Dynamical coupledchannel model of meson production reactions in the nucleon resonance region.
Abstract
A dynamical coupledchannel model is presented for investigating the nucleon resonances (N*) in the meson production reactions induced by pions and photons. Our objective is to extract the N* parameters and to investigate the meson production reaction mechanisms for mapping out the quarkgluon substructure of N* from the data. The model is based on an energyindependent Hamiltonian which is derived from a set of Lagrangians by using a unitary transformation method. The constructed model Hamiltonian consists of (a) {Gamma}V for describing the vertex interactions N*{leftrightarrow}MB,{pi}{pi}N with MB={gamma}N,{pi}N,{epsilon}N,{pi}{Delta},{rho}N,{sigma}N, and {rho}{leftrightarrow}{pi}{pi} and {sigma}{leftrightarrow}{pi}{pi}, (b) v22 for the nonresonant MB{yields}M'B' and {pi}{pi}{yields}{pi}{pi} interactions, (c) vMB,{pi}{pi}N for the nonresonant MB{yields}{pi}{pi}N transitions, and (d) v{pi}{pi}N,{pi}{pi}N for the nonresonant {pi}{pi}N{yields}{pi}{pi}N interactions. By applying the projection operator techniques, we derive a set of coupledchannel equations which satisfy the unitarity conditions within the channel space spanned by the considered twoparticle MB states and the threeparticle {pi}{pi}N state. The resulting amplitudes are written as a sum of nonresonant and resonant amplitudes such that the meson cloud effects on the N* decay can be explicitly calculated for interpreting the extracted N* parameters in terms of hadron structure calculations. We present and explain in detail a numerical method based on amore »
 Authors:
 Publication Date:
 Research Org.:
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC); JAPAN SOCIETY FOR PROMOTION OF SCIENCE
 OSTI Identifier:
 914942
 Report Number(s):
 ANL/PHY/JA58490
Journal ID: ISSN 03701573; PRPLCM; TRN: US0804854
 DOE Contract Number:
 DEAC0206CH11357
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Phys. Rep.; Journal Volume: 439; Journal Issue: 56 ; Feb. 2007
 Country of Publication:
 United States
 Language:
 ENGLISH
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; MESONS; NUCLEONS; PRODUCTION; RESONANCE
Citation Formats
Matsuyama, A., Sato, T., Lee, T.S. H., Physics, Shizuoka Univ., Osaka Univ., and Jefferson Lab. Dynamical coupledchannel model of meson production reactions in the nucleon resonance region.. United States: N. p., 2007.
Web. doi:10.1016/j.physrep.2006.12.003.
Matsuyama, A., Sato, T., Lee, T.S. H., Physics, Shizuoka Univ., Osaka Univ., & Jefferson Lab. Dynamical coupledchannel model of meson production reactions in the nucleon resonance region.. United States. doi:10.1016/j.physrep.2006.12.003.
Matsuyama, A., Sato, T., Lee, T.S. H., Physics, Shizuoka Univ., Osaka Univ., and Jefferson Lab. Thu .
"Dynamical coupledchannel model of meson production reactions in the nucleon resonance region.". United States.
doi:10.1016/j.physrep.2006.12.003.
@article{osti_914942,
title = {Dynamical coupledchannel model of meson production reactions in the nucleon resonance region.},
author = {Matsuyama, A. and Sato, T. and Lee, T.S. H. and Physics and Shizuoka Univ. and Osaka Univ. and Jefferson Lab.},
abstractNote = {A dynamical coupledchannel model is presented for investigating the nucleon resonances (N*) in the meson production reactions induced by pions and photons. Our objective is to extract the N* parameters and to investigate the meson production reaction mechanisms for mapping out the quarkgluon substructure of N* from the data. The model is based on an energyindependent Hamiltonian which is derived from a set of Lagrangians by using a unitary transformation method. The constructed model Hamiltonian consists of (a) {Gamma}V for describing the vertex interactions N*{leftrightarrow}MB,{pi}{pi}N with MB={gamma}N,{pi}N,{epsilon}N,{pi}{Delta},{rho}N,{sigma}N, and {rho}{leftrightarrow}{pi}{pi} and {sigma}{leftrightarrow}{pi}{pi}, (b) v22 for the nonresonant MB{yields}M'B' and {pi}{pi}{yields}{pi}{pi} interactions, (c) vMB,{pi}{pi}N for the nonresonant MB{yields}{pi}{pi}N transitions, and (d) v{pi}{pi}N,{pi}{pi}N for the nonresonant {pi}{pi}N{yields}{pi}{pi}N interactions. By applying the projection operator techniques, we derive a set of coupledchannel equations which satisfy the unitarity conditions within the channel space spanned by the considered twoparticle MB states and the threeparticle {pi}{pi}N state. The resulting amplitudes are written as a sum of nonresonant and resonant amplitudes such that the meson cloud effects on the N* decay can be explicitly calculated for interpreting the extracted N* parameters in terms of hadron structure calculations. We present and explain in detail a numerical method based on a splinefunction expansion for solving the resulting coupledchannel equations which contain logarithmically divergentoneparticleexchange driving terms {sup (E)}{sub M B, M' B'} resulted from the {pi}{pi}N unitarity cut. This method is convenient, and perhaps more practical and accurate than the commonly employed methods of contour rotation/deformation, for calculating the twopion production observables. For completeness in explaining our numerical procedures, we also present explicitly the formula for efficient calculations of a very large number of partialwave matrix elements which are the input to the coupledchannel equations. Results for two pion photoproduction are presented to illustrate the dynamical consequence of the oneparticleexchange driving term Z{sup (E)}{sub M B, M' B'} of the coupledchannel equations. We show that this mechanism, which contains the effects due to {pi}{pi}N unitarity cut, can generate rapidly varying structure in the reaction amplitudes associated with the unstable particle channels {pi}{Delta}, {rho}N, and {sigma}N, in agreement with the analysis of Aaron and Amado [Phys. Rev. D13 (1976) 2581]. It also has large effects in determining the twopion production cross sections. Our results indicate that cautions must be taken to interpret the N* parameters extracted from using models which do not include {pi}{pi}N cut effects. Strategies for performing a complete dynamical coupledchannel analysis of all of available data of meson photoproduction and electroproduction are discussed.},
doi = {10.1016/j.physrep.2006.12.003},
journal = {Phys. Rep.},
number = 56 ; Feb. 2007,
volume = 439,
place = {United States},
year = {Thu Feb 01 00:00:00 EST 2007},
month = {Thu Feb 01 00:00:00 EST 2007}
}

A dynamical coupledchannel model is presented for investigating the nucleon resonances (N*) in the meson production reactions induced by pions and photons. Our objective is to extract the N* parameters and to investigate the meson production reaction mechanisms for mapping out the quarkgluon substructure of N* from the data. The model is based on an energyindependent Hamiltonian which is derived from a set of Lagrangians by using a unitary transformation method.

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