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

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.