  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 $2 p_i p_j$. 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.

High Energy Physics - Theory;High Energy Physics - Phenomenology