  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.
