Tidal effects for spinning particles

TL;DR

This paper derives the tidal action for a spinning spin-1/2 particle, computes its effects on scattering amplitudes, and explores implications for long-range spin-universality in tidal interactions.

Contribution

It introduces the first tidal action for a spin-1/2 particle using Weyl tensor operators and combines amplitude methods to analyze tidal effects in scattering.

Findings

Derived the tidal action for spin-1/2 particles.

Computed leading-order tidal contributions to scattering amplitudes.

Found evidence for spin-universality extending to tidally deformed objects.

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.