The two body problem in general relativity is not exactly solvable. A viable strategy for weakly gravitating systems is to perform a (so-called post-Newtonian) perturbative expansion in terms of the small parameter G (m1+m2) / r.
Moreover, gravitational radiation affects the dynamics of the system not only by inducing dissipation, but also by modifying the conservative dynamics via the so called "tail" terms. Such terms are due, at the lowest level, to the interaction of the radiated gravitons with the Newtonian potential and modify the conservative dynamics at fourth post-Newtonian order, as it was first computed by Blanchet and Damour.
Here we re-produce this result using effective field theory techniques in the framework of the closed-time-path formalism. This tail term is the lowest order example of a short-distance singularity showing up in the conservative dynamics, and it is correctly taken into account within the effective field theory formalism.