Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order

TL;DR

This paper calculates next-to-leading order tidal effects in the conservative dynamics of compact binary systems using an effective field theory approach, providing new corrections to the binding energy and Hamiltonian at ${ m O}(G^3)$.

Contribution

It introduces the first octupole corrections to the binding energy at NLO in the PM expansion and reconstructs a Hamiltonian consistent with recent scattering amplitude results.

Findings

Derived mass and current quadrupole corrections at ${ m O}(G^3)$.

Computed octupole corrections to the binding energy.

Reconstructed a Hamiltonian consistent with scattering amplitude approaches.

Abstract

Using the Effective Field Theory approach together with the Boundary-to-Bound map, we compute the next-to-leading order (NLO) Post-Minkowskian (PM) tidal effects in the conservative dynamics of compact binary systems. We derive the mass and current quadrupole and, for the first time, octupole corrections to the binding energy for circular orbits at ${\cal O}(G^3)$. Our results are consistent with the test-body limit as well as the existent Post-Newtonian literature. We also reconstruct a Hamiltonian incorporating tidal effects to NLO in the PM expansion and find complete agreement with the recent derivation of its quadrupolar part using the classical limit of scattering amplitudes.