PUB - Publikationen an der Universität Bielefeld

The hard-thermal-loop perturbation theory (HTLpt) framework is used tocalculate the thermodynamic functions of a quark-gluon plasma to three-looporder. This is the highest order accessible by finite temperature perturbationtheory applied to a non-Abelian gauge theory before the high-temperatureinfrared catastrophe. All ultraviolet divergences are eliminated byrenormalization of the vacuum, the HTL mass parameters, and the strong couplingconstant. After choosing a prescription for the mass parameters, the three-loopresults for the pressure and trace anomaly are found to be in very goodagreement with recent lattice data down to $T \sim 2-3\,T_c$, which aretemperatures accessible by current and forthcoming heavy-ion collisionexperiments.