pi pi scattering in a nonlocal Nambu -- Jona-Lasinio model

TL;DR

This paper develops a nonlocal Nambu-Jona-Lasinio model with Gaussian form factors to study pi pi scattering, successfully reproducing known low-energy theorems and scattering parameters consistent with experimental data.

Contribution

It introduces a nonlocal extension of the NJL model with Gaussian form factors and demonstrates its effectiveness in describing pi pi scattering phenomena.

Findings

The model satisfies the Weinberg relation.

Calculated scattering lengths agree with phenomenological data.

Results support the chosen form factor and model validity.

Abstract

We consider a nonlocal version of the Nambu and Jona-Lasinio model. The nonlocality is contained in the quark-antiquark bilinears of the four-quark vertices as a form factor of the Gaussian type. The model has three parameters which can be fixed in favour of the values of the pion mass, the pion decay constant f_pi, and the current quark mass. The pi pi scattering amplitude is obtained by calculating the quark box and the sigma-pole diagrams, where sigma is the scalar isoscalar meson. It is shown that this amplitude satisfies the well-known Weinberg relation. We obtain the s, p, d wave scattering lengths in all isotopic channels and the s wave slope parameters. The results are in satisfactory agreement with both phenomenological data and the basic requirements of low-energy theorems, thus supporting to the form factor used.