An important question about resonance extraction is how much resonance poles and residues extracted from data depend on a model used for the extraction, and on the precision of data. We address this question with the dynamical coupled-channel (DCC) m
odel developed in Excited Baryon Analysis Center (EBAC) at JLab. We focus on the P11 pi-N scattering. We examine the model-dependence of the poles by varying parameters to a large extent within the EBAC-DCC model. We find that two poles associated with the Roper resonance are fairly stable against the variation. We also develop a model with a bare nucleon, thereby examining the stability of the Roper poles against different analytic structure of the P11 amplitude below pi-N threshold. We again find a good stability of the Roper poles.
We show that two almost degenerate poles near the $piDelta$ threshold and the next higher mass pole in the $P_{11}$ partial wave of $pi N$ scattering evolve from a single bare state through its coupling with $pi N$, $eta N$ and $pipi N$ reaction chan
nels. This finding provides new information on understanding the dynamical origins of the Roper $N^*(1440)$ and $N^*(1710)$ resonances listed by Particle Data Group. Our results for the resonance poles in other $pi N$ partial waves are also presented.
Within a dynamical coupled-channels model which has already been fixed from analyzing the data of the pi N -> pi N and gamma N -> pi N reactions, we present the predicted double pion photoproduction cross sections up to the second resonance region, W
< 1.7 GeV. The roles played by the different mechanisms within our model in determining both the single and double pion photoproduction reactions are analyzed, focusing on the effects due to the direct gamma N -> pi pi N mechanism, the interplay between the resonant and non-resonant amplitudes, and the coupled-channels effects. The model parameters which can be determined most effectively in the combined studies of both the single and double pion photoproduction data are identified for future studies.
We have performed a dynamical coupled-channels analysis of available p(e,epi)N data in the region of W < 1.6 GeV and Q^2 < 1.45 (GeV/c)^2. The channels included are gamma^* N, pi N, eta N, and pi pi N which has pi Delta, rho N, and sigma N components
. With the hadronic parameters of the model determined in our previous investigations of pi N --> pi N, pi pi N reactions, we have found that the available data in the considered W < 1.6 GeV region can be fitted well by only adjusting the bare gamma^* N --> N^* helicity amplitudes for the lowest N^* states in P33, P11, S11 and D13 partial waves. The sensitivity of the resulting parameters to the amount of data included in the analysis is investigated. The importance of coupled-channels effect on the p(e,e pi)N cross sections is demonstrated. The meson cloud effects, as required by the unitarity conditions, on the gamma^* N --> N^* form factors are also examined. Necessary future developments, both experimentally and theoretically, are discussed.
Within the relativistic quantum field theory, we analyze the differences between the $pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered
perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
As a step toward performing a complete coupled-channels analysis of the world data of pi N, gamma^* N --> pi N, eta N, pi pi N reactions, the pi N --> pi pi N reactions are investigated starting with the dynamical coupled-channels model developed in
Phys. Rev. C76, 065201 (2007). The channels included are pi N, eta N, and pi pi N which has pi Delta, rho N, and sigma N resonant components. The non-resonant amplitudes are generated from solving a set of coupled-channels equations with the meson-baryon potentials defined by effective Lagrangians. The resonant amplitudes are generated from 16 bare excited nucleon (N^*) states which are dressed by the non-resonant interactions as constrained by the unitarity condition. The data of total cross sections and pi N and pi pi invariant mass distributions of pi^+ p --> pi^+ pi^+ n, pi^+ pi^0p and pi^- p --> pi^+ pi^- n, pi^- pi^0 n, pi^0 pi^0 n reactions from threshold to the invariant mass W = 2 GeV can be described to a very large extent. We show the importance of the coupled-channels effects and the strong interference between the contributions from the pi Delta, sigma N, and rho N channels. The large interference between the resonant and non-resonant amplitudes is also demonstrated. Possible future developements are discussed.
