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. 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…

• NS
  National Science Foundation

  Award: DE-SC0009937
• UD
  U.S. Department of Energy

  Awards: DE-SC0009937, DE-SC0013699
• EC
  European Commission
• SN
  Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

  Award: SNF200021179016
• WB
  Walter Burke Institute for Theoretical Physics

  Award: DE-SC0011632
• HE
  H2020 European Research Council