Three-loop matching coefficients for hot QCD: Reduction and gauge independence

Möller J, Schroeder Y. Three-loop matching coefficients for hot QCD: Reduction and gauge independence. JHEP. 2012;2012(8): 25.We perform an integral reduction for the 3-loop effective gauge coupling andscreening mass of QCD at high temperatures, defined as matching coefficientsappearing in the dimensionally reduced effective field theory (EQCD).Expressing both parameters in terms of a set master (sum-) integrals, we showexplicit gauge parameter independence. The lack of suitable methods for solvingthe comparatively large number of master integrals forbids the completeevaluation at the moment. Taking one generic class of masters as an example, wehighlight the calculational techniques involved. The full result would allow toimprove on one of the classic probes for the convergence of the weak-couplingexpansion at high temperatures, namely the comparison of full and effectivetheory determinations of the spatial string tension. Furthermore, the fullresult would also allow to determine one new contribution of order$\order{g^7}$ to the pressure of hot QCD