Pion Polarizability Status Report

TL;DR

This report reviews experimental measurements of charged pion polarizabilities, compares them with theoretical predictions from chiral perturbation theory, and discusses their significance in understanding QCD's chiral symmetry breaking.

Contribution

It provides a comprehensive status update on experimental determinations of pion polarizabilities and compares these results with theoretical models, highlighting consistency with chiral perturbation theory.

Findings

COMPASS and Mark-II measurements agree and match ChPT predictions.

Mainz measurement is inconsistent with dispersion relations and experimental data.

Results support pions as Goldstone bosons of QCD.

Abstract

The electric ${\alpha}_{\pi}$ and magnetic $\beta_{\pi}$ charged pion Compton polarizabilities are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD).They are directly linked to the phenomenon of spontaneously broken chiral symmetry within QCD and to the dynamics of the pion-photon interaction.The combination (${\alpha}_{\pi}-\beta_{\pi}$) was measured by:(1) CERN COMPASS via radiative pion Primakoff scattering (Bremsstrahlung) in the nuclear Coulomb field, ${\pi}^- Z \rightarrow {\pi}^-Z {\gamma}$, (2) SLAC PEP Mark-II via two-photon production of pion pairs, ${\gamma}{\gamma}\rightarrow{\pi}^+{\pi}^-$, and (3) Mainz Microtron via radiative pion photoproduction from the proton, ${\gamma}p\rightarrow{\gamma}{\pi}^+n$. COMPASS and Mark-II agree with one another:(1) ${\alpha}_{\pi}-\beta_{\pi}=4.0\times 10^{-4}fm^3$, (2) ${\alpha}_{\pi}-\beta_{\pi}=4.4 \times 10^{-4}fm^3$. The Mainz value (3) ${\alpha}_{\pi}-\beta_{\pi}=11.6 \times 10^{-4}fm^3$ is excluded here because a dispersion relations calculation using the Mainz value as input gives significantly too large ${\gamma}{\gamma} \rightarrow {\pi}^0{\pi}^0$ cross sections compared to DESY Crystal Ball data. COMPASS and Mark-II values agree well with the two-loop chiral perturbation theory ChPT prediction ${\alpha}_{\pi}-\beta_{\pi}=5.7\times10^{-4}fm^3$, thereby strengthening the identification of the pion with the Goldstone boson of QCD.