# Dynamical coupled-channel model of meson production reactions in the nucleon resonance region.

## Abstract

A dynamical coupled-channel 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 quark-gluon substructure of N* from the data. The model is based on an energy-independent 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 non-resonant MB{yields}M'B' and {pi}{pi}{yields}{pi}{pi} interactions, (c) vMB,{pi}{pi}N for the non-resonant MB{yields}{pi}{pi}N transitions, and (d) v{pi}{pi}N,{pi}{pi}N for the non-resonant {pi}{pi}N{yields}{pi}{pi}N interactions. By applying the projection operator techniques, we derive a set of coupled-channel equations which satisfy the unitarity conditions within the channel space spanned by the considered two-particle MB states and the three-particle {pi}{pi}N state. The resulting amplitudes are written as a sum of non-resonant 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/JA-58490

Journal ID: ISSN 0370-1573; PRPLCM; TRN: US0804854

- DOE Contract Number:
- DE-AC02-06CH11357

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Phys. Rep.; Journal Volume: 439; Journal Issue: 5-6 ; 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 coupled-channel 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 coupled-channel 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 coupled-channel 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 coupled-channel 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 coupled-channel 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 quark-gluon substructure of N* from the data. The model is based on an energy-independent 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 non-resonant MB{yields}M'B' and {pi}{pi}{yields}{pi}{pi} interactions, (c) vMB,{pi}{pi}N for the non-resonant MB{yields}{pi}{pi}N transitions, and (d) v{pi}{pi}N,{pi}{pi}N for the non-resonant {pi}{pi}N{yields}{pi}{pi}N interactions. By applying the projection operator techniques, we derive a set of coupled-channel equations which satisfy the unitarity conditions within the channel space spanned by the considered two-particle MB states and the three-particle {pi}{pi}N state. The resulting amplitudes are written as a sum of non-resonant 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 spline-function expansion for solving the resulting coupled-channel equations which contain logarithmically divergentone-particle-exchange 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 two-pion production observables. For completeness in explaining our numerical procedures, we also present explicitly the formula for efficient calculations of a very large number of partial-wave matrix elements which are the input to the coupled-channel equations. Results for two pion photo-production are presented to illustrate the dynamical consequence of the one-particle-exchange driving term Z{sup (E)}{sub M B, M' B'} of the coupled-channel 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 two-pion 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 coupled-channel analysis of all of available data of meson photo-production and electro-production are discussed.},

doi = {10.1016/j.physrep.2006.12.003},

journal = {Phys. Rep.},

number = 5-6 ; 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}

}