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Gravitational radiative corrections from effective field theory

Walter D. Goldberger, Andreas Ross

TL;DR

This work formulates an effective field theory for long-wavelength gravitational radiation from compact binaries, combining a multipole expansion with a post-Minkowskian (η) treatment of GR nonlinearity. It computes corrections up to η^2, revealing infrared and ultraviolet divergences that are respectively canceled in observables and absorbed into renormalized multipole moments via a renormalization group equation. The approach reproduces known post-Newtonian results up to 3PN (including non-analytic x^3 ln x) and confirms NRGR factorization, while making universal predictions for leading-log series and the structure of scale dependence. Overall, the EFT provides a systematic framework to connect short-distance physics to long-distance gravitational radiation, with controlled resummation of logarithmic contributions.

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.

Gravitational radiative corrections from effective field theory

TL;DR

This work formulates an effective field theory for long-wavelength gravitational radiation from compact binaries, combining a multipole expansion with a post-Minkowskian (η) treatment of GR nonlinearity. It computes corrections up to η^2, revealing infrared and ultraviolet divergences that are respectively canceled in observables and absorbed into renormalized multipole moments via a renormalization group equation. The approach reproduces known post-Newtonian results up to 3PN (including non-analytic x^3 ln x) and confirms NRGR factorization, while making universal predictions for leading-log series and the structure of scale dependence. Overall, the EFT provides a systematic framework to connect short-distance physics to long-distance gravitational radiation, with controlled resummation of logarithmic contributions.

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 () order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

Paper Structure

This paper contains 13 sections, 113 equations, 6 figures.

Table of Contents

  1. Introduction
  2. EFT setup
  3. Calculating observables
  4. Post-Minkowskian corrections
  5. Corrections at order $\eta^1$
  6. Effects at order $\eta^2$
  7. Renormalization
  8. IR structure at higher orders
  9. The multipole expansion
  10. Applications to post-Newtonian systems
  11. Conclusions
  12. Feynman Integrals
  13. UV poles

Figures (6)

  • Figure 1: Leading post-Minkowskian correction.
  • Figure 2: Second order post-Minkowskian corrections.
  • Figure 3: The series of leading IR poles.
  • Figure 4: Feynman diagram yielding the leading terms for $T^{00}$ and $T^{0i}$.
  • Figure 5: Diagrams for $v^2$ corrections to $T^{00}$. Dashed lines denote potential gravitons.
  • ...and 1 more figures