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Abstract

The leading order finite size effects due to spin, namely that of the cubic and quartic spin interaction, are derived for the first time for generic compact binaries via an Effective Field Theory approach. 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 effective action with new higher dimensional nonminimal coupling worldline operators, involving higher-order derivatives of the 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 matched to unity in the black hole case. The nonminimal coupling worldline operators enter the action with the electric and magnetic, even and odd parity type, components of the Weyl tensor coupled to the even and odd worldline spins, 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 the minimal coupling case. This observation is useful for the construction of the Feynman diagrams, and provides an instructive analogy between the leading order spin-orbit and cubic spin interactions, and between the leading order quadratic spin and quartic spin interactions.