Pressure of hot QCD up tog6ln(1/g)

Abstract

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order ${g}^{5}.$ We compute here the last contribution which can be determined perturbatively, ${g}^{6}\mathrm{ln}(1/g),$ by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative ${g}^{6}\mathrm{ln}(1/g)$ terms, once they are summed together with the so far unknown perturbative and nonperturbative ${g}^{6}$ terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.