The relevant scale parameter in the high temperature phase of QCD Original Research Article

We introduce the running coupling constant of QCD in the high temperature phase, g2(T), through a renormalization scheme where the dimensional reduction is optimal at the one-loop level. We then calculate the relevant scale parameter, ΛT, which characterizes the running of g2(T) with T, using the background field method in the static sector. It is found that ΛT/Λ=e(γE+122)/(4π) ≈ 0.148. We further verify that the coupling g2(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 Λt 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.