  We introduce a novel framework to study high-order gravitational effects on a
binary from the scattering of its emitted gravitational radiation. Here we
focus on the radiation-reaction due to the background of the binary's
gravitational potential, namely on the so-called tail effects, as the starting
point to this type of scattering effects. We start from the effective field
theory of a binary composite-particle. Through multi-loop and
generalized-unitarity methods, we derive the causal effective actions of the
dynamical multipoles, the energy spectra, and the observable flux, due to these
effects. We proceed through the third subleading such radiation-reaction
effect, at the four-loop level and seventh order in post-Newtonian gravity,
shedding new light on the higher-order effects, and pushing the state of the
art.
