# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1703.01269