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

TL;DR

This paper reviews low-energy  ext{-} reactions of pions within chiral perturbation theory, providing theoretical cross sections and insights relevant for ongoing experiments measuring pion structure and QCD anomalies.

Contribution

It offers detailed calculations of cross sections for various  ext{-} reactions, including pion Compton scattering and multi-pion production, incorporating pion structure and chiral anomalies.

Findings

Calculated cross sections for  ext{-} reactions.

Analyzed pion structure effects via polarizability.

Provided spectra for radiative  ext{-} processes.

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 $F_{\gamma3\pi}$). 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.