Advertisement

Four-loop cusp anomalous dimension in QED

  • Andrey GrozinEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

The 4-loop C F 3 T F n l and 5-loop C F 4 T F n l terms in the HQET field anomalous dimension γ h are calculated analytically (the 4-loop one agrees with the recent numerical result [1]). The 4-loop C F 3 T F n l and 5-loop C F 4 T F n l terms in the cusp anomalous dimension Γ(φ) are calculated analytically, exactly in φ (the φ → ∞ asymptotics of the 4-loop one agrees with the recent numerical result [2]). Combining these results with the recent 4-loop d F F n l contributions to γ h and to the small-φ expansion of Γ(φ) up to φ4 [3], we now have the complete analytical 4-loop result for the Bloch-Nordsieck field anomalous dimension in QED, and the small-φ expansion of the 4-loop QED cusp anomalous dimension up to φ4.

Keywords

Effective Field Theories Perturbative QCD Renormalization Group Wilson, ’t Hooft and Polyakov loops 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Four-loop wave function renormalization in QCD and QED, Phys. Rev. D 97 (2018) 054032 [arXiv:1801.08292] [INSPIRE].
  2. [2]
    S. Moch, B. Ruijl, T. Ueda, J.A.M. Vermaseren and A. Vogt, Four-loop non-singlet splitting functions in the planar limit and beyond, JHEP 10 (2017) 041 [arXiv:1707.08315] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  3. [3]
    A. Grozin, J. Henn and M. Stahlhofen, On the Casimir scaling violation in the cusp anomalous dimension at small angle, JHEP 10 (2017) 052 [arXiv:1708.01221] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    A.V. Manohar and M.B. Wise, Heavy quark physics, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 10 (2000) 1 [INSPIRE].Google Scholar
  5. [5]
    A.G. Grozin, Heavy quark effective theory, Springer Tracts Mod. Phys. 201 (2004) 1 [INSPIRE].
  6. [6]
    A.G. Grozin, Introduction to effective field theories. 3. Bloch-Nordsieck effective theory, HQET, arXiv:1305.4245 [INSPIRE].
  7. [7]
    A.G. Grozin, Matching heavy-quark fields in QCD and HQET at three loops, Phys. Lett. B 692 (2010) 161 [arXiv:1004.2662] [INSPIRE].
  8. [8]
    K. Melnikov and T. van Ritbergen, The three loop on-shell renormalization of QCD and QED, Nucl. Phys. B 591 (2000) 515 [hep-ph/0005131] [INSPIRE].
  9. [9]
    K.G. Chetyrkin and A.G. Grozin, Three-loop anomalous dimension of the heavy-light quark current in HQET, Nucl. Phys. B 666 (2003) 289 [hep-ph/0303113] [INSPIRE].
  10. [10]
    D.J. Broadhurst and A.G. Grozin, Matching QCD and HQET heavy-light currents at two loops and beyond, Phys. Rev. D 52 (1995) 4082 [hep-ph/9410240] [INSPIRE].
  11. [11]
    A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions, JHEP 01 (2016) 140 [arXiv:1510.07803] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    A. Grozin, Leading and next-to-leading large-n f terms in the cusp anomalous dimension and quark-antiquark potential, PoS(LL2016)053 [arXiv:1605.03886] [INSPIRE].
  13. [13]
    R. Lee, P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment, JHEP 03 (2013) 162 [arXiv:1301.6481] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, Three-loop cusp anomalous dimension in QCD, Phys. Rev. Lett. 114 (2015) 062006 [arXiv:1409.0023] [INSPIRE].
  15. [15]
    G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson loops beyond the leading order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    M. Beneke and V.M. Braun, Power corrections and renormalons in Drell-Yan production, Nucl. Phys. B 454 (1995) 253 [hep-ph/9506452] [INSPIRE].
  17. [17]
    E. Bagan and P. Gosdzinsky, Two-loop renormalization scale dependence of the Isgur-Wise function, Phys. Lett. B 305 (1993) 157 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    J.M. Henn, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, A planar four-loop form factor and cusp anomalous dimension in QCD, JHEP 05 (2016) 066 [arXiv:1604.03126] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    J. Davies, A. Vogt, B. Ruijl, T. Ueda and J.A.M. Vermaseren, Large-n f contributions to the four-loop splitting functions in QCD, Nucl. Phys. B 915 (2017) 335 [arXiv:1610.07477] [INSPIRE].
  20. [20]
    J. Henn, R.N. Lee, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Four-loop photon quark form factor and cusp anomalous dimension in the large-N c limit of QCD, JHEP 03 (2017) 139 [arXiv:1612.04389] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    J.G.M. Gatheral, Exponentiation of eikonal cross-sections in non-Abelian gauge theories, Phys. Lett. B 133 (1983) 90 [INSPIRE].
  22. [22]
    J. Frenkel and J.C. Taylor, Non-Abelian eikonal exponentiation, Nucl. Phys. B 246 (1984) 231 [INSPIRE].
  23. [23]
    S.G. Gorishny, A.L. Kataev, S.A. Larin and L.R. Surguladze, The analytical four-loop corrections to the QED β-function in the MS scheme and to the QED ψ-function: total reevaluation, Phys. Lett. B 256 (1991) 81 [INSPIRE].
  24. [24]
    B. Ruijl, T. Ueda, J.A.M. Vermaseren and A. Vogt, Four-loop QCD propagators and vertices with one vanishing external momentum, JHEP 06 (2017) 040 [arXiv:1703.08532] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.PRISMA Cluster of ExcellenceJohannes Gutenberg UniversityMainzGermany
  2. 2.Budker Institute of Nuclear Physics SB RASNovosibirskRussia
  3. 3.Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations