Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework

TL;DR

This paper derives the quadratic-in-spin Hamiltonian for binary rotating compact objects up to NNNLO in the post-Newtonian expansion, using effective field theory and Feynman integrals, providing new insights into spin interactions.

Contribution

It presents the first calculation of the quadratic-in-spin Hamiltonian at NNNLO in the post-Newtonian framework using an effective field theory approach.

Findings

Derived gauge-invariant binding energy and scattering angle expressions.

Extended previous work on spin-orbit interactions to quadratic-in-spin effects.

Performed three-loop Feynman integral calculations within dimensional regularization.

Abstract

We present the result of the quadratic-in-spin interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to NNNLO corrections within the post-Newtonian expansion. The calculation is performed by employing the effective field theory diagrammatic approach, and it involves Feynman integrals up to three loops, evaluated within the dimensional regularization scheme. The gauge-invariant binding energy and the scattering angle, in special kinematic regimes and spin configurations, are explicitly derived. The results extend our earlier study on the spin-orbit interaction effects.