NNLO hard-thermal-loop trace anomaly for QCD

Recent results of a next-to-next-to-leading order hard-thermal-loop perturbation theory (HTLpt) calculation of the QCD thermodynamics are revisited. The focus is on the trace anomaly scaled by T-2 for pure-glue and N-f = 3 QCD. The comparison to available lattice data suggests that for pure-glue QCD agreement between HTLpt and lattice data for the trace anomaly begins at temperatures above 8 T-c while when including quarks (N-f = 3) agreement begins already at temperatures above 2 T-c. The results in both cases indicate that at very high temperatures the T-2-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.