The sign problem across the QCD phase transition

TL;DR

This paper investigates how the sign problem in QCD varies with temperature and chemical potential, analyzing the impact of the $U_A(1)$ anomaly and the chiral transition endpoint using a two-flavor NJL model.

Contribution

It provides a detailed study of the QCD sign problem across the phase transition, including effects of the $U_A(1)$ anomaly and the chiral endpoint, using a NJL model.

Findings

The sign problem strength varies with temperature and chemical potential.

The $U_A(1)$ anomaly influences the severity of the sign problem.

The interplay between the sign problem and the chiral transition endpoint is characterized.

Abstract

The average phase factor of the QCD fermion determinant signals the strength of the QCD sign problem. We compute the average phase factor as a function of temperature and baryon chemical potential using a two-flavor NJL model. This allows us to study the strength of the sign problem at and above the chiral transition. It is discussed how the $U_A(1)$ anomaly affects the sign problem. Finally, we study the interplay between the sign problem and the endpoint of the chiral transition.