The European Physical Journal C

, Volume 51, Issue 3, pp 645–657 | Cite as

High-loop perturbative renormalization constants for lattice QCD (I): finite constants for Wilson quark currents

  • F. Di Renzo
  • V. Miccio
  • C. Torrero
  • L. ScorzatoEmail author
Regular Article - Theoretical Physics


We present a high order perturbative computation of the renormalization constants ZV, ZA and of the ratio ZP/ZS for Wilson fermions. The computational setup is the one provided by the RI’-MOM scheme. Three- and four-loop expansions are made possible by numerical stochastic perturbation theory. Results are given for various numbers of flavors and/or (within a finite accuracy) for generic nf up to three loops. For the case nf=2 we also present four-loop results. Finite-size effects are well under control, and the continuum limit is taken by means of hypercubic symmetric Taylor expansions. The main indetermination comes from truncation errors, which should be assessed in connection with the convergence properties of the series. The latter is best discussed in the framework of boosted perturbation theory, whose impact we try to assess carefully. Final results and their uncertainties show that high-loop perturbative computations of lattice QCD renormalization constants (RCs) are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, for which results are also for generic nf up to three loops, while a four-loop result is obtained for nf=2.


Anomalous Dimension Zero Mode Continuum Limit Critical Mass Chiral Limit 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • F. Di Renzo
    • 1
  • V. Miccio
    • 2
  • C. Torrero
    • 3
  • L. Scorzato
    • 4
    Email author
  1. 1.Dipartimento di FisicaUniversità di Parma and INFN, Gruppo Collegato di ParmaParmaItaly
  2. 2.Sezione di Milano BicoccaI.N.F.N.MilanoItaly
  3. 3.Faculty of PhysicsUniversity of BielefeldBielefeldGermany
  4. 4.ECT*VillazzanoItaly

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