Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach

TL;DR

This paper analytically investigates the QCD crossover at finite temperature and chemical potential using Dyson-Schwinger equations, deriving a model that aligns well with lattice results and depends on a single scale parameter.

Contribution

It introduces an analytical Dyson-Schwinger approach to study the QCD phase transition at finite temperature and chemical potential, connecting it with a NJL model and lattice data.

Findings

Derived a critical temperature dependence consistent with lattice results

Developed an NJL model from Dyson-Schwinger equations

Found the solution depends on a single fundamental scale

Abstract

We study QCD at finite temperature and non-zero chemical potential to derive the critical temperature at the chiral phase transition (crossover). We solve a set of Dyson--Schwinger partial differential equations using the exact solution for the Yang--Mills quantum field theory based on elliptical functions. We derive a Nambu-Jona--Lasino (NJL) model of the quarks and obtain a very good agreement with recent lattice computations regarding the dependence of the critical temperature on the strong coupling scale. The solution depends on a single scale parameter, as typical for the theory and already known from studies about asymptotic freedom. The study is analytically derived from QCD.