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Journal of High Energy Physics

, 2017:73 | Cite as

Bootstrapping the QCD soft anomalous dimension

  • Øyvind Almelid
  • Claude DuhrEmail author
  • Einan Gardi
  • Andrew McLeod
  • Chris D. White
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Scattering Amplitudes Gauge Symmetry Supersymmetric Gauge Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Øyvind Almelid
    • 1
  • Claude Duhr
    • 2
    • 3
    Email author
  • Einan Gardi
    • 1
  • Andrew McLeod
    • 4
    • 5
  • Chris D. White
    • 6
  1. 1.Higgs Centre for Theoretical Physics, School of Physics and AstronomyThe University of EdinburghEdinburghU.K.
  2. 2.Theoretical Physics Department, CERNGenevaSwitzerland
  3. 3.Center for Cosmology, Particle Physics and Phenomenology (CP3)Université Catholique de LouvainLouvain-La-NeuveBelgium
  4. 4.SLAC National Accelerator LaboratoryStanford UniversityStanfordU.S.A.
  5. 5.Kavli Institute for Theoretical PhysicsUniversity of California Santa BarbaraSanta BarbaraU.S.A.
  6. 6.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonU.K.

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