Speaker
Description
Scattering amplitudes greatly simplify in the Regge limit, and yet exhibit a very interesting structure, which is far richer in the full gauge theory than in the planar limit. Prior to the development of QCD, Regge and others showed that the asymptotic high-energy behaviour of amplitudes is governed by poles and cuts in the complex angular momentum plane. It was also shown (Mandelstam, 1963) that Regge cuts emerge from non-planar diagrams. Here we explore the separation between Regge poles and cuts in perturbative QCD using rapidity evolution equations. We study Regge-pole factorisation in 2 \to n gauge theory amplitudes in multi-Regge kinematics, whose parameters, the impact factors, the trajectory and the Lipatov vertex, can be fully determined from 2 \to 2 and 2 \to 3 amplitudes. The factorisation is broken at Next-to-Next-to-Leading-Logarithmic (NNLL) accuracy by the appearance of a Regge cut owing to multiple Reggeon exchange in the $t$ channel. We compute the multiple Reggeon exchange contributions through four loops and show how to define the NNLL Regge-pole parameters in the presence of a Regge cut, maintaining the non-planar nature of the cut as well as the universality of the Regge pole parameters. Remarkably, this separation between pole and cuts directly leads to the generalization of the Korchemsky-Korchemskaya relation between the singularities of the gluon Regge trajectory and the cusp anomalous dimension to three loops.
