ta N* excitation strength. The phase $ is required by the unitarity condition and is determined by an assumption that relates the phase of the total photoproduction amplitude to the nN scattering phase shift. The UIM developed by the JLab-Yerevan collaboration 9 is similar to MAID. The main difference is that this model uses the Regge parameterization to define the amplitudes at high energies. Both MAID and JLab-Yeveran UIM have been applied extensively to analyze the data of 7r and r\ production reactions. However, their results must be further examined since the important two-pion production channels are not treated explicitly in thses two models. Attempt is being made to improve the JLab-Yeveran approach, as reported by V. Mokeev and I.G. Aznauryan in this proceeding. 2.2.

VPI-GWU

Model

The VPI-GWU model 11 (SAID) can be derived from Eq.(6) by considering three channels: 7./V, TTN, and 7rA. The solution of the resulting 3 x 3 matrix equation leads to TyNt7rN(SAID)

= AI{1 + iT„NtirN)

+ ART^N^N

,

(19)

6

where A/ — /i7Af,7riV ^

=

r;

,

(20)

^v2£A_

(21)

In actual analyses, they simply parameterize Ai and A^ as M ^ / = [W*AT,WJV] + 52PnZQla+n(z) n=0

^ = ^(fr)' Q £>«(^)">

,

(22)

(23)

where fco and qo are the on-shell momenta for pion and photon respectively, z = y/i$~+4m%/ko, QL{Z) is the legendre polynomial of second kind, En = Ey — ra^l + 712^/(2171^)), and pn and pn are free parameters. SAID calculates v^NnN of Eq.(22) from the standard PS Born term and p and u exchanges. The TTN amplitude T^N^N needed to evaluate Eq.(19) is also available in SAID. Once the parameters pn and pn in Eqs.(22)-(23) are determined, the N* parameters are then extracted by fitting the resulting amplitude T^JV.TTAT at energies near the resonance position to a Breit-Wigner parameterization(similar to Eq.(18)). Very extensive data of pion photoproduction have been analyzed by SAID. The extension of SAID to also analyze pion electroproduction data is being pursued. Similar to the UIM models described in the previous subsection, the results from SAID must also be examined because it also does not treat the important two-pion production channels explicitly. Furthermore, their parameterizations Eqs.(22)-(23) need to be justified or improved theoretically.

2.3.

Giessen

and KVI

Models

The coupled-channel models developed by the Giessen group 12 and the KVI group 13 can be obtained from Eq.(6) by taking the approximation K = V. This leads to a matrix equation involving only the on-shell matrix elements of V Ta,b(E) -> £ [ ( 1 + iV(E))-l)a,cVc,b(E).

(24)

7

The interaction V = vbg + vR is calculated from tree diagrams such as those illustrated in Fig.l. The Giessen group has recently completed an analysis with 7./V, nN, 2TYN, rjN, and uN channels. They find strong evidence for the TV* 7315(1675) in TT/V -> uN and Fi 8 (1680) in 7 iV -> uN. The KVI group has focused on the hyperon production reactions, as reported by O. Scholten in this proceeding. While the development of these two K-matrix coupled-channel models is an important step forward, their treatments of the important two-pion channels still need improvements. 2.4. KSU

Model

To derive the Kent State University (KSU) model 14 , we first note that the non-resonant amplitude tbg, denned by a hermitian vbg in Eq.(9), specifies a S-matrix with the following properties Sba%(E) = Sa>b - 2m6{E - H0)tbagb(E)

.^Wif(£VS'(^),

(25)

(26)

c

where the non-resonant scattering operator is J+J(E)

= 6a,c + ga(E)tbagc(E).

(27)

With some derivations, the S-matrix for the scattering T-matrix defined by Eqs.(7)-(14) can then be cast into following distorted — wave form Sa,b(E) = Yl ^T(E)Rc,d(E)J$

(E),

(28)

c,d

with RCtd(E) = Sc,d + 2iTcRd(E).

(29) (30)

Here we have defined TcRd(E) = Yfr]*;tC(E)[G(E)]i,jrN;,d(E).

