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Journal of High Energy Physics

, 2015:197 | Cite as

Proof of the fundamental BCJ relations for QCD amplitudes

  • Leonardo de la Cruz
  • Alexander Kniss
  • Stefan WeinzierlEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

The fundamental BCJ-relation is a linear relation between primitive tree amplitudes with different cyclic orderings. The cyclic orderings differ by the insertion place of one gluon. The coefficients of the fundamental BCJ-relation are linear in the Lorentz invariants 2p i p j . The BCJ-relations are well established for pure gluonic amplitudes as well as for amplitudes in \( \mathcal{N}=4 \) super-Yang-Mills theory. Recently, it has been conjectured that the BCJ-relations hold also for QCD amplitudes. In this paper we give a proof of this conjecture. The proof is valid for massless and massive quarks.

Keywords

Scattering Amplitudes QCD 

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) 2015

Authors and Affiliations

  • Leonardo de la Cruz
    • 1
  • Alexander Kniss
    • 1
  • Stefan Weinzierl
    • 1
    Email author
  1. 1.PRISMA Cluster of Excellence, Institut für PhysikJohannes Gutenberg-Universität MainzMainzGermany

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