The pressure of hot QCD up to g 6 ln ( 1 / g )

The pressure of hot QCD up to g 6 ln(1/g) 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 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 ln(1/g) terms, together with the so far unknown perturbative and non-perturbative g 6 terms, could potentially extend the applicability of the resummed coupling constant series down to surprisingly low temperatures.