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Published May 2021 | Published + Submitted
Journal Article Open

Leading nonlinear tidal effects and scattering amplitudes


We present the two-body Hamiltonian and associated eikonal phase, to leading post-Minkowskian order, for infinitely many tidal deformations described by operators with arbitrary powers of the curvature tensor. Scattering amplitudes in momentum and position space provide systematic complementary approaches. For the tidal operators quadratic in curvature, which describe the linear response to an external gravitational field, we work out the leading post-Minkowskian contributions using a basis of operators with arbitrary numbers of derivatives which are in one-to-one correspondence with the worldline multipole operators. Explicit examples are used to show that the same techniques apply to both bodies interacting tidally with a spinning particle, for which we find the leading contributions from quadratic in curvature tidal operators with an arbitrary number of derivatives, and to effective field theory extensions of general relativity. We also note that the leading post-Minkowskian order contributions from higher-dimension operators manifest double-copy relations. Finally, we comment on the structure of higher-order corrections.

Additional Information

© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: January 20, 2021; Accepted: April 20, 2021; Published: May 20, 2021. We are especially grateful for discussions with Clifford Cheung, Nabha Shah, and Mikhail Solon for discussions and sharing a draft of their article with us. We also thank Dimitrios Kosmopoulos, Andreas Helset and Andrés Luna for discussions. Z.B. and E.S. are supported by the U.S. Department of Energy (DOE) under award number DE-SC0009937. J.P.-M. is supported by the U.S. Department of Energy (DOE) under award number DESC0011632. R.R. is supported by the U.S. Department of Energy (DOE) under grant number DE-SC0013699. C.-H.S. is grateful for support by the Mani L. Bhaumik Institute for Theoretical Physics and by the U.S. Department of Energy (DOE) under award number DE-SC0009919.

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Published - Bern2021_Article_LeadingNonlinearTidalEffectsAn.pdf

Submitted - 2010.08559.pdf


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August 20, 2023
October 20, 2023