Renormalizing Love: tidal effects at the third post-Newtonian order

TL;DR

This paper develops a third post-Newtonian order Hamiltonian for two-body tidal interactions using effective field theory, addressing divergences through renormalization, and derives results for adiabatic tides including binding energy and scattering angles.

Contribution

It introduces a novel third-order post-Newtonian Hamiltonian for dynamical tidal effects using diagrammatic effective field theory and renormalization techniques.

Findings

Derived the effective Hamiltonian with dynamical tidal interactions at third post-Newtonian order.

Calculated the binding energy for circular orbits under adiabatic tides.

Determined the scattering angle in hyperbolic encounters with renormalized tidal effects.

Abstract

We present the conservative effective two-body Hamiltonian at the third order in the post-Newtonian expansion with gravitoelectric quadrupolar dynamical tidal-interactions. Our derivation of the effective two-body Lagrangian is based on the diagrammatic effective field theory approach and it involves Feynman integrals up to three loops, which are evaluated within the dimensional regularization scheme. The elimination of the divergent terms occurring in the effective Lagrangian requires the addition of counterterms to ensure finite observables, thereby introducing a renormalization group flow to the post-adiabatic Love number. As a limiting case of the renormalized dynamical effective Hamiltonian, we also derive the effective Hamiltonian for adiabatic tides, and, in this regime, calculate the binding energy for a circular orbit, and the scattering angle in a hyperbolic scattering.