Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents

TL;DR

This paper develops differential operators and unifying relations for 1-loop Feynman integrands using Berends-Giele currents, reproducing known relations and extending them to (A)dS scalar theories with minimal gluon coupling.

Contribution

It introduces a novel method to construct unifying relations for 1-loop integrands using Berends-Giele currents, including extensions to (A)dS space.

Findings

Reproduces known unifying relations between Yang-Mills and scalar theories.

Extends unifying relations to (A)dS space for scalar theories with minimal gluon coupling.

Provides a new framework for analyzing 1-loop Feynman integrands.

Abstract

Our work focuses on utilizing the Berends-Giele currents to construct differential operators and unifying relations for 1-loop Feynman integrands. We successfully reproduce the known results for the unifying relations between Yang-Mills theory and Yang-Mills scalar theory, and extend the discussion to the (A)dS case for the scalar theory with minimal coupling to gluons.