The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution

TL;DR

The paper computes the gravitational tail contribution to radiation-reaction at $4$PN within NRGR, revealing time non-locality in the effective action and a split into conservative and dissipative parts. The conservative tail contains a UV pole that cancels against an IR singularity in the near zone, enabling a renormalization-group (RG) treatment that resums logarithmic contributions to the binding potential and total mass/energy. The RG flow for circular orbits shows a scale- (or velocity-) dependent logarithmic term, consistent with energy conservation in the radiation theory and with previous PN analyses. The work clarifies the origin and handling of IR/UV divergences in the EFT approach, bridges near- and far-zone physics, and substantiates the completeness of the analytic PN framework while outlining paths to higher-order tail corrections.

Abstract

We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at 4PN order in the dynamics of a binary system. The computation entails a subtle interplay between the near (or potential) and far (or radiation) zones. In particular, we find that the tail contribution to the effective action is non-local in time, and features both a dissipative and a `conservative' term. The latter includes a logarithmic ultraviolet (UV) divergence, which we show cancels against an infrared (IR) singularity found in the (conservative) near zone. The origin of this behavior in the long-distance EFT is due to the point-particle limit -shrinking the binary to a point- which transforms a would-be infrared singularity into an ultraviolet divergence. This is a common occurrence in an EFT approach, which furthermore allows us to use renormalization group (RG) techniques to resum the resulting logarithmic contributions. We then derive the RG evolution for the binding potential and total mass/energy, and find agreement with the results obtained imposing the conservation of the (pseudo) stress-energy tensor in the radiation theory. While the calculation of the leading tail contribution to the effective action involves only one diagram, five are needed for the one-point function. This suggests logarithmic corrections may be easier to incorporate in this fashion. We conclude with a few remarks on the nature of these IR/UV singularities, the (lack of) ambiguities recently discussed in the literature, and the completeness of the analytic Post-Newtonian framework.

Figures (1)

• Figure 1: Feynman diagram for the tail contribution to the radiaction-reaction force. The $M$ in the tail correction may be taken as the leading averaged binding mass/energy, since the scale (and time) dependence enters at higher orders.