$\pi^+$ and $\pi^0$ Polarizabilities from {$\gamma\gamma\rightarrow\pi\pi$} Data on the Base of S-Matrix Approach

Abstract

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