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Report number	EDINBURGH-2017-13 ; CERN-TH-2017-138 ; CP3-17-20 ; SLAC-PUB-17089 ; --QMUL-PH-17-10 ; arXiv:1706.10162
Title	Bootstrapping the QCD soft anomalous dimension
Author(s)	Almelid, Øyvind ; Duhr, Claude ; Gardi, Einan ; McLeod, Andrew ; White, Chris D.
Imprint	2017-06-30. - 37 p.
Note	37 pages, 1 figure
Subject category	hep-th ; Particle Physics - Theory ; hep-ph ; Particle Physics - Phenomenology
Abstract	The soft anomalous dimension governs the infrared singularities of scattering amplitudes to all orders in perturbative quantum field theory, and is a crucial ingredient in both formal and phenomenological applications of non-abelian gauge theories. It has recently been computed at three-loop order for massless partons by explicit evaluation of all relevant Feynman diagrams. In this paper, we show how the same result can be obtained, up to an overall numerical factor, using a bootstrap procedure. We first give a geometrical argument for the fact that the result can be expressed in terms of single-valued harmonic polylogarithms. We then use symmetry considerations as well as known properties of scattering amplitudes in collinear and high-energy (Regge) limits to constrain an ansatz of basis functions. This is a highly non-trivial cross-check of the result, and our methods pave the way for greatly simplified higher-order calculations.
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