Chiral effective-field theory in theΔ(1232)region. II. Radiative pion photoproduction

Abstract

We present a theoretical study of the radiative pion photoproduction on the nucleon ($\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\pi}N{\ensuremath{\gamma}}^{\ensuremath{'}}$) in the $\ensuremath{\Delta}$-resonance region, with the aim to determine the magnetic dipole moment (MDM) of the ${\ensuremath{\Delta}}^{+}(1232)$. The study is done within the framework of chiral effective-field theory, where the expansion is performed (to next-to-leading order) in the $\ensuremath{\delta}$ power-counting scheme, an extension of chiral perturbation theory to the $\ensuremath{\Delta}$-resonance energy region. We present the results for the absorptive part of the $\ensuremath{\Delta}$ MDM, as well as perform a sensitivity study of the dependence of $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\pi}N{\ensuremath{\gamma}}^{\ensuremath{'}}$ observables on the real part of the $\ensuremath{\Delta}$ MDM. We find that an asymmetry for circular polarization of the photon beam may provide a model-independent way to measure the $\ensuremath{\Delta}$ MDM.