(31)

The above set of equations is identical to that used in the KSU model of Ref.14. In practice, the KSU model makes the separable parameterizations TR ~ [ z i r i / 2 / ( £ - Mi - iri/2)] • • • \xnTn/2/(E - Mn - iTn/2)) and • • • exp(iXnAn). w (+) = exp(iXiAi) In recent years, the KSU model has been applied mainly for extracting the A* and E* resonances from the S = — 1 meson-baryon amplitudes. It

has also been used to analyze the data of K~p —> neutrals (K°n, 7r°n, 7r°S° • • •) from the Crystal Ball Collaboration. To make further progress in using this model to extract N* parameters, more theoretical input must be implemented to improve their separable parameterizations of u/+) and rpR

2.5. The CMB

Model

In 1970's a unitary multi-channel isobar model with analyticity was developed15 by the Carnegie-Mellon Berkeley(CMB) collaboration for analyzing the TTN data. The CMB model can be derived by assuming that the non-resonant potential vbg is also of the separable form of vR of Eq. (3) bg V

_rLr^

«. fc " E-ML

r

kaTH,b

+

E-MH-

[6)

The resulting coupled-channel equations are identical to Eqs.(7)-(11), except that tfb = 0 and the sum over N* is now extended to include these two distant poles L and H. By changing the integration variables and adding a subtraction term, Eq.(12) leads to CMB's dispersion relations ^i,j (s) = Y^ 7i,c^c(s)7j,c ,

(33)

Thus CMB model is analytic in structure which marks its difference with all K-matrix models described above. The CMB model has been revived in recent years by the Zagreb group 16 and a Pittsburgh-ANL collaboration 17 to extract the N* parameters from fitting the available empirical irN reaction amplitudes. However, the extension of the CMB model to also analyze the data of electromagnetic meson production reactions remains to be pursued. 2.6. Dynamical

Models

The dynamical models of meson-baryon reactions are the models which account for the off-shell scattering dynamics through the use of the integral equation Eq.(l) or its equivalence Eqs.(7)-(12). The off-shell dynamics is closely related to the meson-baryon scattering wavefuntions in the shortrange region where we want to map out the structure of N*. Thus the

9

development of dynamical models is an important step to interpret the extracted N* parameters. In recent years, the predictions from the dynamical models of Sato and Lee (SL)4 and the Dubna-Mainz-Taiwan (DMT) collaboration 5 are most often used to analyze the data in the A region. The SL model can be derived from Eqs.(7)-(12) by keeping only one resonance N* — A and two channels a,b = irN, 7 AT. In solving exactly the resulting equations the nonresonant interactions vJ>N vN and vJ*N yN are derived from the standard PV Born terms and p and u) exchanges by using an unitary transformation method. The DMT model also only includes nN and jN channels. They however depart from the exact formulation based on Eq.(l) or Eqs.(7)-(12) by using the Walker's parameterization Eq.(18) to describe the resonant amplitude. Accordingly, their definition of the non-resonant amplitude also differs from that defined by Eq.(9) : tbc9b in the right-hand side of Eq.(9) is replaced by the full amplitude Tc^. Furthermore, they follow MAID to calculate the non-resonant interaction vngN N from an energy-dependent mixture of PS and PV Born terms. Extensive data of pion photoproduction and electroproduction in the A region can be described by both the SL and DMT models. However, they have significant differences in the extracted electric E2 and Coulomb C2 form factors of the jN —> A transition. Both models show very large pion cloud effects on the jN —> A transition form factors in the low Q2 region. New data from JLab and Mainz will further test their predictions. The Ohio model 18 has also succeeded in describing the data in the A region. Despite some differences in treating the gauge invariance problem and the A excitation amplitude, its dynamical content is similar to that of SL and DMT models. Eqs.(7)-(12) are used in a 2-N* and 3-channels (nN, r)N, and 7rA) study 19 of TVN scattering in Su partial wave. This work illustrated the extent to which the quark-quark interactions in the constituent quark model can be determined directly by the TTN reaction data. Eqs.(7)-(12) have also been used to show that the coupled-channel effects due to nN channel are very large in u> photoproduction 20 and K photoproduction 21 . All N* identified by the Particle Data Group are included in these two dynamical calculations. The coupled-channel study of both the TTN scattering and 7 AT —> irN in Sn channel by Chen et al 22 includes TTN, r]N, and jN channels. Their nN scattering calculation is performed by using Eq.(l). In their -yN —> TTN

