Dynamical coupled-channel model of meson production reactions in the nucleon resonance region.
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.
- Research Organization:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); JAPAN SOCIETY FOR PROMOTION OF SCIENCE
- DOE Contract Number:
- DE-AC02-06CH11357
- OSTI ID:
- 914942
- Report Number(s):
- ANL/PHY/JA-58490; PRPLCM; TRN: US0804854
- Journal Information:
- Phys. Rep., Vol. 439, Issue 5-6 ; Feb. 2007; ISSN 0370-1573
- Country of Publication:
- United States
- Language:
- ENGLISH
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