Complex singularities around the QCD critical point at finite densities

TL;DR

This paper investigates the complex singularities near the QCD critical point at finite densities using an effective mean field approach, analyzing the structure of partition function zeros and their influence on phase transitions.

Contribution

It provides a concrete analysis of Lee-Yang edge singularities in finite density QCD through a mean field effective theory near the critical point.

Findings

Identification of the crossover as the real part of the singularity

Explicit study of extrema behavior in the complex order parameter plane

Discussion of susceptibilities in the complex plane

Abstract

Partition function zeros provide alternative approach to study phase structure of finite density QCD. The structure of the Lee-Yang edge singularities associated with the zeros in the complex chemical potential plane has a strong influence on the real axis of the chemical potential. In order to investigate what the singularities are like in a concrete form, we resort to an effective theory based on a mean field approach in the vicinity of the critical point. The crossover is identified as a real part of the singular point. We consider the complex effective potential and explicitly study the behavior of its extrema in the complex order parameter plane in order to see how the Stokes lines are associated with the singularity. Susceptibilities in the complex plane are also discussed.