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

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

85 pages, 13 figures

References in corpus (14)

• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Bootstrapping the QCD soft anomalous dimension
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• Three-loop gluon scattering in QCD and the gluon Regge trajectory
• Iterated amplitudes in the high-energy limit
• Disentangling the Regge cut and Regge pole in perturbative QCD
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• The gluon Regge trajectory at three loops from planar Yang-Mills theory