Pion Polarizabilities from $\gamma \gamma \to \pi \pi$ Analysis

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 $({\alpha }_1-{\beta }_1)$ for the charged pion by COMPASS at CERN to an accuracy of 10% by measuring the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ cross-section to an uncertainty of ~1%. Then the same polarizability, but for the ${\pi }^0$, is fixed to be $({\alpha }_1-{\beta }_1{)}_{{\pi }^0}=(-0.9\pm 0.2)\times {10}^{-4}$ fm${}^3$. By analyzing the correlation between uncertainties in the meson polarizability and those in $\gamma \gamma$ cross-sections, we suggest experiments need to measure these cross-sections between $\sqrt{s}\simeq 350$ and 600 MeV. The ${\pi }^0{\pi }^0$ cross-section then makes the $({\alpha }_2-{\beta }_2{)}_{{\pi }^0}$ the easiest helicity-two polarizability to determine.