The effect of an imaginary part of the Schwinger-Dyson equation at finite temperature and density

TL;DR

This paper investigates how the imaginary part of the Schwinger-Dyson equation influences phase transitions at finite temperature and density, revealing its significance near tricritical points and its impact on the chemical potential.

Contribution

It demonstrates the importance of including the imaginary part in the Schwinger-Dyson equation for accurate phase transition analysis at finite temperature and density.

Findings

Imaginary part enhances the first order transition effect.

It shifts the tricritical point's chemical potential by about 200 MeV.

Imaginary part can be neglected away from tricritical points.

Abstract

We examined the effect of an imaginary part of the ladder approximation Schwinger-Dyson equation. We show the imaginary part enhances the effect of the first order transition, and affects a tricritical point. In particular, a chemical potential at a tricritical point is moved about 200(MeV). Thus, one should not ignore the imaginary part. On the other hand, since an imaginary part is small away from a tricritical point, one should be able to ignore an imaginary part. In addition, we also examined the contribution of the wave function renormalization constant.