Magnetic moment of the Delta(1232)-resonance in chiral EFT

The $\Delta(1232)$-isobar is the most distinguished and well-studied nucleon resonance. However, such a fundamental property as its magnetic dipole moment (MDM) has thusfar escaped a precise determination. The problem is generic to any unstable particle whose lifetime is too short for its MDM to be measurable in the usual way through spin precession experiments. A measurement of the MDM of such an unstable particle can apparently be done only indirectly, in a three-step process, where the particle is first produced, then emits a low-energy photon which plays the role of an external magnetic field, and finally decays. In this way the MDM of $\Delta^{++}$ is accessed in the reaction $\pi^+ p \to \pi^+ p \gamma$ while the MDM of $\Delta^+$ can be determined using the radiative pion photoproduction ($\gamma p \to \pi^0 p \gamma^\prime$). In this paper we will present a new chiral effective field theory calculation of the radiative pion photoproduction ($\gamma p \rightarrow \pi^0 p \gamma'$) in the $\Delta$-resonance region. This work is aimed at a model-independent extraction of the $\Delta^+$ magnetic moment from new precise measurements of this reaction. It also predicts the chiral behavior of $\Delta$'s magnetic moment, which can be used to extrapolate the recent lattice QCD results to the physical point.