Gravitational Radiation from Color-Kinematics Duality

TL;DR

This paper demonstrates how to compute classical gravitational radiation from Yang-Mills theory using color-kinematics duality and the double copy, extending the duality beyond leading order and confirming its validity at third post-Minkowskian order.

Contribution

It provides a perturbative calculation of classical radiation in Yang-Mills and dilaton gravity, explicitly manifesting color-kinematics duality at next-to-leading order and beyond, with a novel appearance of the kinematic Jacobi identity.

Findings

Confirmed the double copy relation at third post-Minkowskian order.

Established the presence of the kinematic Jacobi identity beyond field-theory S-matrix.

Extended the Goldberger-Ridgway rules to higher orders.

Abstract

We perturbatively calculate classical radiation in Yang-Mills theory and dilaton gravity, to next-to-leading order in couplings. The radiation is sourced by the scattering of two relativistic massive scalar sources with the dynamical effect taken into account, corresponding to the post-Minkowskian regime in gravity. We show how to arrange the Yang-Mills radiation such that the duality between colors and kinematics is manifest, including the three-term Jacobi identity. The search for duality-satisfying expressions exploits an auxiliary bi-adjoint scalar theory as a guide for locality. The double copy is obtained by replacing the color factors in Yang-Mills with kinematic counterparts, following Bern-Carrasco-Johansson construction in S- matrix. On the gravity side, the radiation is directly computed at the third post-Minkowskian order with massive sources. We find perfect agreement between observables in dilaton gravity and the Yang-Mills double copy. This non-trivially generalizes the leading-order rules by Goldberger and Ridgway. For the first time, the kinematic Jacobi identity appears beyond field-theory S-matrix, suggesting that the color-kinematics duality holds more generally. Our results offer a path for simplifying analytical calculations in post-Minkowskian regime.