Abstract
We report on recent progress in the description of the phase diagram of QCD with heavy quarks at nonzero temperature and chemical potential in the context of a modified perturbative approach. The latter is based on a simple massive extension of the QCD Lagrangian in the Landau-DeWitt gauge, the background field generalization of the Landau gauge. Here, the background field plays the role of an order parameter for the center symmetry, relevant for confinement-deconfinement transition. One-loop results in this approach give a fairly accurate description of the phase diagram both at real and imaginary chemical potential. We comment on issues related to the sign problem in continuum approaches.
Highlights
The low energy regime of Quantum Chromodynamics is not accessible to standard perturbative methods based on the Faddeev-Popov gauge fixing procedure, because the corresponding running coupling becomes large at these scales and even diverges at a finite scale known as ΛQCD
We shall further test the validity of this novel perturbative approach by studying the phase structure of QCD in the heavy-quark limit, for which the lattice has provided a wealth of data to compare with, including the case of a real chemical potential
This means that we can restrict the study of V(, ̄) to pairs (, ̄) that belong to Σ ≡ {(u, v) ∈ C2 | v = u∗}. This means that we can consider V( ) ≡ V(, ̄ = ∗). This fact, together with the tree-level expressions (4), is compatible with our findings in [7], where in the case of an imaginary chemical potential, we argued that the background components r3 and r8 could be taken real
Summary
The low energy regime of Quantum Chromodynamics is not accessible to standard perturbative methods based on the Faddeev-Popov gauge fixing procedure, because the corresponding running coupling becomes large at these scales and even diverges at a finite scale known as ΛQCD. Various ways of dealing with the Gribov ambiguity in the Landau gauge have been proposed in the literature but we shall focus on the proposal of [1], based on the addition of a gluon mass term to the usual Landau gauge-fixed action.1 This modified action remains renormalizable and, interestingly, some of the corresponding RG trajectories yield a running coupling that remains bounded and effectively small, even at low energies [3] which justifies the use of perturbation theory in this regime. We shall further test the validity of this novel perturbative approach by studying the phase structure of QCD in the heavy-quark limit, for which the lattice has provided a wealth of data to compare with, including the case of a real chemical potential In this regime, the relevant transition is the confinement-deconfinement transition, which we study by evaluating the Polyakov loop effective potential V( , ̄). They are strict order parameters only in the limit of infinite quark masses, where they probe the breaking of the center symmetry of Yang-Mills theory at finite temperature, but they remain good signatures of the transition for large but finite quark masses
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