Fierz-complete NJL model study III: Emergence from quark-gluon dynamics

TL;DR

This paper investigates how low-energy effective models like NJL emerge from fundamental quark-gluon interactions using renormalization group flow analysis at finite temperature and density, revealing different dominant interactions and condensate formations.

Contribution

It demonstrates the dynamical emergence of NJL-type models from quark-gluon dynamics and explores the changing dominance of interaction channels at different densities.

Findings

Scalar-pseudoscalar interaction dominates at low density, indicating chiral symmetry breaking.

Finite-temperature phase boundary curvature aligns with lattice QCD results.

At high density, diquark condensates form, influenced by $U_A(1)$ breaking.

Abstract

Our understanding of the dynamics and the phase structure of dense strong-interaction matter is to a large extent still built on the analysis of low-energy models, such as those of the Nambu-Jona-Lasinio-type. In this work, we analyze the emergence of the latter class of models at intermediate and low energy scales from fundamental quark-gluon interactions. To this end, we study the renormalization group flow of a Fierz-complete set of four-quark interactions and monitor their strength at finite temperature and quark chemical potential. At small quark chemical potential, we find that the scalar-pseudoscalar interaction channel is dynamically rendered most dominant by the gauge degrees of freedom, indicating the formation of a chiral condensate. Moreover, the inclusion of quark-gluon interactions leaves a significant imprint on the dynamics as measured by the curvature of the finite-temperature phase boundary which we find to be in accordance with lattice QCD results. At large quark chemical potential, we then observe that the dominance pattern of the four-quark couplings is changed by the underlying quark-gluon dynamics, without any fine-tuning of the four-quark couplings. In this regime, the scalar-pseudoscalar interaction channel becomes subleading and the dominance pattern suggests the formation of a chirally symmetric diquark condensate. In particular, our study confirms the importance of explicit $U_{\mathrm{A}}(1)$ breaking for the formation of this type of condensate at high densities.