# Compton Scattering off Pions and Electromagnetic Polarizabilities

## TL;DR

This paper reviews the theoretical and experimental status of pion electromagnetic polarizabilities, highlighting recent precise measurements that test chiral perturbation theory and deepen understanding of QCD's low-energy regime.

## Contribution

It provides a comprehensive review of pion polarizability measurements, theoretical derivations, and compares experimental results with chiral perturbation theory predictions.

## Key findings

- CERN COMPASS measurement agrees with ChPT predictions
- Charged pion polarizability uncertainties are reduced with recent data
- Pion polarizabilities help confirm the Goldstone boson nature in QCD

## Abstract

The electric ($\alpha_\pi$) and magnetic ($\beta_\pi$) Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the $\gamma\pi\to\gamma\pi$ Compton scattering angular distribution at back scattering angles and $\gamma\gamma\to\pi\pi$ absolute cross sections. Theory derivations are given of the $\gamma\pi\to\gamma\pi$ Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The $\pi^0$ polarizabilities were deduced from DESY Crystal Ball $\gamma\gamma\to\pi^0\pi^0$ data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering $\pi^- Z \to \pi^-Z\gamma$ at CERN COMPASS, (2) two-photon pion pair production $\gamma\gamma\to\pi^+\pi^-$ at SLAC Mark II, and (3) radiative pion photoproduction $\gamma p\to\gamma \pi^+ n$ from the proton at MAMI in Mainz. A stringent test of chiral perturbation theory (ChPT) is possible based on comparisons of precision experimental charged pion polarizabilities with ChPT predictions. Only the CERN COMPASS charged pion polarizability measurement has acceptably small uncertainties. Its value $\alpha_{\pi^\pm}-\beta_{\pi^\pm} = (4.0\pm 1.8)\times 10^{-4}\,\text{fm}^3$ agrees well with the two-loop ChPT prediction $\alpha_{\pi^\pm}-\beta_{\pi^\pm}=(5.7\pm 1.0)\times 10^{-4}\,\text{fm}^3$, strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD.