The gluon Regge trajectory at three loops from planar Yang-Mills theory

Abstract

We compute the three-loop leading-colour corrections to the Yang-Mills Regge trajectory and gluon impact factor. Conjecturing that, in analogy with $\mathcal{N}=4$ super Yang-Mills (SYM), in a suitable scheme $N_c$-subleading terms are absent from the three-loop Regge trajectory, we understand our result as the first computation of the pure gauge, or $n_f=0$, part of the QCD three-loop Regge trajectory. The results are presented both for the bare and renormalised amplitudes and are consistent with predictions from infrared factorisation along with reproducing known results in planar $\mathcal{N}=4$ SYM through a maximal weight truncation. We also include the dependence on a Regge factorisation scale to facilitate future applications in BFKL theory at next-to-next-to leading logarithmic accuracy.

11 pages

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• Exotic tetraquarks at the HL-LHC with JETHAD: A high-energy viewpoint
• Anomalous Dimensions from Soft Regge Constants
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Tetraquark-Jet Systems at the High-Luminosity LHC
• The two-loop Higgs impact factor
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory