A new gauge-invariant double copy for heavy-mass effective theory

TL;DR

The paper introduces a gauge-invariant double-copy framework for heavy-mass effective theories that yields BCJ numerators written directly in terms of field strengths. By employing fusion-rule currents and an associativity-based L-operator, it constructs gauge-invariant, local numerators that automatically satisfy Jacobi relations and crossing symmetry, with explicit results up to six points. The approach yields compact tree-level YM-M and GR-M amplitudes and links to pure YM local BCJ numerators via well-defined limits. This framework promises streamlined constructions for gravity amplitudes in the heavy-mass regime and provides a foundation for future all-multiplicity proofs and subleading corrections.

Abstract

We propose a new form of the colour-kinematics/double-copy duality for heavy-mass effective field theories, which we apply to construct compact expressions for tree amplitudes with heavy matter particles in Yang-Mills and in gravity to leading order in the mass. In this set-up, the new BCJ numerators are fixed uniquely and directly written in terms of field strengths, making gauge invariance manifest. Furthermore, they are local and automatically satisfy the Jacobi relations and crossing symmetry. We construct these BCJ numerators explicitly up to six particles. We also discuss relations of the BCJ numerators in the heavy-mass effective theory with those in pure Yang-Mills amplitudes.