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Published May 24, 2019 | Published + Submitted
Journal Article Open

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 derive the scattering angle at third post-Minkowskian order and find agreement with known results.

Additional Information

© 2019 Published by the American Physical Society. 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. Received 28 January 2019; published 24 May 2019. We thank Alessandra Buonanno, Thibault Damour, Michael Enciso, David Kosower, Andrés Luna, Aneesh Manohar, Smadar Naoz, Julio Parra-Martinez, Rafael Porto, Jan Steinhoff, George Sterman, Justin Vines, and Mark Wise for helpful discussions, including comments on the manuscript. In addition, we especially thank Ira Rothstein for his many insightful comments throughout this project. Z. B. is supported by the U.S. Department of Energy (DOE) under Award No. DE-SC0009937. C. C. is supported by the DOE under Grant No. DE-SC0011632. R. R. is supported by the U.S. Department of Energy (DOE) under Grant No. DE-SC0013699. C. H. S. is supported by the Mani L. Bhaumik Institute for Theoretical Physics. M. P. S. is supported by the DOE under Grant No. DE-SC0011632 and the McCone Fellowship at the Walter Burke Institute. M. Z. is supported by the Swiss National Science Foundation under Contract No. SNF200021179016 and the European Commission through the ERC Grant pertQCD.

Attached Files

Published - PhysRevLett.122.201603.pdf

Submitted - 1901.04424.pdf


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