Abstract
The flavor dependence of the QCD phase diagram presents universal properties in the heavy quark limit. For the wide class of models where the quarks are treated at the one-loop level, we show, for arbitrary chemical potential, that the flavor dependence of the critical quark masses-for which the confinement-deconfinement transition is second order-is insensitive to the details of the (confining) gluon dynamics and that the critical temperature is constant along the corresponding critical line. We illustrate this with explicit results in various such one-loop models studied in the literature: effective matrix models for the Polyakov loop, the Curci-Ferrari model, and a recently proposed Gribov-Zwanziger-type model. We further observe that the predictions which follow from this one-loop universality property are well satisfied by different calculations beyond one-loop order, including lattice simulations. For degenerate quarks, we propose a simple universal law for the flavor dependence of the critical mass, satisfied by all approaches.
Highlights
Understanding the properties of strongly interacting matter in extreme conditions of temperature, density, magnetic field, etc., is a question of topical interest with various implications, e.g., in early universe cosmology and astrophysics [1]
For the wide class of models where the quarks are treated at the one-loop level, we show, for arbitrary chemical potential, that the flavor dependence of the critical quark masses—for which the confinementdeconfinement transition is second order—is insensitive to the details of the gluon dynamics and that the critical temperature is constant along the corresponding critical line
Such calculations are restricted to small baryon chemical potential μB due to the infamous sign problem that prevents the use of standard Monte Carlo algorithms [5]
Summary
The flavor dependence of the QCD phase diagram presents universal properties in the heavy quark limit. For the wide class of models where the quarks are treated at the one-loop level, we show, for arbitrary chemical potential, that the flavor dependence of the critical quark masses—for which the confinementdeconfinement transition is second order—is insensitive to the details of the (confining) gluon dynamics and that the critical temperature is constant along the corresponding critical line. Understanding the properties of strongly interacting matter in extreme conditions of temperature, density, magnetic field, etc., is a question of topical interest with various implications, e.g., in early universe cosmology and astrophysics [1] This relates to some of the most profound aspects of quantum chromodynamics (QCD), namely, the physics of (de)confinement and of chiral symmetry breaking/restoration. Of interest is the limit of infinite quark masses, corresponding to the pure Yang-Mills theory For three colors, the latter presents a first order confinementdeconfinement phase transition in temperature [11].
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