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Title: Scattering Amplitudes and Conservative Binary Dynamics at O ( G 4 )

Abstract

Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G4). As in previous lower-order 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 polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at O(G3) via its relation to the tail effect.

Authors:
; ORCiD logo; ; ORCiD logo; ORCiD logo; ;
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States); Univ. of California, Los Angeles, CA (United States)
Sponsoring Org.:
USDOE; USDOE Office of Science (SC) High Energy Physics (HEP)
OSTI Identifier:
1780516
Alternate Identifier(s):
OSTI ID: 1833718; OSTI ID: 1836505; OSTI ID: 1905620
Grant/Contract Number:  
SC0009937; SC0011632; SC0009919; SC0013699
Resource Type:
Published Article
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Name: Physical Review Letters Journal Volume: 126 Journal Issue: 17; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective field theory; General relativity; Gravitational waves; Perturbation theory; Quantum field theory; Scattering amplitudes

Citation Formats

Bern, Zvi, Parra-Martinez, Julio, Roiban, Radu, Ruf, Michael S., Shen, Chia-Hsien, Solon, Mikhail P., and Zeng, Mao. Scattering Amplitudes and Conservative Binary Dynamics at O ( G 4 ). United States: N. p., 2021. Web. doi:10.1103/PhysRevLett.126.171601.
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Bern, Zvi, Parra-Martinez, Julio, Roiban, Radu, Ruf, Michael S., Shen, Chia-Hsien, Solon, Mikhail P., & Zeng, Mao. Scattering Amplitudes and Conservative Binary Dynamics at O ( G 4 ). United States. https://doi.org/10.1103/PhysRevLett.126.171601
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Bern, Zvi, Parra-Martinez, Julio, Roiban, Radu, Ruf, Michael S., Shen, Chia-Hsien, Solon, Mikhail P., and Zeng, Mao. Mon . "Scattering Amplitudes and Conservative Binary Dynamics at O ( G 4 )". United States. https://doi.org/10.1103/PhysRevLett.126.171601.
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@article{osti_1780516,
title = {Scattering Amplitudes and Conservative Binary Dynamics at O ( G 4 )},
author = {Bern, Zvi and Parra-Martinez, Julio and Roiban, Radu and Ruf, Michael S. and Shen, Chia-Hsien and Solon, Mikhail P. and Zeng, Mao},
abstractNote = {Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G4). As in previous lower-order 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 polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at O(G3) via its relation to the tail effect.},
doi = {10.1103/PhysRevLett.126.171601},
journal = {Physical Review Letters},
number = 17,
volume = 126,
place = {United States},
year = {Mon Apr 26 00:00:00 EDT 2021},
month = {Mon Apr 26 00:00:00 EDT 2021}
}
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https://doi.org/10.1103/PhysRevLett.126.171601
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