Pion Polarizability Status Report (1709.05159v3)

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.