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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

Abstract

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.

Keywords

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.

Notes

Acknowledgements

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.

References

  1. 1.
    F. Di Renzo, E. Onofri, G. Marchesini, P. Marenzoni, Four loop result in SU(3) lattice gauge theory by a stochastic method: lattice correction to the condensate. Nucl. Phys. B 426, 675 (1994) ADSCrossRefGoogle Scholar
  2. 2.
    F. Di Renzo, L. Scorzato, Numerical stochastic perturbation theory for full QCD. J. High Energy Phys. 04, 073 (2004) CrossRefGoogle Scholar
  3. 3.
    F. Di Renzo, V. Miccio, L. Scorzato, C. Torrero, High-loop perturbative renormalization constants for lattice QCD. I. Finite constants for Wilson quark currents. Eur. Phys. J. C 51, 645 (2007) ADSCrossRefGoogle Scholar
  4. 4.
    F. Di Renzo, E.-M. Ilgenfritz, H. Perlt, A. Schiller, C. Torrero, Two-point functions of quenched lattice QCD in numerical stochastic perturbation theory. (I) The ghost propagator in Landau gauge. Nucl. Phys. B 831, 262 (2010) ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    F. Di Renzo, E.-M. Ilgenfritz, H. Perlt, A. Schiller, C. Torrero, Two-point functions of quenched lattice QCD in numerical stochastic perturbation theory. (II) The gluon propagator in landau gauge. Nucl. Phys. B 842, 122 (2011) ADSCrossRefzbMATHGoogle Scholar
  6. 6.
    M. Brambilla, F. Di Renzo, M. Hasegawa, High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and n f=4 Wilson fermions. To be issued soon Google Scholar
  7. 7.
    M. Hasegawa, M. Brambilla, F. Di Renzo, Three loops renormalization constants in numerical stochastic perturbation theory. PoS Lattice 2012, 240 (2012) Google Scholar
  8. 8.
    M. Constantinou et al. (ETM Collaboration), Non-perturbative renormalization of quark bilinear operators with N f=2 (tmQCD) Wilson fermions and the tree-level improved gauge action. J. High Energy Phys. 1008, 068 (2010) ADSCrossRefGoogle Scholar
  9. 9.
    B. Blossier et al. (ETM Collaboration), Renormalisation constants of quark bilinears in lattice QCD with four dynamical Wilson quarks. PoS Lattice 2011, 233 (2011) Google Scholar
  10. 10.
    F. de Soto, C. Roiesnel, On the reduction of hypercubic lattice artifacts. J. High Energy Phys. 0709, 007 (2007) CrossRefGoogle Scholar
  11. 11.
    G. Martinelli, C. Pittori, C.T. Sachrajda, M. Testa, A. Vladikas, A general method for nonperturbative renormalization of lattice operators. Nucl. Phys. B 445, 81 (1995) ADSCrossRefGoogle Scholar
  12. 12.
    J.A. Gracey, Three loop anomalous dimension of nonsinglet quark currents in the RI-prime scheme. Nucl. Phys. B 662, 247 (2003) ADSCrossRefzbMATHGoogle Scholar
  13. 13.
    S. Aoki, K.i. Nagai, Y. Taniguchi, A. Ukawa, Perturbative renormalization factors of bilinear quark operators for improved gluon and quark actions in lattice QCD. Phys. Rev. D 58, 074505 (1998) ADSCrossRefGoogle Scholar
  14. 14.
    A. Skouroupathis, H. Panagopoulos, Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice. Phys. Rev. D 76, 094514 (2007). Phys. Rev. D 78, 119901 (2008) (Erratum) ADSCrossRefGoogle Scholar
  15. 15.
    F. Di Renzo, L. Scorzato, The residual mass in lattice heavy quark effective theory to α 3 order. J. High Energy Phys. 0102, 020 (2001) CrossRefGoogle Scholar
  16. 16.
    F. Di Renzo, L. Scorzato, The N f=2 residual mass in perturbative lattice-HQET for an improved determination of \(m_{b}^{\overline{\mathrm{MS}}}(m_{b}^{\overline{\mathrm{MS}}})\). J. High Energy Phys. 0411, 036 (2004) CrossRefGoogle Scholar
  17. 17.
    Y. Schroder, The static potential in QCD to two loops. Phys. Lett. B 447, 321 (1999) ADSCrossRefGoogle Scholar
  18. 18.
    M. Brambilla, F. Di Renzo, Matching the lattice coupling to the continuum for the tree level Symanzik improved gauge action. PoS Lattice 2010, 222 (2010) Google Scholar
  19. 19.
    A. Skouroupathis, M. Constantinou, H. Panagopoulos, Two-loop additive mass renormalization with clover fermions and Symanzik improved gluons. Phys. Rev. D 77, 014513 (2008) ADSCrossRefGoogle Scholar
  20. 20.
    M. Donnellan, F. Knechtli, B. Leder, R. Sommer, Determination of the static potential with dynamical fermions. Nucl. Phys. B 849, 45 (2011) ADSCrossRefzbMATHGoogle Scholar
  21. 21.
    D. Hesse, M. Dalla Brida, S. Sint, F. Di Renzo, M. Brambilla, The Schrödinger functional in numerical stochastic perturbation theory. PoS Lattice 2013, 325 (2013) Google Scholar
  22. 22.
    G.P. Lepage, P. Mackenzie, On the viability of lattice perturbation theory. Phys. Rev. D 48, 2250 (1993) ADSCrossRefGoogle Scholar

Copyright information

© 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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