Compton Scattering on Pion and Pion Polarizabilities
  The Compton scattering on a charged pion is studied using the dispersion relations. Unknown mass, full width and decay width into \gamma \gamma of the sigma meson are found from a fit to the experimental data for the process \gamma+\gamma \to \pi^0+\pi^0. These parameters are used for the calculation of the cross section of the Compton scattering on the charged pion. The analysis of the obtained results shows that the data on the elastic \gamma\pion scattering in the energy region up to \sqrt{s}=1 GeV (together with the data on process \gamma\gamma \to \pi^0\pi^0) could be used both for a determination of the pion polarizability values with high precision and for research of the sigma meson. 
L.V. Fil'kov, V.L. Kashevarov (Lebedev Physical Institute, Moscow)