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

Abstract

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 ${\pi }^{-}\gamma \to {\pi }^{-}{\pi }^0$ serves as a test of the QCD chiral anomaly (via the $\gamma 3\pi$-coupling constant $F_{\gamma 3\pi }$). 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.

14, pages, 10 figures, submitted to EPJA

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