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

  • M. Brambilla
  • F. Di RenzoEmail author
Regular Article - Theoretical Physics


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.


Renormalization Constant Finite Size Effect Landau Gauge Finite Lattice Wilson Fermion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We warmly thank Luigi Scorzato for the long-lasting collaboration on NSPT and Christian Torrero, who has taken part in the long-lasting project of three-loop computation of LQCD renormalization constants. We are very grateful to M. Bonini, V. Lubicz, C. Tarantino, R. Frezzotti, P. Dimopoulos and H. Panagopoulos for stimulating discussions.

This research is supported by the Research Executive Agency (REA) of the European Union under Grant Agreement No. PITN-GA-2009-238353 (ITN STRONGnet). We acknowledge partial support from both Italian MURST under contract PRIN2009 (20093BMNPR 004) and from I.N.F.N. under i.s. MI11 (now QCDLAT). We are grateful to the AuroraScience Collaboration for the computer time that was made available on the Aurora system. It is a pleasure for F. Di Renzo to thank the Aspen Center for Physics for hospitality during the 2010 summer program: the long process of preparation of this work had a substantial progress on those days.


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© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Dipartimento di Fisica e Scienze della TerraUniversità di Parma and INFN, Gruppo Collegato di ParmaParmaItaly

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