Abstract
With the aim of computing bound waveforms from scattering amplitudes, we explore gravitational two-body dynamics using the Schwinger-Dyson equations and Bethe-Salpeter recursion. We show that the tree-level scattering waveform admits a natural analytic continuation, in rapidity, to the bound waveform, which we confirm from an independent calculation, in the Post-Newtonian expansion, of the time-domain multipoles at large eccentricity. We demonstrate consistency of this scattering-to-bound map with the Damour-Deruelle prescription for orbital elements in the quasi-Keplerian parametrization (which enters into the evaluation of the multipoles) and with the analytic continuation, in the binding energy, of radiated energy and angular momentum at 3PM.
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Acknowledgments
We thank Stefano de Angelis, Carlo Heissenberg, David Kosower, Luke Lippstreu, Donal O’Connell, Karthik Rajeev, Rodolfo Russo, Matteo Sergola and Canxin Shi for useful discussions. We especially thank Kallia Petraki for explaining the bound state formalism developed in [118] to us, and its relevance for the dark matter community. We also thank the participants of the GRAMPA workshop for many useful discussions during the last stages of preparation of this work. RG would like to thank FAPESP grant 2021/14335-0 where part of this work was performed during August 2023. TA & AI are supported by the STFC consolidator grant ST/X000494/1 ‘Particle Theory at the Higgs Centre.’ TA is supported by a Royal Society University Research Fellowship, the Leverhulme Trust grant RPG-2020-386 and the Simons Collaboration on Celestial Holography MP-SCMPS-00001550-11.
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Adamo, T., Gonzo, R. & Ilderton, A. Gravitational bound waveforms from amplitudes. J. High Energ. Phys. 2024, 34 (2024). https://doi.org/10.1007/JHEP05(2024)034
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DOI: https://doi.org/10.1007/JHEP05(2024)034