Tidal effects for spinning particles
Rafael Aoude, Kays Haddad, Andreas Helset
TL;DR
This paper extends tidal actions to spinning bodies by constructing a complete spin-$\tfrac{1}{2}$ action with two Weyl tensors using the Hilbert series and on-shell amplitudes. It computes the leading post-Minkowskian tidal corrections at $O(G^{2})$ for spin-1/2 scattering in both gravity and QED, providing evidence that long-range spin universality holds for tidally deformed objects. From these amplitudes, it derives the conservative two-body Hamiltonian, linear and angular impulses, the eikonal phase, the spin kick, and the aligned-spin scattering angle, including detailed EFT matching relations. The results generalize known scalar tidal effects to spinning bodies, demonstrating universality in the spin-monopole sector and exposing operator-dependent deviations for finite-size corrections. The work bridges on-shell amplitude methods with classical tidal observables and sets the stage for extensions to higher spins and links to Kerr Love-number physics.
Abstract
Expanding on the recent derivation of tidal actions for scalar particles, we present here the action for a tidally deformed spin-$1/2$ particle. Focusing on operators containing two powers of the Weyl tensor, we combine the Hilbert series with an on-shell amplitude basis to construct the tidal action. With the tidal action in hand, we compute the leading-post-Minkowskian tidal contributions to the spin-1/2 -- spin-1/2 amplitude, arising at $\mathcal{O}(G^{2})$. Our amplitudes provide evidence that the observed long range spin-universality for the scattering of two point particles extends to the scattering of tidally deformed objects. From the scattering amplitude we find the conservative two-body Hamiltonian, linear and angular impulses, eikonal phase, spin kick, and aligned-spin scattering angle. We present analogous results in the electromagnetic case along the way.