Pion Polarizability 2022 Status Report

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.