Tidal effects and renormalization at fourth post-Minkowskian order

We determine the adiabatic tidal contributions to the radiation reacted momentum impulse Δpiμ and scattering angle θ between two scattered massive bodies (neutron stars) at next-to-next-to-leading post-Minkowskian order. The state-of-the-art three-loop (fourth post-Mikowskian order) worldline quantum field theory toolkit using dimensional regularization is employed to establish the classical observables. We encounter divergent terms in the gravitoelectric and gravitomagnetic quadrupolar sectors necessitating the addition of postadiabatic counterterms in this classical theory. This leads us to include also the leading postadiabatic tidal contributions to the observables. The resulting renormalization group flow of the associated postadiabatic Love numbers is established and shown to agree with a recent gravitoelectric third post-Newtonian analysis in the nonrelativistic limit. Published by the American Physical Society 2024