Meson-exchange model for pi N scattering and gamma N->pi N reaction

An effective Hamiltonian consisting of bare Delta <---->pi N, gamma N vertex interactions and energy-independent meson-exchange pi N <---->pi N, gamma N transition operators is derived by applying a unitary transformation to a model Lagrangian with N,Delta,pi,rho,omega and gamma fields. With appropriate phenomenological form factors and coupling constants for rho and Delta, the model can give a good description of pi N scattering phase shifts up to the Delta excitation energy region. It is shown that the best reproduction of the recent LEGS data of the photon-asymmetry ratios in gamma p-->pi(0)p reactions provides rather restricted constraints on the coupling strengths G(E) of the electric E2 and G(M) of the magnetic M1 transitions of the bare Delta <---->gamma N vertex and the less well-determined coupling constant g(omega NN) of omega meson. Within the ranges that G(M)=1.9+/-0.05, G(E)=0.0+/-0.025, and 7 less than or equal to g(omega NN)less than or equal to 10.5, the predicted differential cross sections and photon-asymmetry ratios are in an overall good agreement with the data of gamma p-->pi(0)p, gamma p-->pi(+)n, and gamma n-->pi(-)p reactions from 180 MeV to the Delta excitation region. The predicted M(1+) and E(1+) multipole amplitudes are also in good agreement with the empirical values determined by the amplitude analyses. The constructed effective Hamiltonian is free of the nucleon renormalization problem and hence is suitable for nuclear many-body calculations. We have also shown that the assumptions made in the K-matrix method, commonly used in extracting empirically the gamma N-->Delta transition amplitudes from the data, an consistent with our meson-exchange dynamical model. It is found that the helicity amplitudes calculated from our bare gamma N-->Delta vertex are in good agreement with the predictions of the constituent quark model. The differences between these bare amplitudes and the dressed amplitudes, which are closer to the empirical values listed by the Particle Data Group, are shown to be due to the nonresonant meson exchange mechanisms. Within the range 7 less than or equal to g(omega NN)less than or equal to 10.5 of the omega meson coupling favored by the data of the photon-asymmetry ratios in gamma p-->pi(0)p reactions, our values of the E2/M1 ratio for the gamma N-->Delta transition are (0.0+/-1.3)% for the bare vertex and (-1.8+/-0.9)% for the dressed vertex.