https://hal-cea.archives-ouvertes.fr/cea-01297372Grozin, AndreyAndreyGrozinNSU - Novosibirsk State UniversityBINP - Budker Institute of Nuclear Physics - SB RAS - Siberian Branch of the Russian Academy of SciencesHenn, Johannes M.Johannes M.HennPRISMA Cluster of Excellence & Institute for Physics (THEP) - JGU - Johannes Gutenberg - Universität Mainz = Johannes Gutenberg UniversityKorchemsky, Gregory P.Gregory P.KorchemskyIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueMarquard, PeterPeterMarquardDESY - Deutsches Elektronen-Synchrotron [Hamburg]The three-loop cusp anomalous dimension in QCD and its supersymmetric extensionsHAL CCSD2016QCDWilson linesinfrared divergences of scattering amplitudesresumma-tion[PHYS.HPHE] Physics [physics]/High Energy Physics - Phenomenology [hep-ph][PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]De Laborderie, Emmanuelle2016-04-04 11:31:122023-03-24 14:53:022016-04-05 09:38:41enJournal articleshttps://hal-cea.archives-ouvertes.fr/cea-01297372/document10.1007/JHEP01(2016)140text/html; charset=utf-81We 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 $\mathcal{N}=4$ 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.