Unitary model for the γpγ°p reaction and the magnetic dipole moment of the δ{sup +}(1232)

Radiative pion photoproduction in the $\ensuremath{\Delta}(1232)$-resonance region is studied with the aim of accessing the ${\ensuremath{\Delta}}^{+}(1232)$ magnetic dipole moment. We present a unitary model of the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}N$ ($\ensuremath{\pi}N={\ensuremath{\pi}}^{0}p,\phantom{\rule{0.6em}{0ex}}{\ensuremath{\pi}}^{+}n$) reactions, where the $\ensuremath{\pi}N$ rescattering is included in an onshell approximation. In this model, the low-energy theorem which couples the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}N$ process in the limit of a soft final photon to the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\pi}N$ process is exactly satisfied. We study the sensitivity of the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\pi}}^{0}p$ process at higher values of the final photon energy to the ${\ensuremath{\Delta}}^{+}(1232)$ magnetic dipole moment. We compare our results with existing data and give predictions for forthcoming measurements of angular and energy distributions. It is found that the photon asymmetry and a helicity cross section are particularly sensitive to the ${\ensuremath{\Delta}}^{+}$ magnetic dipole moment.