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

Abstract

Using rapidity evolution equations we study two-to-two gauge-theory scattering amplitudes in the Regge limit. We carry out explicit computations at next-to-next-to-leading logarithmic accuracy through four loops and present new results for both infrared-singular and finite contributions to the amplitude. New techniques are devised in order to derive the colour structure stemming from three-Reggeon exchange diagrams in terms of commutators of channel operators, obtaining results that are valid for any gauge group, and apply to scattered particles in any colour representation. We also elucidate the separation between contributions to the Regge cut and Regge pole in the real part of the amplitude to all loop orders. We show that planar contributions due to multiple-Reggeon exchange diagrams can be factorised as a Regge pole along with the single-Reggeon exchange, and when this is done, the singular part of the gluon Regge trajectory is directly determined by the cusp anomalous dimension. We explicitly compute the Regge cut component of the amplitude through four loops and show that it is non-planar. From a different perspective, the new results provide important information on soft singularities in general kinematics beyond the planar limit: by comparing the computed corrections to the general form of the four-loop soft anomalous dimension we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.

132 pages, 13 figures, 1 table; v2: references added, typos corrected, to appear in JHEP

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Cited by in corpus (16)

• The Four Loop QCD Rapidity Anomalous Dimension
• Three-loop gluon scattering in QCD and the gluon Regge trajectory
• Disentangling the Regge cut and Regge pole in perturbative QCD
• The on-shell expansion: from Landau equations to the Newton polytope
• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• The gluon Regge trajectory at three loops from planar Yang-Mills theory
• Anomalous Dimensions from Soft Regge Constants
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• A Collinear Perspective on the Regge Limit
• Building blocks of Cwebs in multiparton scattering amplitudes
• Deciphering Colour Building Blocks of Massive Multiparton Amplitudes at 4-loops and beyond
• The two-loop Higgs impact factor
• Regge poles and cuts and the Lipatov vertex
• Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair
• Effective Field Theory Factorization for Diffraction
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory