N$^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects

TL;DR

This paper derives the third subleading order spin-orbit interaction in post-Newtonian gravity using effective field theory, involving complex multi-loop calculations and extending formal procedures for spin derivatives, providing new gravitational-wave observables.

Contribution

It presents the first derivation of the N$^3$LO spin-orbit interaction in a generic EFT framework, including the full potential, Hamiltonian, and GW observables, advancing precision in gravitational wave modeling.

Findings

Derived the full N$^3$LO spin-orbit interaction potential.

Provided the general Hamiltonian and gauge-invariant GW observables.

Confirmed agreement with existing gravitational wave and scattering data.

Abstract

We present the derivation of the third subleading order (N$^3$LO) spin-orbit interaction at the state of the art of post-Newtonian (PN) gravity via the EFT of spinning objects. The present sector contains the largest and most elaborate collection of Feynman graphs ever tackled to date in sectors with spin, and in all PN sectors up to third subleading order. Our computations are carried out via advanced multi-loop methods. Their most demanding aspect is the imperative transition to a generic dimension across the whole derivation, due to the emergence of dimensional-regularization poles across all loop orders as of the N$^3$LO sectors. At this high order of sectors with spin, it is also critical to extend the formal procedure for the reduction of higher-order time derivatives of spin variables beyond linear order for the first time. This gives rise to a new unique contribution at the present sector. The full interaction potential in Lagrangian form and the general Hamiltonian are provided here for the first time. The consequent gravitational-wave (GW) gauge-invariant observables are also derived, including relations among the binding energy, angular momentum, and emitted frequency. Complete agreement is found between our results, and the binding energy of GW sources, and also with the extrapolated scattering angle in the scattering problem, derived via traditional GR. In contrast with the latter derivation, our framework is free-standing and generic, and has provided theory and results, which have been critical to establish the state of the art, and to push the precision frontier for the measurement of GWs.