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Tail terms in gravitational radiation reaction via effective field theory

S. Foffa, R. Sturani

TL;DR

The paper analyzes the leading gravitational radiation-reaction tail term at $4PN$ using an effective field theory approach with an in-in formalism for dissipative systems. It reproduces the logarithmic tail contribution and demonstrates a renormalization-group flow of the Bondi mass $M$ driven by the quadrupole dynamics, tying the scale dependence to a physical mass renormalization. The finite part of the tail is fixed by matching to full GR results, yielding a conservative $4PN$ energy correction for circular orbits that agrees with extreme mass ratio calculations. Overall, the EFT framework coherently connects PN radiation-reaction effects with RG concepts and corroborates results across PN and EMRI contexts, while outlining ongoing work to complete the full $4PN$ energy function.

Abstract

Gravitational radiation reaction affects the dynamics of gravitationally bound binary systems. Here we focus on the leading "tail" term which modifies binary dynamics at fourth post-Newtonian order, as first computed by Blanchet and Damour. We re-produce this result using effective field theory techniques in the framework of the Lagrangian formalism suitably extended to include dissipation effects. We recover the known logarithmic tail term, consistently with the recent interpretation of the logarithmic tail term in the mass parameter as a renormalization group effect of the Bondi mass of the system.

Tail terms in gravitational radiation reaction via effective field theory

TL;DR

The paper analyzes the leading gravitational radiation-reaction tail term at using an effective field theory approach with an in-in formalism for dissipative systems. It reproduces the logarithmic tail contribution and demonstrates a renormalization-group flow of the Bondi mass driven by the quadrupole dynamics, tying the scale dependence to a physical mass renormalization. The finite part of the tail is fixed by matching to full GR results, yielding a conservative energy correction for circular orbits that agrees with extreme mass ratio calculations. Overall, the EFT framework coherently connects PN radiation-reaction effects with RG concepts and corroborates results across PN and EMRI contexts, while outlining ongoing work to complete the full energy function.

Abstract

Gravitational radiation reaction affects the dynamics of gravitationally bound binary systems. Here we focus on the leading "tail" term which modifies binary dynamics at fourth post-Newtonian order, as first computed by Blanchet and Damour. We re-produce this result using effective field theory techniques in the framework of the Lagrangian formalism suitably extended to include dissipation effects. We recover the known logarithmic tail term, consistently with the recent interpretation of the logarithmic tail term in the mass parameter as a renormalization group effect of the Bondi mass of the system.

Paper Structure

This paper contains 8 sections, 36 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Radiation reaction logarithms from tail term
  3. Finite quantity from tail terms
  4. Conclusion
  5. Useful formulae
  6. Green functions
  7. The radiation reaction computation in coordinate space
  8. The radiation reaction computation in momentum space

Figures (3)

  • Figure 1: Diagram describing the gravitational radiation reaction force at leading order (left) and leading non-linear order (right). The thick line represents the massive binary system, the curly line the the gravitons emitted and absorbed by the system, the dashed line the potential graviton responsible for the Newtonian potential.
  • Figure 2: Series of diagram studied in Goldberger:2012kf showing that the mass monopole undergoes a non-trivial renormalization group flow.
  • Figure 3: Diagram describing the gravitational radiation emitted by a quadrupole source and scattered off the Newtonian potential before escaping to infinite.