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) Γ V for describing the vertex interactions N * ↔ M B, ππN with M B = γN, πN, ηN, π∆, ρN, σN , and ρ ↔ ππ and σ ↔ ππ, (b) v 22 for the non-resonant M B → M ′ B ′ and ππ → ππ interactions, (3) v M B,ππN for the non-resonant M B → ππN transitions, and (4) v ππN,ππN for the non-resonant ππN → ππN 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 M B states and the three-particle ππN 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 divergent one-particle-exchange driving terms Z (E) M B,M ′ B ′ resulted from the ππN 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 (E) M B,M ′ B ′ of the coupled-channel equations. We show that this mechanism, which contains the effects due to ππN unitarity cut, can generate rapidly varying structure in the reaction amplitudes associated with the unstable particle channels π∆, ρN , and σN , in agreement with the analysis of Aaron and Amado [Phys. Rev. D13, 2581(1976]. 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 ππN 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.

Baryons as relativistic three-quark bound states

“…2.6 is solved in dynamical coupled-channel models which also take into account the dispersive parts from intermediate channels. Among those are the Sato-Lee model [70], which has been extended by the EBAC [71][72][73] and ANL/Osaka collaborations [74] and extensively applied to analyze pion photo-and electroproduction data. The Dubna-Mainz-Taiwan (DMT) [75,76], Valencia [77], Jülich-Bonn [78,79] and GSI models [80][81][82] have been developed along similar lines.…”

Electroexcitation of nucleon resonances from CLAS data on single pion electroproduction

“…[18]. Within dynamical reaction models [25][26][27][28], the meson-cloud contribution was identified as the source of this discrepancy. The importance of the pion (cloud) contribution for the γ * p → (1232)P 33 transition is confirmed also by the lattice QCD calculations [29].…”

“…In the case of the N (1440)P 11 and N (1535)S 11 , the mass ordering of these states, the large total width of N (1440)P 11 , and the substantial coupling of N (1535)S 11 to the ηN channel [20] and to strange particles [21,22] are indicative of possible additional qq components in the wave functions of these states [23,24] and/or of alternative descriptions. Within dynamical reaction models [25][26][27][28], the meson-cloud contribution is identified as a source of the long-standing discrepancy between the data and constituent quark model predictions for the γ * N → (1232)P 33 magnetic-dipole amplitude. The importance of pion (cloud) contributions to the transition form factors has also been confirmed by the lattice calculations [29].…”

Dynamical coupled-channels: The key to understanding resonances

“…[3,9] has already been used to study πN scattering and π photoproduction reactions as presented in this contribution. In the near future we expect to extend these studies and perform a consistent study of meson-baryon scattering, single meson electro(photo) production [13] and two-meson photoproduction.…”

“…In this work we will consider the one developed recently, MSL, and which is explained in great detail in Ref. [3].…”