Fierz-complete NJL model study II: towards the fixed-point and phase structure of hot and dense two-flavor QCD

TL;DR

This paper investigates the phase structure of a Fierz-complete NJL model for two-flavor QCD at finite temperature and density, revealing fixed-point dynamics, symmetry breaking patterns, and the impact of diquark condensates on the phase boundary.

Contribution

It provides a detailed renormalization group analysis of a Fierz-complete NJL model, highlighting the role of fixed points and the influence of four-quark interactions on the QCD phase diagram.

Findings

Fixed point dynamics are governed by a one-dimensional subspace in the large-Nc limit.

At high chemical potential, diquark effects dominate and favor chiral symmetry restoration.

Considering a Fierz-complete interaction set shifts the phase boundary to higher temperatures.

Abstract

Nambu-Jona-Lasinio-type models are often employed as low-energy models for the theory of the strong interaction to analyze its phase structure at finite temperature and quark chemical potential. In particular at low temperature and large chemical potential, where the application of fully first-principles approaches is currently difficult at best, this class of models still plays a prominent role to guide our understanding of the dynamics of dense strong-interaction matter. In this work, we consider a Fierz-complete version of the Nambu-Jona-Lasinio model with two massless quark flavors and study its renormalization group flow and fixed-point structure at leading order of the derivative expansion of the effective action. Sum rules for the various four-quark couplings then allow us to monitor the strength of the breaking of the axial $U_{\rm A}(1)$ symmetry close to and above the phase boundary. We find that the dynamics in the ten-dimensional Fierz-complete space of four-quark couplings can only be reduced to a one-dimensional space associated with the scalar-pseudoscalar coupling in the strict large-$N_{\rm c}$ limit. Still, the interacting fixed point associated with this one-dimensional subspace appears to govern the dynamics at small quark chemical potential even beyond the large-$N_{\rm c}$ limit. At large chemical potential, corrections beyond the large-$N_{\rm c}$ limit become important and the dynamics is dominated by diquarks, favoring the formation of a chirally symmetric diquark condensate. In this regime, our study suggests that the phase boundary is shifted to higher temperatures when a Fierz-complete set of four-quark interactions is considered.