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

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

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91 Scopus citations

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.

Original languageEnglish (US)
Article number201603
JournalPhysical review letters
Volume122
Issue number20
DOIs
StatePublished - May 24 2019

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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