Pion Polarizability Status Report

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)SLACPEPMark-IIviatwo-photonproductionofpionpairs,${\gamma}{\gamma}\rightarrow{\pi}^+{\pi}^-$, and (3) Mainz Microtron via radiative pion photoproduction from the proton, $\gamma p\to \gamma {\pi }^{+}n$. COMPASS and Mark-II agree with one another:(1) ${\alpha }_{\pi }-{\beta }_{\pi }=4.0\times {10}^{-4}f{m}^3$, (2) ${\alpha }_{\pi }-{\beta }_{\pi }=4.4\times {10}^{-4}f{m}^3$. The Mainz value (3) ${\alpha }_{\pi }-{\beta }_{\pi }=11.6\times {10}^{-4}f{m}^3$ is excluded here because a dispersion relations calculation using the Mainz value as input gives significantly too large $\gamma \gamma \to {\pi }^0{\pi }^0$ cross sections compared to DESY Crystal Ball data. COMPASS and Mark-II values agree well with the two-loop chiral perturbation theory ChPT prediction ${\alpha }_{\pi }-{\beta }_{\pi }=5.7\times {10}^{-4}f{m}^3$, thereby strengthening the identification of the pion with the Goldstone boson of QCD.