Dynamical model for pion photoproduction in theΔregion

A phenomenological model for pion photoproduction is constructed incorporating the dynamics of pions, nucleons, and Δ’s. The importance of nonresonant background interactions for the elastic πN scattering and pion photoproduction is emphasized. The photoproduction amplitudes calculated in our model satisfy two-body unitarity, so that the requirement imposed by Watson’s theorem is automatically fulfilled. By fitting the amplitudes to data, M1 and E2 γN→Δ transition amplitudes are estimated, eliminating background contributions. The results are $A_{1/2}$(M1)=(-84±5)×${10}^{\mathrm{-}3}$ ${\mathrm{GeV}}^{\mathrm{-}1/2}$ and E2/M1=(3.7±0.4) %. Our M1 amplitude disentangled from the πN rescattering term is in good agreement with the quark model predictions. The sign and magnitude of our E2 amplitude are, however, incompatible with the existing quark models.