NNLO hard-thermal-loop thermodynamics for QCD

We calculate the thermodynamic functions of a quark-gluon plasma for general Nc and Nf to three-loop order using hard-thermal-loop perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum, the HTL mass parameters, and the strong coupling constant. We show that at three loops, the results for the pressure and trace anomaly are in very good agreement with recent lattice data down to temperatures T∼2Tc.