The Relevant Scale Parameter in the High Temperature Phase of QCD

Abstract

We introduce the running coupling constant of QCD in the high temperature phase, ${\tilde{g}}^2(T)$, through a renormalization scheme where the dimensional reduction is optimal at the one-loop level. We then calculate the relevant scale parameter, ${\Lambda }_T$, which characterizes the running of ${\tilde{g}}^2(T)$ with $T$, using the background field method in the static sector. It is found that ${\Lambda }_T/{\Lambda }_{\overline{\text{MS}}}=e^{({\gamma }_E+1/22)}/(4\pi )\approx 0.148$. We further verify that the coupling ${\tilde{g}}^2(T)$ is also optimal for lattice perturbative calculations. Our result naturally explains why the high temperature limit of QCD sets in at temperatures as low as a few times the critical temperature. In addition, our ${\Lambda }_T$ agrees remarkably well with the scale parameter determined from the lattice measurement of the spatial string tension of the SU(2) gauge theory at high $T$.

Comments: 13 pages, RevTeX 3.0, no figures. Full postscript version available via anonymous ftp (192.84.132.4) at ftp://risc0.ca.infn.it/pub/private/lissia/infnca-th-94-24.ps