Two-loop computation of the Schrodinger functional in lattice QCD

We compute the Schrodinger functional (SF) for the case of lattice QCD with Wilson fermions (with and without SW improvement) at two-loop order in lattice perturbation theory. This allows us to extract the three-loop beta-function in the SF-scheme. These results are required to compute the running coupling, the Lambda-parameter and quark masses by finite size; techniques with negligible systematic errors. In addition our results enable the implementation of two-loop O(a) improvement in SF-simulations. (C) 2000 Elsevier Science B,V. All rights reserved.