Tree- and one-loop-level double copy for the (anti)self-dual sectors of Yang-Mills and gravity

TL;DR

This paper explores the double copy relationship between (anti)self-dual Yang-Mills and gravity at tree and one-loop levels, revealing natural color-kinematics duality and deriving Kawai-Lewellen-Tye relations for arbitrary external particles.

Contribution

It introduces a perturbiner-based approach to analyze off-shell amplitudes, deriving explicit double copy structures and master numerators at one loop for the first time.

Findings

Color-kinematics duality holds off-shell in (anti)self-dual sectors.

Explicit Kawai-Lewellen-Tye relations are obtained for any number of external particles.

Double copy structures are confirmed at both tree and one-loop levels.

Abstract

By employing the perturbiner method we study the tree- and one-loop-level amplitudes in (anti)self-dual Yang-Mills, focusing on color-kinematics duality and double copy features; they arise naturally even in the fully off-shell case. In particular, we calculate the respective the Kawai-Lewellen-Tye relations for tree-level Berends-Giele currents and color-kinematics master numerators at one loop, both cases for any number of external particles.