$\pi - \pi$ Scattering Lengths and Chiral Condensate in NJL Model

TL;DR

This paper calculates the S-wave pion-pion scattering lengths and chiral condensate within an extended NJL model, showing results consistent with experimental data and other theoretical approaches.

Contribution

It extends the NJL model beyond mean-field approximation to accurately compute scattering lengths and chiral condensate, aligning with experimental and lattice results.

Findings

Calculated $a_0^0$ and $a_0^2$ scattering lengths agree with experimental data.

Chiral condensate estimated around $-(250 \text{MeV})^3$, consistent with lattice and sum rule results.

Results support the validity of the extended NJL model in low-energy QCD phenomena.

Abstract

Within the general framework of SU(2) Nambu-Jona-Lasinio model beyond mean-field approximation, the S-wave $\pi - \pi$ scattering lengths $a_0^0$ and $a_0^2$ are calculated. The numerical results are in agreement with that analyzed from recent experiment $\pi N \to \pi \pi N$ data by using Chew-Low-Goebel technique, and the corresponding chiral condensate $<{\bar q}q>$ is around $-(250 {\rm MeV})^3$, which is close to the ones obtained from lattice and sum rules.