The QCD phase diagram from Schwinger–Dyson equations

We study the phase diagram of quantum chromodynamics (QCD). For this purpose we employ the Schwinger–Dyson equations (SDEs) technique and construct a truncation of the infinite tower of equations by demanding a matching with the lattice results for the quark–anti-quark condensate at finite temperature (T), for zero quark chemical potential (μ), that is, the region where lattice calculations are expected to provide reliable results. We compute the evolution of the phase diagram away from T = 0. To chart the chiral symmetry restoration transition, we follow the evolution of the derivative of the condensate with respect to the temperature as a function of T and μ. The behavior of this thermodynamic variable clearly demonstrates the existence of a cross-over for μ less than a critical value. However, the derivative of the condensate with respect to the temperature develops a singularity near μ ≈ 0.22 GeV marking the onslaught of a first order phase transition characterized by the existence of a critical point. The critical line continues until μ ≈ 0.44 GeV where Tc = 0 and thus chiral symmetry is finally restored. For the deconfinement transition we look for the violation of the axiom of reflection positivity in the quark propagator. The critical end point appears to be the same as observed for the transition to chirally symmetric phase. However, near T = 0 axis, due to lack of data points, we are unable to claim against coincidental chiral symmetry restoration and deconfinement transitions along that axis. (paper)