Five-loop quark mass and field anomalous dimensions for a general gauge group

  • Thomas Luthe
  • Andreas Maier
  • Peter Marquard
  • York Schröder
Open Access
Regular Article - Theoretical Physics

Abstract

We present analytical five-loop results for the quark mass and quark field anomalous dimensions, for a general gauge group and in the \( \overline{\mathrm{MS}} \) scheme. We confirm the values known for the gauge group SU(3) from an independent calculation, and find full agreement with results available from large-Nf studies.

Keywords

Perturbative QCD Renormalization Group 

References

  1. [1]
    P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Scalar correlator at O(α s4), Higgs decay into b-quarks and bounds on the light quark masses, Phys. Rev. Lett. 96 (2006) 012003 [hep-ph/0511063] [INSPIRE].
  2. [2]
    R. Tarrach, The Pole Mass in Perturbative QCD, Nucl. Phys. B 183 (1981) 384 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    O.V. Tarasov, Anomalous Dimensions Of Quark Masses In Three Loop Approximation (in Russian), preprint JINR-P2-82-900 (1982).Google Scholar
  4. [4]
    S.A. Larin, The Renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
  5. [5]
    J.A.M. Vermaseren, S.A. Larin and T. van Ritbergen, The four loop quark mass anomalous dimension and the invariant quark mass, Phys. Lett. B 405 (1997) 327 [hep-ph/9703284] [INSPIRE].
  6. [6]
    K.G. Chetyrkin, Quark mass anomalous dimension to O(α S4), Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [INSPIRE].
  7. [7]
    P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Quark Mass and Field Anomalous Dimensions to O(α s5), JHEP 10 (2014) 076 [arXiv:1402.6611] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    T. Luthe, A. Maier, P. Marquard and Y. Schröder, Towards the five-loop β-function for a general gauge group, JHEP 07 (2016) 127 [arXiv:1606.08662] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    P. Nogueira, Abusing qgraf, Nucl. Instrum. Meth. A 559 (2006) 220 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
  12. [12]
    M. Tentyukov and J.A.M. Vermaseren, The Multithreaded version of FORM, Comput. Phys. Commun. 181 (2010) 1419 [hep-ph/0702279] [INSPIRE].
  13. [13]
    J. Kuipers, T. Ueda, J.A.M. Vermaseren and J. Vollinga, FORM version 4.0, Comput. Phys. Commun. 184 (2013) 1453 [arXiv:1203.6543] [INSPIRE].
  14. [14]
    T. van Ritbergen, A.N. Schellekens and J.A.M. Vermaseren, Group theory factors for Feynman diagrams, Int. J. Mod. Phys. A 14 (1999) 41 [hep-ph/9802376] [INSPIRE].
  15. [15]
    M. Misiak and M. Münz, Two loop mixing of dimension five flavor changing operators, Phys. Lett. B 344 (1995) 308 [hep-ph/9409454] [INSPIRE].
  16. [16]
    T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The Four loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [INSPIRE].
  17. [17]
    K.G. Chetyrkin, M. Misiak and M. Münz, β-functions and anomalous dimensions up to three loops, Nucl. Phys. B 518 (1998) 473 [hep-ph/9711266] [INSPIRE].
  18. [18]
    T. Luthe, Fully massive vacuum integrals at 5 loops, Ph.D. Thesis, Bielefeld University, Bielefeld Germany (2015).Google Scholar
  19. [19]
    P. Marquard and D. Seidel, crusher (unpublished).Google Scholar
  20. [20]
    K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
  22. [22]
    T. Luthe and Y. Schröder, Fun with higher-loop Feynman diagrams, J. Phys. Conf. Ser. 762 (2016) 012066 [arXiv:1604.01262] [INSPIRE].CrossRefGoogle Scholar
  23. [23]
    R.H. Lewis, fermat, http://home.bway.net/lewis/.
  24. [24]
    H.R.P. Ferguson, D.H. Bailey and S. Arno, Analysis of PSLQ, an integer relation finding algorithm, Math. Comput. 68 (1999) 351.ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    V.A. Smirnov, Analytic tools for Feynman integrals, Springer Tracts Mod. Phys. 250 (2012) 1.MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    M. Roth and A. Denner, High-energy approximation of one loop Feynman integrals, Nucl. Phys. B 479 (1996) 495 [hep-ph/9605420] [INSPIRE].
