Pion polarizabilities from a γγ→ππ analysis

Here, we present results for pion polarizabilities predicted using dispersion relations from our earlier Amplitude Analysis of world data on two photon production of meson pairs. The helicity-zero polarizabilities are rather stable and insensitive to uncertainties in cross-channel exchanges. The need is first to confirm the recent result on (α₁−β₁) for the charged pion by COMPASS at CERN to an accuracy of 10% by measuring the γγ→π⁺π⁻ cross-section to an uncertainty of ~1\%. Then the same polarizability, but for the π⁰, is fixed to be (α₁−β₁)_π⁰=(0.9±0.2)×10⁻⁴ fm³. By analyzing the correlation between uncertainties in the meson polarizability and those in γγ cross-sections, we suggest experiments need to measure these cross-sections between √s≃350 and 600~MeV. The π⁰π⁰ cross-section then makes the (α₂−β₂)_π⁰ the easiest helicity-two polarizability to determine.