NLO gravitational quartic-in-spin interaction

Authors: Michele Levi and Fei Teng

Preprint number: UUITP-32/20

Abstract: In this work we derive for the first time the complete gravitational quartic-in-spin effective action at the next-to-leading order for the interaction of generic compact binaries via the effective field theory for gravitating spinning objects and its extension to this sector. This sector, which enters at the fifth post-Newtonian (5PN) order for rapidly rotating compact objects, completes finite size effects up to this order, beyond the current state of the art for generic compact binary dynamics at the 4PN order. At this order in spins with gravitational nonlinearities we have to take into account additional terms, which arise from a new type of worldline couplings, due to the fact that at this order the Tulczyjew gauge for the rotational degrees of freedom, which involves the linear momentum, can no longer be approximated only in terms of the four-velocity. One of the main motivations for us to tackle this sector is also to see what happens when we go to a sector, which corresponds to the gravitational Compton scattering with quantum spins of two, and possibly also get an insight on the inability to uniquely fix its amplitude when spins of five halves and higher are involved. A general  observation that we can clearly make already is that even-parity sectors  in the order of the spin are easier to handle than odd ones. In the quantum context this corresponds to the greater ease of dealing with bosons compared to fermions.