Correction to Nambu-Jona-Lasinio model from QCD at the next-to-leading order

TL;DR

This paper derives the next-to-leading order corrections to the Nambu-Jona-Lasinio model from QCD, providing a systematic way to connect low-energy strong interactions with fundamental theory and analyzing their effects on phase transition properties.

Contribution

It introduces a systematic expansion method from QCD to compute higher order corrections to the NJL model and demonstrates its stability and impact on the chiral transition.

Findings

Higher order corrections can be systematically computed from QCD.

The corrections do not alter the critical temperature of the chiral transition.

The method applies to both Yukawa models and QCD in the chiral limit.

Abstract

We evaluate the next-to-leading order correction to the Nambu-Jona-Lasinio model starting from quantum chromodynamics. We show that a systematic expansion exists, starting from a given set of exact classical solutions, so that higher order corrections could in principle be computed at any order. In this way, we are able to fix the constants of the Nambu-Jona-Lasinio model from quantum chromodynamics and analyze the behavior of strong interactions at low energies. The technique is to expand in powers of currents of the generating functional. We apply it to a simple Yukawa model with self-interaction showing how this has a Nambu-Jona-Lasinio model and its higher order corrections as a low-energy limit. The same is shown to happen for quantum chromodynamics in the chiral limit with two quarks. We prove stability of the NJL model so obtained. Then, we prove that the correction term we obtained does not change the critical temperature of the chiral transition of the Nambu-Jona-Lasinio model at zero chemical potential.