Bern, Zvi and Parra-Martinez, Julio and Roiban, Radu and Sawyer, Eric and Shen, Chia-Hsien
(2020)
*Leading Nonlinear Tidal Effects and Scattering Amplitudes.*
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(Submitted)
https://resolver.caltech.edu/CaltechAUTHORS:20201111-121307251

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## Abstract

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.

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Additional Information: | 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 DE-SC0011632. 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. | ||||||||||||

Group: | Walter Burke Institute for Theoretical Physics | ||||||||||||

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Record Number: | CaltechAUTHORS:20201111-121307251 | ||||||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20201111-121307251 | ||||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||

ID Code: | 106612 | ||||||||||||

Collection: | CaltechAUTHORS | ||||||||||||

Deposited By: | Joy Painter | ||||||||||||

Deposited On: | 11 Nov 2020 20:27 | ||||||||||||

Last Modified: | 11 Nov 2020 20:27 |

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