Massive spinning-particle gravitational amplitudes are obtained by dimensional reduction of massless double copy amplitudes, fixing g=2 and matter couplings, and the Goldberger-Ridgway classical double copy is identified with a compactification of N=4 supergravity.
Proof of the fundamental BCJ relations for QCD amplitudes
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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 $2 p_i p_j$. 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.
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On the Double Copy for Spinning Matter
Massive spinning-particle gravitational amplitudes are obtained by dimensional reduction of massless double copy amplitudes, fixing g=2 and matter couplings, and the Goldberger-Ridgway classical double copy is identified with a compactification of N=4 supergravity.