Critical endpoint in the presence of a chiral chemical potential

TL;DR

This paper examines the reliability of using lattice QCD simulations with a chiral chemical potential to locate the critical endpoint in the QCD phase diagram, finding that model conflicts are resolved when appropriate regularization is applied.

Contribution

It demonstrates that proper regularization aligns PNJL model predictions with lattice QCD and DSE results, challenging the usefulness of chiral chemical potential simulations for locating the critical endpoint.

Findings

Regularization suppresses high-momentum quark contributions.

Model results conflict with lattice QCD and DSE without proper regularization.

Simulations with μ₅>0 are unlikely to reveal the critical endpoint.

Abstract

A class of Polyakov-loop-modified Nambu--Jona-Lasinio (PNJL) models have been used to support a conjecture that numerical simulations of lattice-regularized quantum chromodynamics (QCD) defined with a chiral chemical potential can provide information about the existence and location of a critical endpoint in the QCD phase diagram drawn in the plane spanned by baryon chemical potential and temperature. That conjecture is challenged by conflicts between the model results and analyses of the same problem using simulations of lattice-regularized QCD (lQCD) and well-constrained Dyson-Schwinger equation (DSE) studies. We find the conflict is resolved in favor of the lQCD and DSE predictions when both a physically-motivated regularization is employed to suppress the contribution of high-momentum quark modes in the definition of the effective potential connected with the PNJL models and the four-fermion coupling in those models does not react strongly to changes in the mean-field that is assumed to mock-up Polyakov loop dynamics. With the lQCD and DSE predictions thus confirmed, it seems unlikely that simulations of lQCD with $\mu_5>0$ can shed any light on a critical endpoint in the regular QCD phase diagram.