ON THE CONVERGENCE OF PERTURBATIVE QCD AT HIGH-TEMPERATURE

The free energy for QCD at high temperature T is calculated to order g (5) using effective-field-theory methods to separate the contributions from the momentum scales 2 pi T and gT. The effects of the scale 2 pi T enter through the coefficients in the effective Lagrangian for the 3-dimensional effective theory obtained by dimensional reduction. The perturbation series for these coefficients seem to be well behaved if the running coupling constant is sufficiently small: alpha(s)(2 pi T) much less than 1. For the contribution to the free energy from the sca le gT, the perturbation series is well behaved only if alpha(s)(2 pi T ) is an order of magnitude smaller. The implication for applications o f perturbative QCD to the quark-gluon plasma is briefly discussed.