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

Abstract

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, à la Cachazo, He, and Yuan. We derive the BCJ relations obeyed by these massive amplitudes.