A minimal quasiparticle approach for the QGP and its large-$N_c$ limits

Abstract

We propose a quasiparticle approach allowing to compute the equation of state of a generic gauge theory with gauge group SU($N_c$) and quarks in an arbitrary representation. Our formalism relies on the thermal quasiparticle masses (quarks and gluons) computed from Hard-Thermal-Loop techniques, in which the standard two-loop running coupling constant is used. Our model is minimal in the sense that we do not allow any extra ansatz concerning the temperature-dependence of the running coupling. We first show that it is able to reproduce the most recent equations of state computed on the lattice for temperatures higher than 2 $T_c$. In this range of temperatures, an ideal gas framework is indeed expected to be relevant. Then we study the accuracy of various inequivalent large-$N_c$ limits concerning the description of the QCD results, as well as the equivalence between the QCD$_{AS}$ limit and the ${\cal N}=1$ SUSY Yang-Mills theory. Finally, we estimate the dissociation temperature of the $\Upsilon$-meson and comment on the estimations' stability regarding the different considered large-$N_c$ limits.