Abstract
We analyze the amplitude of radiative charged pion photoproduction within the framework of heavy baryon chiral perturbation theory 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 in the $\ensuremath{\pi}N$ chiral Lagrangian at order ${p}^{3}$ are comparable with the contributions of the charged pion polarizabilities. As a result, it is necessary to take the effects of these low-energy constants 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 $\ensuremath{\gamma}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}$ system.
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