Local-in-Time Conservative Binary Dynamics at Fifth Post-Minkowskian and First Self-Force Orders

We report the local-in-time conservative dynamics of nonspinning binary systems at fifth Post-Minkowskian (5PM) and first self-force (1SF) orders. This follows from an explicit calculation of the 5PM/1SF nonlocal-in-time tail-type contribution to the deflection angle via worldline effective field theory techniques. Proceeding as in [2403.04853], we subtract the nonlocal tail terms from the result in [2403.07781] and reconstruct a local-in-time Hamiltonian in isotropic gauge – valid for generic orbits. For completeness, we reinstate the nonlocal terms relevant for elliptic-like motion up to 6PN/1SF in a small-eccentricity expansion. Via the connection between the (source) energy flux in [2210.05541] and tail effects, we also derive the SF-exact logarithmic-dependent part of the full 5PM bound Hamiltonian. Our results provide the most accurate description to date of the dynamics of bound compact objects within the framework of relativistic scattering computations.