On an exactly solvable confining quark model and its thermodynamics

We perform an exact computation of the grand partition function of a model of confined quarks at arbitrary temperatures and quark chemical potentials. The model is inspired by a version of QCD where the perturbative BRST symmetry is broken in the infrared, while perturbative QCD is recovered in the ultraviolet. The theory leads, even at tree level, to a quark mass function compatible with nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. In spite of being defined at tree level, the model produces a non-trivial and stable thermodynamic behaviour at arbitrary values of temperature or chemical potential. Results for the pressure and the trace anomaly as a function of temperature qualitatively resemble those of non-perturbative interactions as observed in lattice simulations. The cold and dense thermodynamics is also contains non-trivial features, being unlike a gas of free massive particles.

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