$π^+$ and $π^0$ Polarizabilities from {$γγ\rightarrowππ$} Data on the Base of S-Matrix Approach

Abstract

We suggest the most model-independent and simple description of the $γγ\rightarrowππ$ process near threshold in framework of S-matrix approach. The amplitudes contain the pion polarizabilities and rather restricted information about $ππ$ interaction. Application of these formulae for description of MARK-II \cite{M2} and Crystal Ball \cite{CB} data gives: $(α-β)^{C}=(6.0\pm 1.2)\cdot 10^{-42} {\rm cm}^{3}$, $(α-β)^{N}=(-1.4\pm 2.1)\cdot 10^{-42} cm^3$ (in units system $e^2 = 4 πα$) at the experimental values of $ππ$ scattering lengths. Both values are compartible with current algebra predictions.