Thermodynamics of an exactly solvable confining quark model

Abstract

Abstract. The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a version of QCD where the usual (perturbative) BRST symmetry is broken in the infrared, while possessing a quark mass function compatible with nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. Even though the model is defined at tree level, we show that it produces a non-trivial and stable thermodynamic behaviour at any temperature or chemical potential. Results for the pressure, the entropy and the trace anomaly as a function of the temperature are qualitatively compatible with the effect of non-perturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain non-trivial features, being far away from an ideal gas picture. IntroductionGiven the difficulty to address the problem of confinement in strongly interacting systems directly from its fundamental theory, Quantum Chromodynamics (QCD), several alternative approaches have been proposed. One of the main such approaches is that of effective models of QCD, which are quantum field theories that possess one or more fundamental aspects of the original theory but being nevertheless easier to have some information extracted.Regarding the quark sector of QCD, two quite sucessful models in the description of chiral symmetry breaking and its restoration at high temperature are the Linear Sigma Model with quarks (LSM) [1], and the Nambu-Jona-Lasinio (NJL) Model [2]. In their original formulations, these models do not address the issue of quark confinement. Indeed, in both models quarks are effectively treated as on-shell quasiparticles. Two possible directions that can be taken towards a simultaneous description of both chiral and confinement dynamics are represented either by the coupling of the Polyakov loop to quark degrees of freedom (the so-called PLSM and PNJL models) [3,4,5,6,7,8], or by considering nonlocal interactions between quarks as a result of their nonperturbative coupling to gluons, as in the nonlocal versions of the NJL model [9,10,11,12,13]. Following [14,15,16,17,18], we consider a third possibility, which is inspired by the (refined) Gribov-Zwanziger effective theory for infrared QCD [19,20,21], although not equivalent to it.Although it has been long clear that quarks and gluons are confined to hadrons, a definite theoretical criterion for confinement is not yet a settled issue. A sufficient condition for the