One-Loop Yang-Mills Integrands from Scattering Equations

TL;DR

This paper develops a method to connect one-loop gauge theory integrands with quadratic propagators using scattering equations and double forward limits, validated by unitarity cuts.

Contribution

It introduces a novel approach to derive quadratic propagator integrands from linear ones in gauge theories via scattering equations and forward limits.

Findings

Consistent with four-dimensional unitarity cuts

Demonstrated through explicit examples

Provides a framework for further generalizations

Abstract

We investigate in the context of the scattering equations, how one-loop linear propagator integrands in gauge theories can be linked to integrands with quadratic propagators using a double forward limit. We illustrate our procedure through examples and demonstrate how the different parts of the derived quadratic integrand are consistent with cut-integrands derived from four-dimensional generalized unitarity. We also comment on applications and discuss possible further generalizations.