Extraction of the charged pion polarizabilities from radiative charged pion photoproduction in Heavy Baryon Chiral Perturbation Theory

We analyze the amplitude of radiative charged pion photoproduction within the framework of heavy baryon chiral perturbation theory (HBChPT) and discuss the best experimental setup for the extraction of the charged pion polarizabilities from the differential cross section. We find that the contributions from two unknown low energy constants(LECs) in the $\pi N$ chiral Lagrangian at order $p^{3}$ are comparable with the contributions of the charged pion polarizabilities. As a result, it is necessary to take these two LECs' effects into account. Furthermore, we discuss the applicability of the extrapolation method and conclude that this method is applicable only if the polarization vector of the incoming photon is perpendicular to the scattering plane in the center of mass frame of the final $\gamma-\pi$ system.