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

TL;DR

This paper extends the scattering equations framework to incorporate massive particles, deriving new amplitude expressions and BCJ relations for gauge and gravitational interactions involving massive scalars.

Contribution

It generalizes scattering equations to include massive particles and derives BCJ relations for these extended amplitudes.

Findings

Provides a formula for tree-level amplitudes with massive scalars and gluons/gravitons.

Derives BCJ relations for amplitudes involving massive particles.

Shows the applicability in arbitrary spacetime dimensions.

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.