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arXiv · 2608.26284

Gravitational Compton Amplitude to All Orders in Perturbation Theory

Miguel Correia·Giulia Isabella·Anna M. Wolz
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Abstract

We show how amplitudes from the scattering of gravitational waves off compact objects in worldline effective field theory can be efficiently computed to arbitrary order in Newton's constant $G$. Our approach solves an effective wave equation for the partial-wave amplitude in which Wilson coefficients (tidal Love numbers) enter through boundary conditions at short distances. We then perform the sum over partial waves to obtain the momentum-space Compton amplitude in terms of elliptic polylogarithms. We reproduce recent results through $\mathcal{O}(G^4)$ and obtain new predictions up to $\mathcal{O}(G^7)$, with Love numbers first contributing at $\mathcal{O}(G^5)$. We find the first ultraviolet divergence in a classical gravitational amplitude at $\mathcal{O}(G^7)$, showing that a pure point-particle description is not consistent in general relativity. Matching to black hole perturbation theory, we show that static Love numbers vanish on-shell and predict subleading non-zero Schwarzschild black hole Love numbers.

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Miguel Correia, Giulia Isabella, Anna M. Wolz. 2026-08-26. Gravitational Compton Amplitude to All Orders in Perturbation Theory. https://arxiv.org/abs/2608.26284

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