From Jacobi off-shell currents to integral relations

TL;DR

This paper explores off-shell currents derived from Jacobi identities in gauge theories, revealing their structure, relation to colour-kinematics duality, and deriving one-loop integral relations with applications to collider physics.

Contribution

It introduces a new representation of off-shell currents based on three-point Feynman rules, facilitating the construction of higher-multiplicity numerators and deriving integral relations via Loop-Tree duality.

Findings

Off-shell currents can be expressed schematically with three-point rules.

The approach clarifies the Colour-Kinematics duality.

Explicit one-loop integral relations for QCD processes are provided.

Abstract

In this paper, we study off-shell currents built from the Jacobi identity of the kinematic numerators of $gg\to X$ with $X=ss,q\bar{q},gg$. We find that these currents can be schematically written in terms of three-point interaction Feynman rules. This representation allows for a straightforward understanding of the Colour-Kinematics duality as well as for the construction of the building blocks for the generation of higher-multiplicity tree-level and multi-loop numerators. We also provide one-loop integral relations through the Loop-Tree duality formalism with potential applications and advantages for the computation of relevant physical processes at the Large Hadron Collider. We illustrate these integral relations with the explicit examples of QCD one-loop numerators of $gg\to ss$.