Gravitational radiative corrections from effective field theory

TL;DR

This paper develops an effective field theory framework for modeling gravitational radiation from compact systems, capturing non-linear corrections and renormalization effects, and verifies its consistency with established post-Newtonian results.

Contribution

It introduces a diffeomorphism invariant EFT for gravitational radiation that systematically includes post-Minkowskian corrections and renormalization techniques, extending the NRGR framework to 3PN order.

Findings

Successfully reproduces 3PN gravitational wave energy flux corrections.

Demonstrates UV divergence renormalization and IR divergence cancellation.

Confirms the scale factorization in the NRGR approach up to 3PN.

Abstract

In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from non-relativistic binaries, including long distance effects up to 3PN ($v^6$) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.