Compton Scattering on the Charged Pion and the Process γγ\to π^0 π^0

Abstract

The Compton scattering on a charged pion and the process γγ\to π^0π^0 are studied using the dispersion relations. Unknown parameters of the S-wave ππinteraction, represented as a board Breit-Wignar resonance, and a sum and a difference of the π^0 meson polarizabilities are found from a fit to the experimental data for the process γ+γ\to π^0+π^0. This fit gives α+β=0.98\pm 0.03 and α-β=-1.6\pm 2.2. The found parameters of the S-wave ππinteraction are used for the calculation of the cross section of the Compton scattering on π^{\pm} meson. The analysis of the obtained results shows that the experimental data for the elastic γπscattering in the energy region up to 1 GeV together with the data for the process γ+γ\to π^0+π^0 could be used both for a determination of the pion polarizability values with quite high accuracy and for study of the S-wave ππinteraction.