Leading order finite size effects with spins for inspiralling compact binaries

TL;DR

This paper derives the leading order finite size effects due to spin for generic compact binaries using effective field theory, completing the finite size effects up to the fourth post-Newtonian order.

Contribution

It introduces new higher dimensional nonminimal coupling operators and Wilson coefficients to account for cubic and quartic in spin interactions in inspiralling binaries.

Findings

Derived cubic and quartic in spin finite size effects for the first time.

Fixed Wilson coefficients to unity for black holes.

Established a coupling hierarchy in the nonrelativistic gravitational field decomposition.

Abstract

The leading order finite size effects due to spin, namely that of the cubic and quartic in spin interactions, are derived for the first time for generic compact binaries via the effective field theory for gravitating spinning objects. These corrections enter at the third and a half and fourth post-Newtonian orders, respectively, for rapidly rotating compact objects. Hence, we complete the leading order finite size effects with spin up to the fourth post-Newtonian accuracy. We arrive at this by augmenting the point particle effective action with new higher dimensional nonminimal coupling worldline operators, involving higher-order derivatives of the gravitational field, and introducing new Wilson coefficients, corresponding to constants, which describe the octupole and hexadecapole deformations of the object due to spin. These Wilson coefficients are fixed to unity in the black hole case. The nonminimal coupling worldline operators enter the action with the electric and magnetic components of the Weyl tensor of even and odd parity, coupled to even and odd worldline spin tensors, respectively. Moreover, the non relativistic gravitational field decomposition, which we employ, demonstrates a coupling hierarchy of the gravito-magnetic vector and the Newtonian scalar, to the odd and even in spin operators, respectively, which extends that of minimal coupling. This observation is useful for the construction of the Feynman diagrams, and provides an instructive analogy between the leading order spin-orbit and cubic in spin interactions, and between the leading order quadratic and quartic in spin interactions.