Note on single-trace EYM amplitudes with MHV configuration

TL;DR

This paper extends a known formula for tree-level single-trace Einstein-Yang-Mills (EYM) amplitudes in the MHV configuration, expressing them in terms of pure gluon amplitudes with gravitons splitting into collinear gluon pairs.

Contribution

It generalizes the existing formula for EYM amplitudes to more complex cases beyond one and two gravitons.

Findings

Derived a general formula for MHV EYM amplitudes with multiple gravitons.

Expressed EYM amplitudes in terms of pure gluon amplitudes.

Confirmed the splitting of gravitons into collinear gluon pairs in the generalized case.

Abstract

In the maximally-helicity-violating (MHV) configuration, tree-level single-trace Einstein-Yang-Mills (EYM) amplitude with one and two gravitons have been shown to satisfy a formula where each graviton splits into a pair of collinear gluons. In this paper, we extend this formula to more general cases. We provide a general formula which expresses tree-level single-trace MHV amplitudes in terms of pure gluon amplitudes, where each graviton turns into a pair of collinear gluons.