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, 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, Λ T , which characterizes the running of g 2 (T) with T , using the background field method in the static sector. It is found that Λ T /Λ=e( γE+ 1 22 )/(4π) ≈ 0.148 . We further verify that the coupling 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 Λ 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 .