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Using rapidity evolution equations we study two-to-two gauge-theoryscattering amplitudes in the Regge limit. We carry out explicit computations atnext-to-next-to-leading logarithmic accuracy through four loops and present newresults for both infrared-singular and finite contributions to the amplitude.New techniques are devised in order to derive the colour structure stemmingfrom three-Reggeon exchange diagrams in terms of commutators of channeloperators, obtaining results that are valid for any gauge group, and apply toscattered particles in any colour representation. We also elucidate theseparation between contributions to the Regge cut and Regge pole in the realpart of the amplitude to all loop orders. We show that planar contributions dueto multiple-Reggeon exchange diagrams can be factorised as a Regge pole alongwith the single-Reggeon exchange, and when this is done, the singular part ofthe gluon Regge trajectory is directly determined by the cusp anomalousdimension. We explicitly compute the Regge cut component of the amplitudethrough four loops and show that it is non-planar. From a differentperspective, the new results provide important information on softsingularities in general kinematics beyond the planar limit: by comparing thecomputed corrections to the general form of the four-loop soft anomalousdimension we derive powerful constraints on its kinematic dependence, openingthe way for a bootstrap-based determination.

Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops