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


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.


Scattering Amplitudes QCD 


Open Access

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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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