QCD at finite temperature and chemical potential from Dyson–Schwinger equations

Abstract

We review results for the phase diagram of QCD, the properties of quarks and gluons and the resulting properties of strongly interacting matter at finite temperature and chemical potential. The interplay of two different but related transitions in QCD, chiral symmetry restoration and deconfinement, leads to a rich phenomenology when external parameters such as quark masses, volume, temperature and chemical potential are varied. We discuss the progress in this field from a theoretical perspective, focusing on non-perturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We aim at a pedagogical overview on the physics associated with the structure of this framework and explain connections to other approaches, in particular with the functional renormalization group and lattice QCD. We discuss various aspects associated with the variation of the quark masses, assess recent results for the QCD phase diagram including the location of a putative critical end-point for N f = 2 + 1 and N f = 2 + 1 + 1, discuss results for quark spectral functions and summarise aspects of QCD thermodynamics and fluctuations.

Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations

“…Results for QCD with heavy quarks and at physical quark masses (N f = 2 + 1 and N f = 2 + 1 + 1) but zero chemical potential agree with corresponding lattice results, see Ref. [29] for an overview. A critical end point has been found at T CEP , µ CEP B = (117, 488) MeV which corresponds to a ratio µ CEP B / T CEP ≈ 4.2, i.e., large chemical potential.…”

“…Another highly non-trivial result is the matching of the unquenched gluon propagator [25] with lattice results [85], as discussed and summarized in Ref. [29]. Our result for the phase diagram at non-zero chemical potential is shown in the right diagram of Fig.…”

“…This notion is supported by results from Dyson-Schwinger equations [24][25][26][27][28], see Ref. [29] for a recent review.…”

“…Before we discuss fluctuations, we present our updated result for the QCD phase diagram with N f = 2 + 1 quark flavors, which closely resembles the one already published in Refs. [26,29]. Overall, changes due to the slightly adapted strange quark mass and the different regularization scheme are very small.…”

A Study of the Properties of the QCD Phase Diagram in High-Energy Nuclear Collisions

“…This is the characteristic experimental signature of the critical point we are looking for in the heavy-ion collision experiment. Theoretically, the properties of QCD phase diagram at finite baryon density and the signatures of conserved charge fluctuations near the QCD critical point have been extensively studied by various model calculations, such as Lattice QCD [10,[18][19][20][21][22]98], NJL, PNJL model [99][100][101][102][103][104][105][106], PQM, FRG model [107][108][109], Dyson-Schwinger Equation (DSE) method [110][111][112][113], chiral hydrodynamics [114] and other effective models [94, [115][116][117][118][119]. However, one should keep in mind that the above results are under the assumption of thermal equilibrium with infinite and static medium.…”