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Gravitational Wave Scattering via the Born Series: Scalar Tidal Matching to O(G7) and Beyond

Simon Caron-Huot1, Miguel Correia1, Giulia Isabella2, and Mikhail Solon2

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Phys. Rev. Lett. 135, 191601 – Published 6 November, 2025

DOI: https://doi.org/10.1103/qd3c-nfz6

Abstract

We introduce a novel method to compute gravitational wave amplitudes within the framework of effective field theory. By reinterpreting the Feynman diagram expansion as a Born series, our method offers several key advantages. It directly yields partial wave amplitudes, streamlining the matching with black hole perturbation theory. Long-distance gravitational interactions are unambiguously factorized from short-distance tidal effects, including dissipation, which are systematically incorporated via an in-in worldline effective action. Crucially, at every order in perturbation theory, integrals are expressed in terms of harmonic polylogarithms, enabling an end-to-end computation scalable to arbitrary orders. We illustrate the method with new predictions for scalar black hole Love numbers and their renormalization group equations to O(G7).

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Phys. Rev. Lett. 135, 191601– Published 6 November, 2025
  • Received 22 April 2025
  • Accepted 20 October 2025
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