Pion Polarizability 2022 Status Report

TL;DR

This report reviews the current experimental and theoretical status of charged pion polarizabilities, highlighting recent measurements, ongoing experiments, and their implications for understanding pion structure within quantum chromodynamics.

Contribution

It provides a comprehensive overview of recent experimental results and theoretical calculations of pion polarizabilities, emphasizing the consistency of the COMPASS measurement with QCD predictions.

Findings

COMPASS measurement of pion polarizability agrees with ChPT predictions

Mainz value for polarizability is inconsistent with dispersion relations and experimental data

Ongoing experiments aim to refine polarizability measurements

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 characterize the induced dipole moments of the pion during ${\gamma}{\pi}$ Compton scattering. Pion polarizabilities affect the shape of the ${\gamma}{\pi}$ Compton scattering angular distribution.The combination $({\alpha}_{\pi} - {\beta}_{\pi})$ was measured by: (1) CERN COMPASS via ${\pi} Z \rightarrow {\pi} Z {\gamma}$ radiative pion Primakoff scattering in the nuclear Coulomb field, (2) SLAC PEP Mark-II via two-photon production of pion pairs, ${\gamma} {\gamma} \rightarrow {\pi}^+ {\pi}^-$, and (3) Mainz Microtron MAMI via radiative pion photoproduction from the proton, ${\gamma} p \rightarrow {\gamma} {\pi}^+ n$. Ongoing and planned pion polarizability experiments (CERN COMPASS, BESIII at Beijing, JLab at Newport News) are also described. The Mark-II pion polarizability 95% confidence interval is approximately $0-11 \times 10^{-4} {fm}^{3}$, based on $({\alpha}_{\pi} - {\beta}_{\pi}) = (4.4 \pm 3.2) \times 10^{-4} {fm}^{3}$. The Mainz value $({\alpha}_{\pi} - {\beta}_{\pi}) = 11.6 \times 10^{-4} {fm}^{3}$ is excluded on the basis of a dispersion relations calculation which uses the Mainz value as input, and gives significantly too large ${\gamma} {\gamma} \rightarrow {\pi}^{0} {\pi}^{0}$ cross sections compared to DESY Crystal Ball data. To date, only the COMPASS polarizability measurement has acceptably small uncertainties. Its value $({\alpha}_{\pi} - {\beta}_{\pi}) = (4.0 \pm 1.8) \times 10^{-4} {fm}^{3}$ agrees well with the two-loop ChPT prediction $({\alpha}_{\pi} - {\beta}_{\pi}) = (5.7 \pm 1.0) \times 10^{-4} {fm}^{3}$, thereby strengthening the identification of the pion with the Goldstone boson of QCD.