Cross sections for low-energy ${\pi }^{-}\gamma$ reactions

We review the cross sections for low-energy ${\pi }^{-}\gamma$ reactions in the framework of chiral perturbation theory. Charged pion Compton scattering, ${\pi }^{-}\gamma \to {\pi }^{-}\gamma$, is considered up to one-loop order where the pion’s internal structure enters through the difference of the electric and magnetic pion polarizability, ${\alpha }_{\pi }-{\beta }_{\pi }$. The ongoing COMPASS experiment aims at measuring this important structure constant with high statistics using the Primakoff effect. In the same way, the reaction $\pi^- \gamma \to \pi^- \pi^0$servesasatestoftheQCDchiralanomaly(viathe$\gamma 3\pi$-couplingconstant$F_{\gamma3\pi}$). Furthermore, we calculate the total cross sections for neutral and charged pion-pair production, $\pi^- \gamma \to \pi^- \pi^0\pi^0$and$\pi^- \gamma \to \pi^-\pi^+\pi^-$, which are governed by the chiral $\pi \pi$-interaction. Finally, we investigate the radiative (correction) process ${\pi }^{-}\gamma \to {\pi }^{-}\gamma \gamma$ and calculate the corresponding two-photon mass spectrum. This information will be useful for analyzing the ${\pi }^{-}$ Primakoff scattering events with photons in the final state.