Radiative pion photoproduction in covariant chiral perturbation theory

Abstract

We present a calculation of radiative pion photoproduction in the framework of covariant chiral perturbation theory with explicit $\Delta (1232)$ degrees of freedom. The analysis is performed employing the small scale expansion scheme adjusted for the $\Delta$ region. Depending on the channel, we include contributions up to next-to-next-to-leading order. We fit the available experimental data for the reaction $\gamma p\to \gamma p{\pi }^0$ and extract the value of the ${\Delta }^{+}$ magnetic moment. Errors from the truncation of the small scale expansion are estimated using the Bayesian approach. We compare our results both with the previous studies within the $\delta$-expansion scheme and with the $\Delta$-less theory. We also give predictions for radiative charged-pion photoproduction.

Comments: 50 pages, 35 figures. Treatment of the $\Delta$-resonance is improved by means of a more consistent choice of its renormalized mass in the complex mass scheme. The results have been updated accordingly