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

Abstract

We suggest the most model-independent and simple description of the $\gamma \gamma \to \pi \pi$ 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: $(\alpha -\beta {)}^C=(6.0\pm 1.2)\cdot 10^{-42}{\mathrm{cm}}^3$, $(\alpha -\beta {)}^N=(-1.4\pm 2.1)\cdot 10^{-42}c{m}^3$ (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.

Comments: LaTeX, 14 pages plus 6 figures (not included, available upon request) , ISU-IAP.Th93-03, Irkutsk