Abstract
We generalize the scattering equations to include both massless and massive particles. We construct an expression for the tree-level n-point amplitude with n-2 gluons or gravitons and a pair of massive scalars in arbitrary spacetime dimension as a sum over the (n-3)! solutions of the scattering equations, a la Cachazo, He, and Yuan. We derive the BCJ relations obeyed by these massive amplitudes.
Highlights
Of (n − 2) gluons and a pair of massive particles ψ of arbitrary spin transforming in the fundamental representation of the gauge group
We have examined color-kinematic duality for gauge theories with massive particles in representations other than the adjoint
We derived the form of the BCJ relations for tree-level amplitudes with n − 2 gluons and a pair of massive particles that are implied by color-kinematic duality
Summary
The number and form of the BCJ relations among color-ordered amplitudes are completely fixed by the rank and null eigenvectors of the propagator matrix. We explicitly define this matrix, and determine the relationship between the propagator matrices for the n-gluon amplitude and the amplitude for (n − 2) gluons and a pair of massive fundamentals. This allows us to derive the form of the BCJ relations among massive amplitudes, provided color-kinematic duality is satisfied
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