10

calculation, they neglect the jN —> rjN —-> TVN coupled-channel effect, and follow the procedure of the DMT model to evaluate the resonant term in terms of the Walker's parameterization (Eq.(18)). They find that four N* are needed to fit the empirical amplitudes in Sn channel up to W = 2 GeV. This approach is being extended to also fit the rcN —> TVN and 7/V —> TVN amplitudes in all partial waves. A coupled-channel calculation based on Eq.(l) has been carried out by the Julich group 24 for TVN scattering. They are able to describe the TVN phase shifts up to W = 1.9 GeV by including ivN, r]N, nA, pN and aN channels and 5 TV* resonances : P 33 (1232), 5n(1535), Sn(1530), 511(1650) and £>i3(1520). They find that the Roper resonance Pn(1440) is completely due to the meson-exchange coupled-channel effects. A coupled channel calculation based on Eq.(l) for both the ivN scattering and 7/V —> ivN up to W = 1.5 GeV has been reported by Fuda and Alarbi 23 . They include TVN, 7/V, rjN, and 7rA channels and 4 N* resonances : P 33 (1232), Pn(1440), 5n(1535), and £>i3(1520). They adjust the parameters of their model to fit the empirical multipole amplitudes in low partial waves. Much simpler coupled-channel calculations have been performed by using separable interactions. In the model of Gross and Surya 25 , such separable interactions are from simplifying the meson-exchange mechanisms in Figs l.(a)-(c) as a contact term like Fig. 1(d). They include only ivN and 7/V channels and 3 resonances: P 33 (1232), Pn(1440) and -Di3(1520), and restrict their investigation up to W < 1.5 GeV. To account for the inelasticities in P n and Du, the N* —» 7rA coupling is introduced in these two partial waves. The inelasticities in other partial waves are neglected. A similar separable simplification is also used in the chiral coupledchannel models 26,27 for strange particle production. There the separable interactions are directly deduced from the SU(3) effective chiral lagrangians. They are able to fit the total cross section data for various strange particle production reaction channels without introducing N* resonance states. In recent years, this model has been further extended by Lutz and Kolomeitsev28 to also fit the TVN scattering data. It will be interesting to explore the consequencies of their model in descrbing the electromagnetic meson production reactions. 3. Dynamical Coupled-channel model with 7T7riV unitarity All of the models described in section 2 do not account for all of the effects due to the TVTVN channels which contribute about 1/2 of the ivN and 7 N

11

71 p - > 7C7CN Effects of ititN cut 0.02

1

'

• 0.015

1

'

1

i

r

Unitary ItitN cal.

No Z-diagram

A

/

\

/

it

| 717CN

A cut

-

- • - .

/

\ ~—'' /

I

-

-

j It

A I\

,\

0.005

' i

rooo

-

\ ,

i

1600

1 1800

M^(MeV)

Fig. 2. Invariant mass distribution da/dM^+p of 7r+p —> -KTTN a t W = 1880 MeV. The results are from the dynamical coupled-channel model of Ref.29.

total cross sections in the higher mass N* region. Consequently, the N* parameters extracted from these models could have uncertainties due to the violation of TVKN unitarity condition. One straightforward way to improve the situation is to extend the Hamiltonian formulation of Ref.4 to include (a) p —• 7T7T and a —» mr decay mechanisms as specified in 1"V of Eq.(15), (b) v-mr for non-resonant nn interactions, (c) VMN,TT-KN for non-resonant MN —> TVKN transitions with MN = 7iV or nN, and (d) VT^N.-K-WN for non-resonant TTTTN —> 7r7riV interactions. Such a dynamical coupled-channel model has been developed recently by Matsuyama, Sato, and Lee 29 (MSL). The coupled-channel equations from this model can also be cast into the form of Eqs.(7)-(14) except that the driving term of Eq.(9) is replaced by

9. v:% + Za,b(E),

(35)

12

where rN



E — Ho — VnN:7rN

< a\Ev(E)\b

Vmr N ,TTTV N

(36)

> 6a,b

with F = Ty

+ VTTN^WN

= rA

(37)

Note that T,v(E) in Eq.(36) has been defined by Eq(14) for describing the propagator Eq.(13) of unstable channels 7rA, pN, and aN. Obviously Zafi(E) contains the non-resonant multiple scattering mechanisms within the rnvN subspace. It generates TTTTN unitarity cuts which cause numerical complications in using the driving term Va,b of Eq.(35) to solve the coupledchannel Eq.(9). We have employed the Spline-function method developed in Ref.30 to overcome this difficulty such that the resulting meson-baryon

yp->jc 7t p 1

i

'

'

1

'

1

-

0.0002

-

/; 3L\\

Sum

f! \* \

s •a

1/

"li

-

'

\

t^YN^MB^TUlN)

/ /

^r? t (yN -> N -xtnN) R

/

/

t

JiA, pN, ON

-7mN) x \