Spinning particles, axion radiation, and the classical double copy

TL;DR

This work extends the classical double copy to spinning particles by computing gluon radiation from spinning color charges and applying color-to-kinematics replacements to obtain gravitational radiation in a theory with graviton, dilaton, and axion fields. Consistency of the double copy in four dimensions fixes the chromomagnetic coupling to $kappa = -1$ (corresponding to a gyromagnetic ratio $g = 2$) and, together with fixed dilaton/axion couplings, yields a bulk action matching string gravity. The axion radiation amplitudes computed on the gauge and gravity sides agree exactly under these couplings, strengthening the link between BCJ duality and classical gravity and guiding future extensions to higher spin and tidal effects in the double-copy framework.

Abstract

We extend the perturbative double copy between radiating classical sources in gauge theory and gravity to the case of spinning particles. We construct, to linear order in spins, perturbative radiating solutions to the classical Yang-Mills equations sourced by a set of interacting color charges with chromomagnetic dipole spin couplings. Using a color-to-kinematics replacement rule proposed earlier by one of the authors, these solutions map onto radiation in a theory of interacting particles coupled to massless fields that include the graviton, a scalar (dilaton) $φ$ and the Kalb-Ramond axion field $B_{μν}$. Consistency of the double copy imposes constraints on the parameters of the theory on both the gauge and gravity sides of the correspondence. In particular, the color charges carry a chromomagnetic interaction which, in $d=4$, corresponds to a gyromagnetic ratio equal to Dirac's value $g=2$. The color-to-kinematics map implies that on the gravity side, the bulk theory of the fields $(φ,g_{μν},B_{μν})$ has interactions which match those of $d$-dimensional `string gravity,' as is the case both in the BCJ double copy of pure gauge theory scattering amplitudes and the KLT relations between the tree-level $S$-matrix elements of open and closed string theory.

Figures (2)

• Figure 1: Feynman diagrams for the perturbative expansion of ${\tilde{J}}^\mu_a(k)$ up to order ${\cal O}(g^2_s)$. The diagram $(a)$ represents corrections to the spin-independent color current due to the equations of motion. Diagrams $(b)$-$(d)$ correspond to a single insertion of the spin-dependent color current.
• Figure 2: Perturbative corrections to axion emission. Dashed lines, wavy lines, and curly lines denote respectively scalar, graviton, and axion propagators.