On the Double Copy for Spinning Matter

TL;DR

This paper investigates the double copy construction for amplitudes involving massive spinning particles, revealing how these relations originate from massless theories and applying them to classical objects like black holes.

Contribution

It demonstrates that double copy relations for spinning matter can be derived from massless theories via compactification and provides new Lagrangians and classical interpretations for these relations.

Findings

Double copy relations for spinning particles originate from massless theories.

New Lagrangians for spin-1 matter reproduce interactions with up to two massive lines.

Smooth transition from quantum to classical double copy relations at five points.

Abstract

We explore various tree-level double copy constructions for amplitudes including massive particles with spin. By working in general dimensions, we use that particles with spins $s\leq 2$ are fundamental to argue that the corresponding double copy relations partially follow from compactification of their massless counterparts. This massless origin fixes the coupling of gluons, dilatons and axions to matter in a characteristic way (for instance fixing the gyromagnetic ratio), whereas the graviton couples universally reflecting the equivalence principle. For spin-1 matter we conjecture all-order Lagrangians reproducing the interactions with up to two massive lines and we test them in a classical setup, where the massive lines represent spinning compact objects such as black holes. We also test the amplitudes via CHY formulae for both bosonic and fermionic integrands. At five points, we show that by applying generalized gauge transformations one can obtain a smooth transition from quantum to classical BCJ double copy relations for radiation, thereby providing a QFT derivation for the latter. As an application, we show how the theory arising in the classical double copy of Goldberger and Ridgway can be naturally identified with a certain compactification of $\mathcal{N}=4$ Supergravity.