Unitary model for the $\gamma p\to \gamma {\pi }^{0}p$ reaction and the magnetic dipole moment of the ${\Delta }^{+}(1232)$

Abstract

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

Comments: 23 pages, 18 figures