Determination of $\pi^+-$ meson polarizabilities from the $\gamma\gamma->\pi^+\pi^-$ process

Abstract

A fit of the experimental data to the total cross section of the process $\gamma\gamma->\pi^+\pi^-$ in the energy region from threshold to 2500 MeV has been carried out using dispersion relations with subtractions for the invariant amplitudes, where the dipole and the quadrupole polarizabilities of the charged pion are free parameters. As a result, the sum and the difference of the electric and magnetic dipole and quadrupole polarizabilities of the charged pion have been found: $(alpha_1+\beta_1)=(0.18+0.11-0.02)10^(-4)fm^3$, $(alpha_1-\beta_1)=(13.0+3.6-1.9)10^(-4)fm^3$, $(alpha_2+\beta_2)=(0.133+- 0.015)10^(-4)fm^5$, $(alpha_2-\beta_2)=(25.0+0.8-0.3)10^(-4)fm^5$. These values agree with the dispersion sum rule predictions. The value found for the difference of the dipole polarizabilities is consistent with the results obtained from scattering of high energy $\pi^-$ mesons off the Coulomb field of heavy nuclei (Serpukhov (1983)) and from radiative $\pi^+$ photoproduction from the proton at MAMI (2005), while it is at variance with the calculations in the framework of chiral perturbation theory.