Classical gravitational scattering from a gauge-invariant double copy

TL;DR

This paper introduces a novel gauge-invariant double copy method to compute classical black hole scattering angles directly from amplitudes, simplifying calculations and including radiation effects up to third post-Minkowskian order.

Contribution

It develops a new approach using gauge-invariant BCJ numerators in a heavy-mass effective field theory to directly extract classical scattering angles from amplitudes.

Findings

Computed scattering angle up to third post-Minkowskian order.

Derived D-dimensional loop integrand expressions including radiation.

Eliminated the need for subtracting iteration terms in calculations.

Abstract

We propose a method to compute the scattering angle for classical black hole scattering directly from two massive particle irreducible diagrams in a heavy-mass effective field theory approach to general relativity, without the need of subtracting iteration terms. The amplitudes in this effective theory are constructed using a recently proposed novel colour-kinematic/double copy for tree-level two-scalar, multi-graviton amplitudes, where the BCJ numerators are gauge invariant and local with respect to the massless gravitons. These tree amplitudes, together with graviton tree amplitudes, enter the construction of the required $D$-dimensional loop integrands and allow for a direct extraction of contributions relevant for classical physics. In particular the soft/heavy-mass expansions of full integrands is circumvented, and all iterating contributions can be dropped from the get go. We use this method to compute the scattering angle up to third post-Minkowskian order in four dimensions, including radiation reaction contributions, also providing the expression of the corresponding integrand in $D$ dimensions.