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Numerical Stochastic Perturbation Theory was able to get three- (and evenfour-) loop results for finite Lattice QCD renormalization constants. Morerecently, a conceptual and technical framework has been devised to tame finitesize effects, which had been reported to be significant for (logarithmically)divergent renormalization constants. In this work we present three-loop resultsfor fermion bilinears in the Lattice QCD regularization defined by tree-levelSymanzik improved gauge action and n_f=2 Wilson fermions. We discuss bothfinite and divergent renormalization constants in the RI'-MOM scheme. Sincerenormalization conditions are defined in the chiral limit, our results alsoapply to Twisted Mass QCD, for which non-perturbative computations of the samequantities are available. We emphasize the importance of carefully accountingfor both finite lattice space and finite volume effects. In our opinion thelatter have in general not attracted the attention they would deserve.

european physical journal. c, particles and fields

High-loop perturbative renormalization constants for Lattice QCD (II):  three-loop quark currents for tree-level Symanzik improved gauge action and  n_f=2 Wilson fermions