Three-loop cusp anomalous dimension and a conjecture for $n$ loops

Abstract

I present analytical expressions for the cusp anomalous dimension in QCD through three loops in terms of elementary functions and ordinary polylogarithms. I observe interesting relations between the results at different loops and provide a conjecture for the $n$-loop cusp anomalous dimension in terms of the lower-loop results. I also present numerical results and simple approximate formulas for the cusp anomalous dimension relevant to top-quark production.

16 pages, 5 figures; a new section has been added and several other additions/changes made in v2

References in corpus (16)

• Two-loop soft anomalous dimensions for single top quark associated production with a W- or H-
• Next-to-next-to-leading-order collinear and soft gluon corrections for t-channel single top quark production
• NNLL resummation for s-channel single top quark production
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• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
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• The three-loop cusp anomalous dimension in QCD
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• The Massive Soft Anomalous Dimension Matrix at Two Loops
• NNNLO soft-gluon corrections for the top-antitop pair production cross section
• NNNLO soft-gluon corrections for the top-quark $p_T$ and rapidity distributions
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Multiple Gluon Exchange Webs

Cited by in corpus (13)

• Soft anomalous dimensions for single-top production at three loops
• Soft-gluon corrections in top-quark production
• Resummation for $2\to n$ processes in single-particle-inclusive kinematics
• Associated production of a top quark with a photon via anomalous couplings
• Soft-gluon corrections for the associated production of a single top quark and a Higgs boson
• Soft anomalous dimensions and resummation in QCD
• Four-loop massive cusp anomalous dimension in QCD: a calculation from asymptotics
• QCD cusp anomalous dimension: current status
• On the cusp anomalous dimension in the ladder limit of $\mathcal{N}=4$ SYM
• Single-top and top-antitop cross sections
• Theoretical results for charged-Higgs production
• Three-loop soft anomalous dimensions for top-quark processes
• Three-loop soft anomalous dimensions in QCD