Regular Article - Theoretical Physics
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
Dipartimento di Fisica e Scienze della Terra, Università di Parma and INFN, Gruppo Collegato di Parma, 43100, Parma, Italy
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Revised: 12 November 2013
Published online: 7 December 2013
Numerical Stochastic Perturbation Theory was able to get three- (and even four-) loop results for finite Lattice QCD renormalization constants. More recently, a conceptual and technical framework has been devised to tame finite size effects, which had been reported to be significant for (logarithmically) divergent renormalization constants. In this work we present three-loop results for fermion bilinears in the Lattice QCD regularization defined by tree-level Symanzik improved gauge action and n f =2 Wilson fermions. We discuss both finite and divergent renormalization constants in the RI’-MOM scheme. Since renormalization conditions are defined in the chiral limit, our results also apply to Twisted Mass QCD, for which non-perturbative computations of the same quantities are available.
We emphasize the importance of carefully accounting for both finite lattice space and finite volume effects. In our opinion the latter have in general not attracted the attention they would deserve.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013