Chiral and effective $U(1)_{\rm A}$ symmetry restoration in QCD

TL;DR

This paper investigates how the restoration of chiral and $U(1)_{A}$ symmetries occurs in QCD near the phase transition, emphasizing the role of topological effects and four-quark interactions at finite temperature.

Contribution

It provides a Fierz-complete analysis of four-quark interactions derived from QCD, exploring the impact of the 't Hooft coupling on symmetry restoration and phase transition universality.

Findings

Chiral transition in two-flavor QCD likely belongs to the $O(4)$ universality class.

The robustness of the results is tested against variations in the 't Hooft coupling.

Topological effects significantly influence the nature of the phase transition.

Abstract

The nature and location of the QCD phase transition close to the chiral limit restricts the phase structure of QCD with physical pion masses at non-vanishing density. At small pion masses, explicit $U(1)_{\rm A}$-breaking, as induced by a non-trivial topological density, is of eminent importance. It triggers the 't Hooft interactions and also manifests itself in the interplay of four-quark interactions at low momentum scales. In the present work, we perform a Fierz-complete analysis of the emergence of four-quark interactions from the QCD dynamics at finite temperature, subject to a given 't Hooft coupling at large momentum scales. The variation of the latter allows us to test the robustness of our findings. Taking an estimate of the effect of the topological running of the 't Hooft coupling into account, our analysis suggests that the chiral transition in QCD with two massless quark flavours falls into the $O(4)$ universality class.