Constructing EYM amplitudes by inverse soft limit

TL;DR

This paper demonstrates that Einstein-Yang-Mills (EYM) MHV amplitudes can be constructed using the inverse soft limit (ISL) method, reproducing known spanning forest formulas and introducing new graph-based identities.

Contribution

It shows how to derive EYM MHV amplitudes with ISL, connecting soft limit techniques to spanning forest formulas and graph identities.

Findings

EYM MHV amplitudes constructed via ISL match known formulas

New graph-based identities related to Schouten identity introduced

Method bridges soft limit techniques with spanning forest representations

Abstract

It is well known that gravity amplitudes in four dimensions can be reconstructed by the inverse soft limit (ISL) method. According to ISL, a tree level $n$-graviton maximally-helicity-violating (MHV) amplitude is expressed in terms of deformed $(n-1)$-graviton amplitudes accompanied by soft graviton factors. On another hand, single- and double-trace tree-level Einstein-Yang-Mills (EYM) MHV amplitudes have been proven to satisfy spanning forest formulas, where each edge in a forest has the same form with a term in soft graviton factor. It is not transparent that the formulas satisfied by EYM amplitudes can be constructed with ISL. In this paper, we construct the single- and double-trace MHV amplitudes in EYM, by the ISL and show that the known formulas can be precisely reproduced. Interesting identities which are based on Schouten identity and characterized by graphs are also introduced.