The entropy of the QCD plasma

Abstract

Self-consistent approximations in terms of fully dressed propagators provide a simple expression for the entropy of an ultrarelativistic plasma, which isolates the contribution of the elementary excitations as a leading contribution. Further approximations, whose validity is checked on a soluble model involving a scalar field, allow us to calculate the entropy of the QCD plasma. We obtain an accurate description of lattice data for purely gluonic QCD, down to temperatures of about twice the transition temperature.

Figures (3)

• Figure 1: Comparison of perturbative and HTL-improved approximations to the entropy in the large-$N$ scalar O($N$)-model. See text for detailed explanations.
• Figure 2: NLO contributions to $\delta \Pi_T$ at hard momentum. Thick dashed and wiggly lines with a blob represent HTL-resummed longitudinal and transverse propagators.
• Figure 3: HTL-improved results for the 2-loop entropy ${\cal S}/{\cal S}_{\rm SB}$ in purely gluonic QCD (full lines) with $\bar{\mu}$ varied between $\pi T$ and $4\pi T$; our estimates for NLO effects are given by the dash-dotted lines. The lattice result for the entropy is represented by the dark-gray band. For comparison, the HTL-resummed results of Ref. ABS for the 1-loop pressure are given by the dotted lines, the lattice results for $P/P_{\rm SB}$ by the light-gray band. [Because of the weak temperature-dependence of the theoretical results the predictions for ${\cal S}/{\cal S}_{\rm SB}$ are approximately those for $P/P_{\rm SB}$ and vice versa.]