Pion Polarizability in the NJL model and Possibilities of its Experimental Studies in Coulomb Nuclear Scattering

TL;DR

This paper calculates the charge pion polarizability within the NJL model, highlighting the dominance of quark loops and the significant sigma-pole contribution, and discusses experimental prospects for observing these effects in Coulomb nuclear scattering.

Contribution

It provides a detailed calculation of pion polarizability in the NJL model, emphasizing the role of quark and meson loops and the sigma-pole effect, with implications for experimental detection.

Findings

Quark loop contribution dominates the polarizability.

Meson loops largely cancel each other out.

Sigma-pole contribution causes strong t-dependence.

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 $(m^2_\sigma-t)^{-1}$ plays the main role and contains strong t-dependence of the effective pion polarizability at the region $|t|\geq 4M_\pi^2$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb Nuclear Scattering are estimated for the COMPASS experiment.