NLO gravitational quartic-in-spin interaction

TL;DR

This work derives the complete next-to-leading order (NLO) gravitational quartic-in-spin interaction for generic compact binaries, using an extended EFT framework for gravitating spinning objects that includes worldline couplings quadratic in curvature. It introduces composite worldline couplings arising from spin-dependent corrections to the linear momentum and a new quadratic-curvature operator with a novel Wilson coefficient, yielding a comprehensive set of spin interactions up to the hexadecapole. The results assemble a total NLO S^4 action at $5PN$ for maximally spinning bodies, including all relevant spin-induced multipoles and two-graviton exchanges (plus one-loop cubic self-interactions), and are supplemented by a forthcoming reduced action and observables. Overall, the paper pushes the precision frontier for spinning-gravity dynamics and clarifies conceptual features associated with higher-spin classical and quantum limits, with direct relevance to high-accuracy gravitational-wave templates and gravitational Compton scattering studies. A future publication will provide the reduced action, equations of motion, Hamiltonian, and gauge-invariant observables for consistency checks and phenomenological use.

Abstract

In this paper we derive for the first time the complete gravitational quartic-in-spin interaction of generic compact binaries at the next-to-leading order in the post-Newtonian (PN) expansion. The derivation builds on the effective field theory for gravitating spinning objects, and its recent extensions, in which new type of worldline couplings should be considered, as well as on the extension of the effective action of a spinning particle to quadratic order in the curvature. The latter extension entails a new Wilson coefficient that appears in this sector. This work pushes the precision frontier with spins at the fifth PN (5PN) order for maximally-spinning compact objects, and at the same time informs us of the gravitational Compton scattering with higher spins.

Figures (6)

• Figure 1: The gravitational Compton scattering with two massive spin particles and two gravitons.
• Figure 2: The Feynman graphs of one-graviton exchange, that contribute to the NLO quartic-in-spin interaction at the 5PN order for maximally-rotating compact objects. At the linear level we only have three types of interaction, similar to the LO in Levi:2014gsa, of either a quadrupole-quadrupole, octupole-dipole or a hexadecapole-monopole type. The graphs are easily constructed following the nice analogies pointed out in Levi:2014gsa among the interactions according to the parity of the multipole moments involved. Notice that we have here the three graphs that appeared at the LO with the quadratic time insertions on the propagators at graphs (a2), (b2), (c2), and a new hexadecapole coupling with the KK vector field at graph (c3).
• Figure 3: The Feynman graphs of two-graviton exchange at the NLO quartic-in-spin interaction. These graphs contain all relevant interactions among the mass, spin and spin-induced multipoles up to the hexadecapole. In particular at this nonlinear level there are also interactions with the various multipoles on two different points of the worldline, which occurs as of the NLO spin-squared sector Levi:2015msaLevi:2015ixaLevi:2019kgk, such as a spin dipole and a spin-induced quadrupole or two spin-induced quadrupoles on the same worldline. The graph (a1) contains a new two-graviton coupling to the hexadecapole.
• Figure 4: The Feynman graphs with cubic self-gravitational interaction, i.e. at one-loop level, at the NLO quartic-in-spin interaction. There are no vertices with time dependence here, similar to the NLO quadratic-in-spin sector of even-parity Levi:2015msa. These graphs contain all possible interactions among the mass, spin and spin-induced multipoles up to the hexadecapole.
• Figure 5: The Feynman graphs of one- and two-graviton exchange from composite worldline couplings that appear at the NLO quartic-in-spin interaction. These graphs with the composite couplings, that are cubic and quartic in the spin, yield similar graphs to the corresponding ones with the elementary spin-induced octupole and hexadecapole in figure \ref{['s4nlo1g']}(b1), (c1), and figure \ref{['s4nlo2g']}(a1), (b1).