QCD trace anomaly

Abstract

In this brief report we compare the predictions of a recent next-to-next-to-leading order hard-thermal-loop perturbation theory (HTLpt) calculation of the QCD trace anomaly to available lattice data. We focus on the trace anomaly scaled by ${T}^{2}$ in two cases: ${N}_{f}=0$ and ${N}_{f}=3$. When using the canonical value of $\ensuremath{\mu}=2\ensuremath{\pi}T$ for the renormalization scale, we find that for Yang-Mills theory (${N}_{f}=0$) agreement between HTLpt and lattice data for the ${T}^{2}$-scaled trace anomaly begins at temperatures on the order of $8{T}_{c}$, while when including quarks (${N}_{f}=3$) agreement begins already at temperatures above $2{T}_{c}$. In both cases we find that at very high temperatures the ${T}^{2}$-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.