Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame

TL;DR

This paper presents a recursive expansion of Einstein-Yang-Mills amplitudes using the CHY formalism, connecting them to pure Yang-Mills amplitudes and introducing a spanning tree structure for efficient evaluation.

Contribution

It introduces a new recursive method for expanding EYM amplitudes in terms of pure YM amplitudes using spanning trees and graph rules, applicable in general dimensions.

Findings

Recursive expansion valid for arbitrary helicities

Spanning tree structure for amplitude representation

Graph rules for direct coefficient evaluation

Abstract

Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients.