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Nucleon resonances within a dynamical coupled-channels model of pi N and gamma N reactions

The nucleon resonances are investigated within a dynamical coupled-channels model of pi N and gamma N reactions up to the invariant mass W = 2 GeV. The meson-baryon (MB) channels included in the calculations are MB = pi N, eta N, K Lambda, K Sigma, and pi pi N that has pi Delta, rho N, and sigma N resonant components. The meson-baryon amplitudes T_{M'B',MB}(W) are calculated from solving a set of coupled-channels integral equations defined by an interaction Hamiltonian consisting of (a) meson-exchange interactions v_{M'B',MB} derived from phenomenological Lagrangian, and (b) vertex interactions N* --> MB for describing the transition of a bare excited nucleon state N* to a channel MB. The parameters of v_{M'B',MB} are mainly constrained by the fit to the data of pi N --> pi N in the low energy region up to W =1.4 GeV. The bare masses of N* and the N* --> MB parameters are then determined in simultaneous fits to the data of pi N --> pi N up to W =2.3 GeV and those of pi N --> eta N, K Lambda, K Sigma and gamma N --> pi N, eta N, K Lambda, K Sigma up to W = 2.1 GeV. The pole positions and residues of nucleon resonances are extracted by analytically continuing the meson-baryon amplitudes T_{M'B',MB}(W) to the complex Riemann energy surface. From the extracted residues, we have determined the N* --> pi N, gamma N, eta N, K Lambda, K Sigma transition amplitudes at resonance poles. We compare the resonance pole positions from our analysis with those given by Particle Data Group and the recent coupled-channels analyses by the Juelich and Bonn-Gatchina groups. Four results agree well only for the first N* in each spin-parity-isospin (J^P,I) channel. For higher mass states, the number of states and their resonance positions from four results do not agree well. We discuss the possible sources of the discrepancies and the need of additional data from new hadron facilities such as J-PARC.