Quadratic-in-spin interactions at the fifth post-Newtonian order probe new physics

Authors: Jung-Wook Kim, Michèle Levi, Zhewei Yin

Preprint number: UUITP-61/21

Abstract: We derive the observable binding energies and their relations to the angular momentum for the next-to-next-to-next-to-leading order (N^3LO) of all quadratic-in-spin interactions in post-Newtonian (PN) gravity. Our results are valid for all generic compact binaries, and enter at the fifth PN order for maximally-rotating compact objects, thus pushing the state of the art. This is accomplished through an extension of the effective field theory of spinning gravitating objects. We find a new operator that contributes to the observables, making the associated Wilson coefficient a new probe for candidate theories of gravity and for QCD.