Connection between the Dipole Polarizabilities of Charged and Neutral π-Mesons

Abstract

In light of the contribution of the states with isospin I = 0in the difference of the amplitudes of the processes γγ → π+π− and 0 being very small, the dispersion sum rules for the difference betweenthe dipole polarizabilities of the charged and neutral pions are analyzed as a function of the σ meson’s parameters. Using the value of the chiral theory of perturbations for (α1 − β1)π0 = −1.9, (α1 − β1)π± =9.4−8.2 is found for the σ meson parameter within the region mσ = 400−550 MeV, Γσ = 400−600 MeV, Γσ→γγ = 0−3 keV. Estimated optimum value of decay width σ → γγ yields Γσ→γγ 0.7 keV.