Tidal effects and renormalization at fourth post-Minkowskian order

TL;DR

This paper calculates tidal effects on scattering and momentum transfer between neutron stars at high post-Minkowskian order using quantum field theory, addressing divergences through renormalization and linking to previous non-relativistic results.

Contribution

It introduces a novel 4PM order analysis of tidal effects with renormalization group flow of Love numbers, advancing the understanding of classical gravitational scattering.

Findings

Renormalization group flow of Love numbers established.

Divergences in quadrupolar sectors addressed with counterterms.

Results agree with previous 3PN non-relativistic analysis.

Abstract

We determine the adiabatic tidal contributions to the radiation reacted momentum impulse $\Delta p_i^\mu$ and scattering angle $\theta$ between two scattered massive bodies (neutron stars) at next-to-next-to-leading post-Minkowskian (PM) order. The state-of-the-art three-loop (4PM) worldline quantum field theory toolkit using dimensional regularization is employed to establish the classical observables. We encounter divergent terms in the gravito-electric and gravito-magnetic quadrupolar sectors necessitating the addition of post-adiabatic counterterms in this classical theory. This leads us to include also the leading post-adiabatic tidal contributions to the observables. The resulting renormalization group flow of the associated post-adiabatic Love numbers is established and shown to agree with a recent gravito-electric third post-Newtonian analysis in the non-relativistic limit.