Thermodynamics of an exactly solvable confining quark model

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 softly BRST-broken version of QCD and possesses 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 nontrivial 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 nonperturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain nontrivial features, being far away from an ideal gas picture.

More on the nonperturbative Gribov-Zwanziger quantization of linear covariant gauges

“…The ensuing Refined Gribov-Zwanziger gluon and ghost propagators are in qualitative agreement with the most recent lattice data [19][20][21][22]. Also, developments as the inclusion of matter [23], glueball spectrum [24,25], thermodynamics [26][27][28][29][30][31][32] and generalization to supersymmetric theories [33,34] were made.…”

The continuity of the gauge fixing condition n⋅ ∂n⋅A= 0

“…Refs. [7][8][9][10][11][12][13][14][15][16][17]). The Gribov region method is extended to linear covariant gauges in [18] through the field dependent BRST transformation [19][20][21].…”

Thermodynamics of an exactly solvable confining quark model

“…The quantities ϕ i (i = 0, 1, 2, 3) are known functions of the internal momentum p 2 [18]. The µ−dependent term is given by A closed expression for (14) can be found at the zero-temperature limit.…”

“…can be cast in a functional integral form and straightforwardly calculated [18]. The result is convinently split into a µ−independent term plus a (T, µ)−dependent term as…”

“…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…”