Relation between the dipole polarizabilities of charged and neutral pions

Abstract

Using the fact that the contribution of the states with isospin I=0 in the difference of the amplitudes of the processes γγ->π^+π^- and γγ->π^0π^0 is very small, we have analyzed the dispersion sum rules for the difference between the dipole polarizabilities of the charged and neutral pions as a function of the σ-meson parameters. Then taken into account the current perturbation value of (α-β)_π^0=-1.9, we have found (α-β)_π^(+-)=9.4--8.2 for values of the σ-meson parameter within the region: M_s=400--550 MeV, Γ_s=400--600 MeV, Γ_{\s->γγ}= 0--3 keV. It has been shown that the value of the decay width of the h_1(1170)- meson into γπ^0 can be found if the difference (α-β)_π^(+-) is reliably determined from the experiment. Estimation of the optimal value of the decay width σ->γγhas given Γ_{\s->γγ}<0.7$keV.

6 pages, 2 figures, a few references added, misprints corrected