First estimates of the $(\alpha + \beta)^{\pi}$ from two--photon experiments

Abstract

We carry out the semi--model analysis of existing data on the angular distributions of the $\gamma\gamma\rightarrow\pi^+ \pi^- ,\ \pi^0 \pi^0$ reactions with purpose to obtain S-wave cross section and D-wave's parameters. In the first time we obtain from experiment the sum of electrical and magnetic pion polarizabilities: $(\alpha + \beta)^{\pi^+} = 0.28 \pm 0.07$ (MARK-II \cite{M2}), \ \ $(\alpha + \beta)^{\pi^+} = 0.38 \pm 0.05$ (CELLO \cite{CELLO}), \ \ $(\alpha + \beta)^{\pi^0} = 1.26 \pm 0.06$ (Crystal Ball \cite{CB}) \ \ in units of $10^{-42} \ cm^3$ ($e^2=4 \pi \alpha$).