The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions

• Published in: The journal of high energy physics Vol. 2016; no. 1; pp. 1 - 65
• Main Authors: Grozin, Andrey G., Henn, Johannes M., Korchemsky, Gregory P., Marquard, Peter
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2016; Springer Verlag (Germany)
• Subjects: Classical and Quantum Gravitation; Coupling; Cusps; Differential equations; Elementary Particles; High Energy Physics - Phenomenology; High Energy Physics - Theory; Mathematical analysis; Physics; Physics and Astronomy; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Singularities; String Theory; Supersymmetry; Texts; Wilson; t Hooft and Polyakov loops; Scattering Amplitudes; infrared divergences of scattering amplitudes; QCD; Wilson lines; resumma-tion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2016)140

A bstract We present the details of the analytic calculation of the three-loop angle-dependent cusp anomalous dimension in QCD and its supersymmetric extensions, including the maximally supersymmetric N = 4 super Yang-Mills theory. The three-loop result in the latter theory is new and confirms a conjecture made in our previous paper. We study various physical limits of the cusp anomalous dimension and discuss its relation to the quark-antiquark potential including the effects of broken conformal symmetry in QCD. We find that the cusp anomalous dimension viewed as a function of the cusp angle and the new effective coupling given by light-like cusp anomalous dimension reveals a remarkable universality property — it takes the same form in QCD and its supersymmetric extensions, to three loops at least. We exploit this universality property and make use of the known result for the three-loop quark-antiquark potential to predict the special class of nonplanar corrections to the cusp anomalous dimensions at four loops. Finally, we also discuss in detail the computation of all necessary Wilson line integrals up to three loops using the method of leading singularities and differential equations.