Bern, Zvi and Parra-Martinez, Julio and Roiban, Radu and Ruf, Michael S. and Shen, Chia-Hsien and Solon, Mikhail P. and Zeng, Mao (2022) Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G⁴). Physical Review Letters, 128 (16). Art. No. 161103. ISSN 0031-9007. doi:10.1103/physrevlett.128.161103. https://resolver.caltech.edu/CaltechAUTHORS:20220520-231732000
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Abstract
We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G⁴) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight 2. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.
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| Alternate Title: | Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G4) | ||||||||||||||||
| Additional Information: | 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 21 December 2021; accepted 26 January 2022; published 22 April 2022) We thank Johannes Blümlein, Martin Bojowald, Alessandra Buonanno, Clifford Cheung, Thibault Damour, Enrico Herrmann, Mohammed Khalil, David Kosower, Andrés Luna, Andreas Maier, Philipp Maierhöfer, Aneesh Manohar, Peter Marquard, Rafael Porto, Ira Rothstein, Jan Steinhoff, Johann Usovitsch, and Justin Vines for helpful discussions. Z. B. is supported by the U.S. Department of Energy (DOE) under Grant No. DE-SC0009937. J. P.-M. is supported by the DOE under Grant No. DE-SC0011632. R. R. is supported by the DOE under Grant No. DE-SC00019066. C.-H. S. is supported by the DOE under Grant No. DE-SC0009919. M. Z.’s work is supported by the U.K. Royal Society through Grant No. URF\R1\20109. We also are grateful to the Mani L. Bhaumik Institute for Theoretical Physics for support. | ||||||||||||||||
| Group: | Walter Burke Institute for Theoretical Physics | ||||||||||||||||
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| Issue or Number: | 16 | ||||||||||||||||
| DOI: | 10.1103/physrevlett.128.161103 | ||||||||||||||||
| Record Number: | CaltechAUTHORS:20220520-231732000 | ||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20220520-231732000 | ||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||
| ID Code: | 114855 | ||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||
| Deposited By: | George Porter | ||||||||||||||||
| Deposited On: | 24 May 2022 17:50 | ||||||||||||||||
| Last Modified: | 24 May 2022 17:50 |
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