Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order

TL;DR

Adapting methods for integration and matching from effective field theory, the conservative Hamiltonian is extracted for compact spinless binaries at third post-Minkowskian order and is in complete agreement with corresponding terms in state-of-the-art expressions at fourth post-Newtonian order.

Abstract

We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. Adapting methods for integration and matching from effective field theory, we extract the conservative Hamiltonian for compact spinless binaries at third post-Minkowskian order. The resulting Hamiltonian is in complete agreement with corresponding terms in state-of-the-art expressions at fourth post-Newtonian order as well as the probe limit at all orders in velocity. We also derive the scattering angle at third post-Minkowskian order.

Figures (2)

• Figure 1: Unitarity cuts needed for the classical scattering amplitude. The shaded ovals represent tree amplitudes while the exposed lines depict on-shell states. The wiggly and straight lines denote gravitons and massive scalars, respectively.
• Figure 2: The eight independent diagrams showing the propagator structure of integrals from which the classical contributions are extracted.