A consistent dynamical model for pion-photoproduction

Abstract

Pion-photoproduction amplitude is calculated within a consistent isobar model already used to fix the Δ+ + (1232 MeV) parameters in pion-nucleon scattering and bremsstrahlung. This amplitude is expressed in terms of (physical) on-shell quantities and off-shell contributions coming from final state interactions. These latter are isolated in principal value integrals on the non-polar part of the pion-nucleon K-matrix, being the main effect of them to dress the bare form factors present in the γ N → Δ vertex. First, we hide the dressing into effective form factors getting at kγ2 = 0, GM = 2.97 ± 0.08 and GE = 0.055 ± 0.010 in full consistence with recent chiral effective field theory calculations. Then, different models to regularize the mentioned integrals are analyzed. We choose those better describing the non-resonant multipoles, in order to get model independent results for the resonant ones. Finally, we try to predict the bare form factors getting GM0 = 1.69 ± 0.02 and GE0 = 0.028 ± 0.008, which are consistent with recent lattice quark calculations and other more sophisticated dynamical models.