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.