We perform various resummations of the hot QCD pressure based on the actual knowledge of the perturbation series which includes the $\sim g_s^6\ln (1/g_s)$ and part of the $\sim g_s^6$ terms. Resummations are performed separately for the short- and long-distance parts. The $\sim g_s^6$ term of the short-distance pressure is estimated on the basis of the known UV cutoff dependence of the long-distance part. The resummations are of the Padé and Borel-Padé type, using in addition the (Padé)resummed expression for the squared Debye screening mass $m_{\mathrm{E}}^2$ and, in some cases, even for the electrostatic QCD coupling parameter $g_{\mathrm{E}}^2$. The resummed results depend weakly on the yet unknown $\sim g_s^6$ terms and on the short-range renormalization scale, at all temperatures. The dependence on the long-range renormalization scale is appreciable at low temperatures $T\lesssim 1\mathrm{G}\mathrm{e}\mathrm{V}$. The resulting dependence of pressure on temperature $T$ is compatible with the results of the lattice calculations at low $T$.

• Received 3 June 2004

DOI:https://doi.org/10.1103/PhysRevD.70.114016