Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles

Understand

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.