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

Mao Zeng,Radu Roiban,Zvi Bern,Chia-Hsien Shen,Mikhail P Solon,Clifford Cheung

doi:10.1103/physrevlett.122.201603

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 and find agreement with known results.

Highlights

Introduction.—The recent discovery of gravitational waves at LIGO/Virgo [1] has launched an extraordinary new era in astronomy, astrophysics and cosmology
Existing theory benchmarks come from a variety of approaches, including the effective one-body formalism [3], numerical relativity [4], the self-force formalism [5], and perturbative analysis using post-Newtonian (PN) [6,7,8,9,10], postMinkowskian (PM) [11,12,13], and effective field theory (EFT) [14] methods
We can calculate in strictly D 1⁄4 4 dimensions for the classical dynamics, where spinor helicity variables [20,21] dramatically simplify the required tree amplitudes

Summary

Introduction

Introduction.—The recent discovery of gravitational waves at LIGO/Virgo [1] has launched an extraordinary new era in astronomy, astrophysics and cosmology. Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order 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.

Results

Conclusion