Pion polarizability in the Nambu–Jona-Lasinio model and possibilities of its experimental studies in Coulomb nuclear scattering

Abstract

The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model, where the quark loops (in the mean field approximation) and the meson loops (in the $1/{N}_{c}$ approximation) are taken into account. We show that quark loop contribution dominates because the meson loops strongly conceal each other. The sigma-pole contribution $({m}_{\ensuremath{\sigma}}^{2}\ensuremath{-}t{)}^{\ensuremath{-}1}$ plays the main role and contains strong $t$-dependence of the effective pion polarizability at the region $|t|\ensuremath{\ge}4{M}_{\ensuremath{\pi}}^{2}$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb nuclear scattering are estimated for the COMPASS experiment.