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Article
Report number	arXiv:2111.10664 ; CERN-TH-2021-200
Title	Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
Author(s)	Falcioni, Giulio (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Maher, Niamh (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Milloy, Calum (INFN, Turin ; Turin U.) ; Vernazza, Leonardo (INFN, Turin ; Turin U. ; CERN)
Publication	2022-03-08
Imprint	2021-11-20
Number of pages	134
Note	132 pages, 13 figures, 1 table; v2: references added, typos corrected, to appear in JHEP
In:	JHEP 2203 (2022) 053
DOI	10.1007/JHEP03(2022)053
Subject category	hep-th ; Particle Physics - Theory ; hep-ph ; Particle Physics - Phenomenology
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.
Copyright/License	publication: © 2022-2024 The Authors (License: CC-BY-4.0), sponsored by SCOAP³ preprint: (License: CC BY 4.0)

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