  27. [27]
    T. Binoth and G. Heinrich, Numerical evaluation of multiloop integrals by sector decomposition, Nucl. Phys. B 680 (2004) 375 [hep-ph/0305234] [INSPIRE].
  28. [28]
    A.V. Smirnov, FIESTA4: Optimized Feynman integral calculations with GPU support, Comput. Phys. Commun. 204 (2016) 189 [arXiv:1511.03614] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    T. Luthe and Y. Schröder, Five-loop massive tadpoles, PoS(LL2016)074 [arXiv:1609.06786] [INSPIRE].
  30. [30]
    T. Luthe, A. Maier, P. Marquard and Y. Schröder, Complete renormalization of QCD at five loops, in preparation.Google Scholar
  31. [31]
    H. Georgi, Lie algebras in particle physics, Front. Phys. 54 (1999) 1 [INSPIRE].MathSciNetGoogle Scholar
  32. [32]
    P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, private communication.Google Scholar
  33. [33]
    A.V. Smirnov and M. Tentyukov, Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals, Nucl. Phys. B 837 (2010) 40 [arXiv:1004.1149] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    P.A. Baikov and K.G. Chetyrkin, Four Loop Massless Propagators: An Algebraic Evaluation of All Master Integrals, Nucl. Phys. B 837 (2010) 186 [arXiv:1004.1153] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    R.N. Lee, A.V. Smirnov and V.A. Smirnov, Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve, Nucl. Phys. B 856 (2012) 95 [arXiv:1108.0732] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  36. [36]
    P.A. Baikov, Explicit solutions of the three loop vacuum integral recurrence relations, Phys. Lett. B 385 (1996) 404 [hep-ph/9603267] [INSPIRE].
  37. [37]
    P.A. Baikov, A Practical criterion of irreducibility of multi-loop Feynman integrals, Phys. Lett. B 634 (2006) 325 [hep-ph/0507053] [INSPIRE].
  38. [38]
    K.G. Chetyrkin and A. Retey, Renormalization and running of quark mass and field in the regularization invariant and MS-bar schemes at three loops and four loops, Nucl. Phys. B 583 (2000) 3 [hep-ph/9910332] [INSPIRE].
  39. [39]
    M. Czakon, The Four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [INSPIRE].
  40. [40]
    P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Massless Propagators, R(s) and Multiloop QCD, Nucl. Part. Phys. Proc. 261-262 (2015) 3 [arXiv:1501.06739] [INSPIRE].CrossRefGoogle Scholar
  41. [41]
    P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Five-Loop Running of the QCD coupling constant, arXiv:1606.08659 [INSPIRE].
  42. [42]
    J.A.M. Vermaseren, Axodraw, Comput. Phys. Commun. 83 (1994) 45 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  43. [43]
    J.C. Collins and J.A.M. Vermaseren, Axodraw Version 2, arXiv:1606.01177 [INSPIRE].
  44. [44]
    J.A. Gracey, Quark, gluon and ghost anomalous dimensions at O(1/N f) in quantum chromodynamics, Phys. Lett. B 318 (1993) 177 [hep-th/9310063] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    M. Ciuchini, S.E. Derkachov, J.A. Gracey and A.N. Manashov, Quark mass anomalous dimension at O(1/N f2) in QCD, Phys. Lett. B 458 (1999) 117 [hep-ph/9903410] [INSPIRE].
  46. [46]
    M. Ciuchini, S.E. Derkachov, J.A. Gracey and A.N. Manashov, Computation of quark mass anomalous dimension at O(1/N f2) in quantum chromodynamics, Nucl. Phys. B 579 (2000) 56 [hep-ph/9912221] [INSPIRE].

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Thomas Luthe
    • 1
  • Andreas Maier
    • 2
  • Peter Marquard
    • 3
  • York Schröder
    • 4
  1. 1.Faculty of PhysicsUniversity of BielefeldBielefeldGermany
  2. 2.Institute for Particle Physics PhenomenologyDurham UniversityDurhamUnited Kingdom
  3. 3.Deutsches Elektronen Synchrotron (DESY)ZeuthenGermany
  4. 4.Grupo de Física de Altas EnergíasUniversidad del Bío-BíoChillánChile

Personalised recommendations