A consistent dynamical model for pion-photoproduction

Pion-photoproduction amplitude is calculated within a consistent isobar model already used to fix the Δ++(1232MeV) 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 γN→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.