Abstract
We calculate the small angle expansion of the four-loop QCD cusp anomalous dimension. As a byproduct of our calculation, we also obtain the four-loop anomalous dimension of the heavy-quark field in HQET. The validity of the calculational setup is cross-checked by the independent calculation of the four-loop QCD beta-function from heavy-quark-gluon vertex renormalization in HQET. We check the obtained results for the cusp anomalous dimension and heavy-quark field anomalous dimension against available analytical and numerical results. Finally, we find that the maximal transcendentality contribution to the QCD Bremsstrahlung function coincides, up to a factor 3/2, with the Bremsstrahlung function in \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory, at least, through 4 loops.
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References
A.M. Polyakov, Gauge fields as rings of glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Loop space formalism and renormalization group for the infrared asymptotics of QCD, Phys. Lett. B 171 (1986) 459 [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Factorization of hard processes in QCD, Adv. Ser. Direct. High Energy Phys. 5 (1989) 1 [hep-ph/0409313] [INSPIRE].
J.C. Collins, Sudakov form-factors, Adv. Ser. Direct. High Energy Phys. 5 (1989) 573 [hep-ph/0312336] [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in N = 4 super Yang-Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [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].
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-Nf terms in the cusp anomalous dimension and quark-antiquark potential, PoS LL2016 (2016) 053 [arXiv:1605.03886] [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. Grozin, Four-loop cusp anomalous dimension in QED, JHEP 06 (2018) 073 [Addendum ibid. 01 (2019) 134] [arXiv:1805.05050] [INSPIRE].
R. Brüser, A. Grozin, J.M. Henn and M. Stahlhofen, Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles, JHEP 05 (2019) 186 [arXiv:1902.05076] [INSPIRE].
R. Brüser, C. Dlapa, J.M. Henn and K. Yan, Full angle dependence of the four-loop cusp anomalous dimension in QED, Phys. Rev. Lett. 126 (2021) 021601 [arXiv:2007.04851] [INSPIRE].
J.M. Henn and T. Huber, The four-loop cusp anomalous dimension in N = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals, JHEP 09 (2013) 147 [arXiv:1304.6418] [INSPIRE].
M.S. Bianchi and A. Mauri, ABJM θ-Bremsstrahlung at four loops and beyond, JHEP 11 (2017) 173 [arXiv:1709.01089] [INSPIRE].
M.S. Bianchi and A. Mauri, ABJM θ-Bremsstrahlung at four loops and beyond: non-planar corrections, JHEP 11 (2017) 166 [arXiv:1709.10092] [INSPIRE].
M. Neubert, Heavy quark symmetry, Phys. Rept. 245 (1994) 259 [hep-ph/9306320] [INSPIRE].
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].
R.N. Lee and A.F. Pikelner, Four-loop HQET propagators from the DRA method, arXiv:2211.03668 [INSPIRE].
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].
M. Czakon, The four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [INSPIRE].
F. Herzog, B. Ruijl, T. Ueda, J.A.M. Vermaseren and A. Vogt, The five-loop β-function of Yang-Mills theory with fermions, JHEP 02 (2017) 090 [arXiv:1701.01404] [INSPIRE].
T. Luthe, A. Maier, P. Marquard and Y. Schröder, The five-loop β-function for a general gauge group and anomalous dimensions beyond Feynman gauge, JHEP 10 (2017) 166 [arXiv:1709.07718] [INSPIRE].
K.G. Chetyrkin, G. Falcioni, F. Herzog and J.A.M. Vermaseren, Five-loop renormalisation of QCD in covariant gauges, JHEP 10 (2017) 179 [Addendum ibid. 12 (2017) 006] [arXiv:1709.08541] [INSPIRE].
A. Grozin, Lectures on QED and QCD: practical calculation and renormalization of one- and multi-loop Feynman diagrams, World Scientific, Singapore (2007).
A.A. Vladimirov, Method for computing renormalization group functions in dimensional renormalization scheme, Theor. Math. Phys. 43 (1980) 417 [Teor. Mat. Fiz. 43 (1980) 210] [INSPIRE].
M. Tentyukov and J. Fleischer, A Feynman diagram analyzer DIANA, Comput. Phys. Commun. 132 (2000) 124 [hep-ph/9904258] [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
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].
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].
J. Hoff, The Mathematica package TopoID and its application to the Higgs boson production cross section, J. Phys. Conf. Ser. 762 (2016) 012061 [arXiv:1607.04465] [INSPIRE].
A.V. Smirnov and F.S. Chuharev, FIRE6: Feynman Integral REduction with modular arithmetic, Comput. Phys. Commun. 247 (2020) 106877 [arXiv:1901.07808] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [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].
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].
B. Fiol, J. Martínez-Montoya and A. Rios Fukelman, Wilson loops in terms of color invariants, JHEP 05 (2019) 202 [arXiv:1812.06890] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory, Nucl. Phys. B 661 (2003) 19 [Erratum ibid. 685 (2004) 405] [hep-ph/0208220] [INSPIRE].
A.V. Kotikov, L.N. Lipatov, A.I. Onishchenko and V.N. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. 632 (2006) 754] [hep-th/0404092] [INSPIRE].
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Grozin, A.G., Lee, R.N. & Pikelner, A.F. Four-loop QCD cusp anomalous dimension at small angle. J. High Energ. Phys. 2022, 94 (2022). https://doi.org/10.1007/JHEP11(2022)094
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DOI: https://doi.org/10.1007/JHEP11(2022)094