One-loop central-emission vertex for two gluons in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory

• Published in: The journal of high energy physics 2022-08, Vol.2022 (8), p.1-88
• Main Authors: Emmet P. Byrne, Vittorio Del Duca, Lance J. Dixon, Einan Gardi, Jennifer M. Smillie
• Format: Article
• Language: English
• Subjects: Higher-Order Perturbative Calculations; Resummation; Scattering Amplitudes
• ISSN: 1029-8479
• DOI: 10.1007/JHEP08(2022)271

Abstract 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 $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ = 4 SYM. Finally, as expected, in the MRK limit the two-gluon CEV neatly factorises in terms of two single-emission CEVs.