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We compute the conservative dynamics of non-spinning binaries at fourthPost-Minkowskian order in the large-eccentricity limit, including bothpotential and radiation-reaction tail effects. This is achieved by obtainingthe scattering angle in the worldline effective field theory approach andderiving the bound radial action via analytic continuation. The associatedintegrals are bootstrapped to all orders in velocities through differentialequations, with boundary conditions in the potential and radiation regions. Thelarge angular momentum expansion captures all the local-in-time effects as wellas the trademark logarithmic corrections for generic bound orbits. Agreement isfound in the overlap with the state-of-the-art in Post-Newtonian theory.

Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion