Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories

TL;DR

This paper introduces a double-cover extension of the CHY formalism to achieve a novel factorization method for gauge theory amplitudes, simplifying the soft limit analysis and providing a new graphical and algorithmic framework.

Contribution

It presents a new double-cover approach to factorize gauge theory amplitudes within the CHY formalism, offering a different pole structure and a graphical algorithm.

Findings

New graphical representation for YM and YMS amplitudes

An algorithm for amplitude decomposition into three-point blocks

Simplification of the soft limit in the CHY approach

Abstract

In this work we show how a double-cover (DC) extension of the Cachazo, He and Yuan formalism (CHY) can be used to provide a new realization for the factorization of the amplitudes involving gluons and scalar fields. First, we propose a graphic representation for a color-ordered Yang-Mills (YM) and special Yang-Mills-Scalar (YMS) amplitudes within the scattering equation formalism. Using the DC prescription, we are able to obtain an algorithm (integration-rules) which decomposes amplitudes in terms of three-point building-blocks. It is important to remark that the pole structure of this method is totally different to ordinary factorization (which is a consequence of the scattering equations). Finally, as a byproduct, we show that the soft limit in the CHY approach, at leading order, becomes trivial by using the technology described in this paper.