One-loop central-emission vertex for two gluons in N = 4 super Yang-Mills theory

Emmet P. Byrne*, Vittorio Del Duca, Lance J. Dixon, Einan Gardi, Jennifer M. Smillie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

A necessary ingredient for extending the BFKL equation to next-to-next-to-leading logarithmic (NNLL) accuracy is the one-loop central emission vertex (CEV) for two gluons which are not strongly ordered in rapidity. Here we consider the one-loop six-gluon amplitude in N = 4 super Yang-Mills (SYM) theory in a central next-to-multi-Regge kinematic (NMRK) limit, we show that its dispersive part factorises in terms of the two-gluon CEV, and we use it to extract the one-loop two-gluon CEV for any helicity configuration within this theory. This is a component of the two-gluon CEV in QCD. Although computed in the NMRK limit, both the colour structure and the kinematic dependence of the two-gluon CEV capture much of the complexity of the six-gluon amplitudes in general kinematics. In fact, the transcendental functions of the latter can be conveniently written in terms of impact factors, trajectories, single-emission CEVs and a remainder, which is a function of the conformally invariant cross ratios which characterise the six-gluon amplitudes in planar N = 4 SYM. Finally, as expected, in the MRK limit the two-gluon CEV neatly factorises in terms of two single-emission CEVs.
Original languageEnglish
Article number271
Pages (from-to)1-86
Number of pages86
JournalJournal of High Energy Physics
Issue number8
Publication statusPublished - 26 Aug 2022

Keywords / Materials (for Non-textual outputs)

  • Higher-Order Perturbative Calculations
  • Resummation
  • Scattering Amplitudes


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