Radiative corrections to pion-nucleus bremsstrahlung

TL;DR

This paper calculates one-loop radiative corrections to virtual pion Compton scattering, crucial for precise extraction of pion polarizabilities from experimental data, including effects of pion structure and soft photon radiation.

Contribution

It provides analytical expressions for ${ m O}(\alpha)$ corrections to virtual pion Compton scattering amplitudes, incorporating pion structure effects and soft photon radiation, relevant for experimental analyses.

Findings

Radiative corrections can be up to -3% at low energies.

Derived analytical formulas for virtual Compton scattering amplitudes.

Included pion polarizability difference in correction calculations.

Abstract

We calculate the one-photon loop radiative corrections to virtual pion Compton scattering $\pi^- \gamma^* \to \pi^- \gamma$, that subprocess which determines in the one-photon exchange approximation the pion-nucleus bremsstrahlung reaction $\pi^- Z\to \pi^- Z \gamma$. Ultraviolet and infrared divergencies of the loop integrals are both treated by dimensional regularization. Analytical expressions for the ${\cal O}(\alpha)$ corrections to the virtual Compton scattering amplitudes, $A(s,u,Q)$ and $B(s,u,Q)$, are derived with their full dependence on the (small) photon virtuality $Q$ from 9 classes of contributing one-loop diagrams. Infrared finiteness of these virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $\lambda$. In the region of low $\pi^- \gamma$ center-of-mass energies, where the pion-nucleus bremsstrahlung process is used to extract the pion electric and magnetic polarizabilities, we find radiative corrections up to about -3% for $\lambda=5 $MeV. Furthermore, we extend our calculation of the radiative corrections to virtual pion Compton scattering $\pi^-\gamma^* \to \pi^- \gamma$ by including the leading pion structure effect in form of the polarizability difference $\alpha_\pi - \beta_\pi$. Our analytical results are particularly relevant for analyzing the data of the COMPASS experiment at CERN which aims at measuring the pion electric and magnetic polarizabilities with high statistics using the Primakoff effect.