πN scattering and γN → Nπ photoproduction within the unitary improved Born approximation

Abstract

Following the programme of describing consistently several processes where the isobar Δ(1232 MeV) nucleon resonance appears as an intermediate state, in this work we propose to unitarize our old improved Born approximation already used to describe successfully π+p elastic and radiative scattering, to treat pion photoproduction. First we add the effect of final state interactions and make a new determination of the mass, width and the coupling constant to the pion–nucleon state of the Δ resonance. Then extending the model for pion photoproduction and using the resonance parameters determined previously, we are able to define effective form factors (at k2γ = 0) for the γN → Δ vertex with values GM = 2.97 ± 0.08 and GE = 0.055 ± 0.010, by fitting the data for the M3/21+ and E3/21+ multipoles. These values are fully consistent with recent chiral effective field theory calculations, and using them we can predict satisfactorily the data for other multipoles and the photoproduction cross section. Finally, we intend a model-independent determination of the bare form factors making a dynamical dressing of the vertex, getting G0M = 1.69 ± 0.02, G0E = 0.028 ± 0.008 and R0EM = −1.67 ± 0.45%, which are compared with different quark models.