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

TL;DR

This paper employs effective field theory to analyze the tail effect in gravitational radiation reaction at 4PN order, revealing non-local time behavior, UV/IR singularities, and applying renormalization group techniques for resummation.

Contribution

It introduces a novel EFT-based calculation of the tail effect, demonstrating the cancellation of IR and UV divergences and deriving RG evolution for binary system parameters.

Findings

Tail contribution is non-local in time with dissipative and conservative parts.

UV divergence cancels with IR singularity from near zone, due to point-particle limit.

RG techniques successfully resum logarithmic corrections in gravitational dynamics.

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.