Scattering equations and virtuous kinematic numerators and dual-trace functions

Understand

Inspired by recent developments on scattering equations, we present a constructive procedure for computing symmetric, amplitude-encoded, BCJ numerators for n-point gauge-theory amplitudes, thus satisfying the three virtues identified by Broedel and Carrasco.

• We also develop a constructive procedure for computing symmetric, amplitude-encoded dual-trace functions (tau) for n-point amplitudes.
• These can be used to obtain symmetric kinematic numerators that automatically satisfy color-kinematic duality.
• The S_n symmetry of n-point gravity amplitudes formed from these symmetric dual-trace functions is completely manifest.