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.