On the Double Copy for Spinning Matter
Yilber Fabian Bautista, Alfredo Guevara
TL;DR
This work studies tree-level double-copy constructions for amplitudes with massive spinning matter in general dimensions, showing that for spins $s\le 2$ the gravitational amplitudes arise from compactification of massless gauge theories and that the graviton couples universally while other fields (dilaton, axion) have couplings fixed by the massless origin. It develops a one-matter-line $\tfrac{1}{2}\otimes\tfrac{1}{2}$ construction and a $0\otimes1$ gravitational sector, alongside a detailed Lagrangian program that realizes these double-copy relations across QCD and gravity and checks them with CHY-type methods. The analysis extends to two-matter-line setups via BCJ duality, covering elastic and inelastic scattering, and culminates in a robust description of classical radiation through generalized gauge transformations that preserve the double-copy structure. The results connect the classical double copy of Goldberger and Ridgway to a compactification of $N=4$ Supergravity in $d$ dimensions and illuminate how dilaton and axion couplings are fixed by high-energy and soft-theorem constraints, with broad implications for spinning compact objects and gravitational wave physics.
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.