Classical gravitational scattering from a gauge-invariant double copy

TL;DR

This work introduces a gauge-invariant, double-copy-based HEFT framework to compute the classical gravitational scattering angle directly from 2MPI diagrams, avoiding iteration-term subtractions. By working in D dimensions and organizing amplitudes with a heavy-mass expansion, the authors derive compact tree-level amplitudes, perform unitarity cuts, and obtain a complete 2MPI two-loop (3PM) result including radiation reaction, expressed via a canonical master-integral basis. The deflection angle is extracted from the HEFT phase in impact-parameter space, and the obtained 3PM results agree with established calculations in the literature. An all-loop probe-limit conjecture is formulated, suggesting a universal structure for leading classical contributions across loop orders and offering a potential bridge to radial-action and eikonal formalisms. The framework provides a dimensionally robust, gauge-invariant route to classical GR observables with clear connections to existing amplitude methods and potential extensions to higher loops and spin.

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.