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Unitary model for the $γp \to γπ^0 p$ reaction and the magnetic dipole moment of the $Δ^+(1232)$

Radiative pion photoproduction in the $Δ(1232)$ resonance region is studied with the aim to access the $Δ^+(1232)$ magnetic dipole moment. We present a unitary model of the $γp \to γπN$ ($πN = π^0 p, π^+ n$) reactions, where the $πN$ rescattering is included in an on-shell approximation. In this model, the low energy theorem which couples the $γp \to γπN$ process in the limit of a soft final photon to the $γp \to πN$ process is exactly satisfied. We study the sensitivity of the $γp \to γπ^0 p$ process at higher values of the final photon energy to the $Δ^+(1232)$ 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 $Δ^+$ magnetic dipole moment.