U_A(1) Anomaly in Hot and Dense QCD and the Critical Surface

TL;DR

This paper investigates how the U_A(1) anomaly influences the chiral phase transition in hot and dense QCD, exploring the potential restoration of U_A(1) symmetry and its effects on the critical surface and the QCD critical end point.

Contribution

It combines Ginzburg-Landau theory and NJL model to analyze U_A(1) restoration effects on the critical surface in QCD at finite density, providing a quantitative fit to lattice results.

Findings

The critical surface shrinks near zero chemical potential with increasing density.

The critical end point may still exist due to potential expansion of the critical surface at higher densities.

Lattice data on eta' mass and topological susceptibility can test U_A(1) restoration effects.

Abstract

We discuss the chiral phase transition in hot and dense QCD with three light flavors. Inspired by the well known fact that the U_A(1) anomaly could induce first order phase transitions, we study the effect of the possible restoration of the U_A(1) symmetry at finite density. In particular, we explore the link between the U_A(1) restoration and the recent lattice QCD results of de Forcrand and Philipsen, in which the first order phase transition region near zero chemical potential (mu) shrinks in the quark mass and mu space when mu is increased. Starting from the Ginzburg-Landau theory for general discussions, we then use the Nambu--Jona-Lasinio model for quantitative studies. With the partial U_A(1) restoration modeled by the density dependent 't Hooft interaction, we fit the shrinking of the critical surface found in de Forcrand and Philipsen's lattice calculation at low mu. At higher mu, the critical surface might shrink or expand, depending on the scenarios. This raises the possibility that despite the shrinking of the critical surface at lower mu, the QCD critical end point might still exist due to the expansion at higher mu. In this case, very high precision lattice data will be needed to detect the back-bending of the critical surface with the currently available analytic continuation or Taylor expansion approaches. Lattice computations could, however, test whether the U_A(1) restoration is responsible for the shrinking of the critical surface by computing eta' mass or the topological susceptibility at small mu.