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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, and Mao Zeng
Phys. Rev. Lett. 122, 201603 – Published 24 May 2019

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.

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  • Received 28 January 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.201603

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Zvi Bern1, Clifford Cheung2, Radu Roiban3, Chia-Hsien Shen1, Mikhail P. Solon2, and Mao Zeng4

  • 1Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
  • 2Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125
  • 3Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 4Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland

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Issue

Vol. 122, Iss. 20 — 24 May 2019

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