Padé-related resummations of the pressure of quark-gluon plasma by approximate inclusion of g s 6 terms

We perform various resummations of the hot QCD pressure based on the actual knowledge of the perturbation series which includes the similar tog(s)(6)ln(1/g(s)) and part of the similar tog(s)(6) terms. Resummations are performed separately for the short- and long-distance parts. The similar tog(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 Pade and Borel-Pade type, using in addition the (Pade)resummed expression for the squared Debye screening mass m(E)(2) and, in some cases, even for the electrostatic QCD coupling parameter g(E)(2). The resummed results depend weakly on the yet unknown similar tog(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 Tless than or similar to1 GeV. The resulting dependence of pressure on temperature T is compatible with the results of the lattice calculations at low T.