NLO gravitational quartic-in-spin interaction

TL;DR

This paper derives the complete next-to-leading order gravitational quartic-in-spin interaction for generic compact binaries using effective field theory, advancing the precision of spin interactions in post-Newtonian gravity.

Contribution

It provides the first derivation of the full quartic-in-spin interaction at NLO in PN expansion, including new worldline couplings and a novel Wilson coefficient.

Findings

Pushes spin interaction calculations to 5PN order for maximally-spinning objects

Informs gravitational Compton scattering with higher spins

Introduces new effective field theory extensions for spinning objects

Abstract

In this paper we derive for the first time the complete gravitational quartic-in-spin interaction of generic compact binaries at the next-to-leading order in the post-Newtonian (PN) expansion. The derivation builds on the effective field theory for gravitating spinning objects, and its recent extensions, in which new type of worldline couplings should be considered, as well as on the extension of the effective action of a spinning particle to quadratic order in the curvature. The latter extension entails a new Wilson coefficient that appears in this sector. This work pushes the precision frontier with spins at the fifth PN (5PN) order for maximally-spinning compact objects, and at the same time informs us of the gravitational Compton scattering with higher spins.