Three-loop corrections to the soft anomalous dimension in multileg scattering

Almelid, Øyvind; Gardi, Einan; Duhr, Claude

doi:10.1103/PhysRevLett.117.172002

Article
Report number	arXiv:1507.00047 ; CERN-PH-TH-2015-148 ; CP3-15-18 ; EDINBURGH 2015-08
Title	Three-loop corrections to the soft anomalous dimension in multileg scattering
Related title	Three-loop corrections to the soft anomalous dimension in multi-leg scattering
Author(s)	Almelid, Øyvind (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.)
Publication	2016
Imprint	30 Jun 2015
Number of pages	6
Note	v2: remaining diagrams computed; colour conservation accounted for; strict collinear factorization shown to hold. Some references added. 6 pages, 2 figures
In:	Phys. Rev. Lett. 117 (2016) 172002
DOI	10.1103/PhysRevLett.117.172002
Subject category	Particle Physics - Phenomenology
Abstract	We present the three-loop result for the soft anomalous dimension governing long-distance singularities of multi-leg gauge-theory scattering amplitudes of massless partons. We compute all contributing webs involving semi-infinite Wilson lines at three loops and obtain the complete three-loop correction to the dipole formula. We find that non-dipole corrections appear already for three coloured partons, where the correction is a constant without kinematic dependence. Kinematic dependence appears only through conformally-invariant cross ratios for four coloured partons or more, and the result can be expressed in terms of single-valued harmonic polylogarithms of weight five. While the non-dipole three-loop term does not vanish in two-particle collinear limits, its contribution to the splitting amplitude anomalous dimension reduces to a constant, and it only depends on the colour charges of the collinear pair, thereby preserving strict collinear factorization properties. Finally we verify that our result is consistent with expectations from the Regge limit.
Copyright/License	arXiv nonexclusive-distrib. 1.0 preprint: © 2015-2025 CERN (License: CC-BY-4.0) publication: © 2016-2025 The Author(s) (License: CC-BY-3.0)