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 \gamma \gamma->\pi^+\pi^- and \gamma\gamma->\pi^0\pi^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 \sigma-meson parameters. Then taken into account the current perturbation value of (\alpha-\beta)_\pi^0=-1.9, we have found (\alpha-\beta)_\pi^(+-)=9.4--8.2 for values of the \sigma-meson parameter within the region: M_s=400--550 MeV, \Gamma_s=400--600 MeV, \Gamma_{\s->\gamma\gamma}= 0--3 keV. It has been shown that the value of the decay width of the h_1(1170)- meson into \gamma\pi^0 can be found if the difference (\alpha-\beta)_\pi^(+-) is reliably determined from the experiment. Estimation of the optimal value of the decay width \sigma->\gamma\gamma has given \Gamma_{\s->\gamma\gamma}<0.7$keV.