S-wave $\pi - \pi$ Scattering Lengths in the SU(2) NJL Model Beyond Mean-field Approximation

TL;DR

This paper calculates the S-wave pion-pion scattering lengths in the SU(2) NJL model beyond mean-field approximation, demonstrating how model parameters can be uniquely determined from scattering data.

Contribution

It extends the NJL model calculations of pion-pion scattering lengths beyond mean-field approximation and establishes a method to determine model parameters from scattering data.

Findings

Scattering lengths $a_0$ and $a_2$ are calculated to lowest order in $1/N_c$ expansion.

Model parameters can be uniquely determined using the universal curve of $a_0$ and $a_2$.

The approach links scattering data with NJL model parameter determination.

Abstract

The S-wave $\pi - \pi$ scattering lengths $a_0$ and $a_2$ are calculated to the lowest order of $1/N_c$ expansion in the general framework of SU(2) NJL model beyond mean-field approximation. It is shown that using the universal curve of $a_0$ and $a_2$ the four NJL parameters, i.e., the current quark mass $m_0$, the four fermion coupling constant $G$, the quark momentum cut-off $\Lambda_f$ and the meson momentum cut-off $\Lambda_b$, also the S-wave $\pi - \pi$ scattering lengths in NJL model can be uniquely determined.