THE RUNNING COUPLING AT FINITE TEMPERATURE

We propose the ensemble averaged running coupling as the meaningful measure of the coupling strength of an equilibrium gas and consider its scaling behaviour. We show that the high temperature limit of the average coupling is obtained by keeping the temperature to the renormalization point ratio, T/mu, fixed. In hot QCD gas this implies asymptotic freedom and a beta function which is independent of T up to two loops. In the MOM scheme a minimal sensitivity to temperature is obtained with the choice mu = 2.6 T.