On the Convergence of Perturbative QCD at High Temperature

Abstract

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 $T$ and $gT$. The effects of the scale $T$ 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: ${\alpha }_s(2\pi T)\ll 1$. For the contribution to the free energy from the scale $gT$, the perturbation series is well-behaved only if ${\alpha }_s(2\pi T)$ is an order of magnitude smaller. The implication for applications of perturbative QCD to the quark-gluon plasma are briefly discussed.

Comments: 12 pages, LaTeX