Cross sections for low-energy $π^-γ$ reactions

Abstract

We review the cross sections for low-energy $π^- γ$ reactions in the framework of chiral perturbation theory. Charged pion Compton scattering, $π^- γ\to π^-γ$, is considered up to one-loop order where the pion's internal structure enters through the difference of the electric and magnetic pion polarizability, $α_π- β_π$. The ongoing COMPASS experiment aims at measuring this important structure constant with high statistics using the Primakoff effect. In the same way, the reaction $π^- γ\to π^- π^0$ serves as a test of the QCD chiral anomaly (via the $γ3π$-coupling constant $F_{\gamma3π}$). Furthermore, we calculate the total cross sections for neutral and charged pion-pair production, $π^- γ\to π^- π^0π^0$ and $π^- γ\to π^-π^+π^-$, which are governed by the chiral $ππ$-interaction. Finally, we investigate the radiative (correction) process $π^- γ\to π^- γγ$ and calculate the corresponding two-photon mass spectrum. This information will be useful for analyzing the $π^-$ Primakoff scattering events with photons in the final state.