| Summary: | We establish and develop a novel methodology to treat higher-order non-linear effects of gravitational radiation that is scattered from binary inspirals, which employs modern scattering-amplitudes methods on the effective picture of the binary as a composite particle. We spell out our procedure to study such effects: assembling tree amplitudes via generalized-unitarity methods and employing the closed-time-path formalism to derive the causal effective actions, which encompass the full conservative and dissipative dynamics. We push through to a new state of the art for these higher-order effects, up to the third subleading tail effect, at order GN5 and the 5-loop level, which corresponds to the 8.5PN order. We formulate the consequent dissipated energy for these higher-order corrections, and carry out a renormalization analysis, where we uncover new subleading RG flow of the quadrupole coupling. For all higher-order tail effects we find perfect agreement with partial observable results in PN and self-force theories, where available.
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