Abstract
The 4-loop C 3 F T F n l and 5-loop C 4 F 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 3 F T F n l and 5-loop C 4 F 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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].
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].
A.V. Manohar and M.B. Wise, Heavy quark physics, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 10 (2000) 1 [INSPIRE].
A.G. Grozin, Heavy quark effective theory, Springer Tracts Mod. Phys. 201 (2004) 1 [INSPIRE].
A.G. Grozin, Introduction to effective field theories. 3. Bloch-Nordsieck effective theory, HQET, arXiv:1305.4245 [INSPIRE].
A.G. Grozin, Matching heavy-quark fields in QCD and HQET at three loops, Phys. Lett. B 692 (2010) 161 [arXiv:1004.2662] [INSPIRE].
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].
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].
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].
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].
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].
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].
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].
G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson loops beyond the leading order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].
M. Beneke and V.M. Braun, Power corrections and renormalons in Drell-Yan production, Nucl. Phys. B 454 (1995) 253 [hep-ph/9506452] [INSPIRE].
E. Bagan and P. Gosdzinsky, Two-loop renormalization scale dependence of the Isgur-Wise function, Phys. Lett. B 305 (1993) 157 [INSPIRE].
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].
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].
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].
J.G.M. Gatheral, Exponentiation of eikonal cross-sections in non-Abelian gauge theories, Phys. Lett. B 133 (1983) 90 [INSPIRE].
J. Frenkel and J.C. Taylor, Non-Abelian eikonal exponentiation, Nucl. Phys. B 246 (1984) 231 [INSPIRE].
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].
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].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1805.05050
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Grozin, A. Four-loop cusp anomalous dimension in QED. J. High Energ. Phys. 2018, 73 (2018). https://doi.org/10.1007/JHEP06(2018)073
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)073