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We develop an Effective Field Theory (EFT) formalism to solve for theconservative dynamics of binary systems in gravity via Post-Minkowskian (PM)scattering data. Our framework combines a systematic EFT approach to computethe deflection angle in the PM expansion, together with the 'Boundary-to-Bound'(B2B) dictionary introduced in [1910.03008, 1911.09130]. Due to the nature ofscattering processes, a remarkable reduction of complexity occurs both in thenumber of Feynman diagrams and type of integrals, compared to a direct EFTcomputation of the potential in a PM scheme. We provide two illustrativeexamples. Firstly, we compute all the conservative gravitational observablesfor bound orbits to 2PM, which follow from only one topology beyond leadingorder. The results agree with those in [1910.03008, 1911.09130], obtainedthrough the 'impetus formula' applied to the classical limit of the one loopamplitude in Cheung et al. [1808.02489]. For the sake of comparison wereconstruct the conservative Hamiltonian to 2PM order, which is equivalent tothe one derived in [1808.02489] from a matching calculation. Secondly, wecompute the scattering angle due to tidal effects from the electric- andmagnetic-type Love numbers at leading PM order. Using the B2B dictionary wethen obtain the tidal contribution to the periastron advance. We also constructa Hamiltonian including tidal effects at leading PM order. Although relying on(relativistic) Feynman diagrams, the EFT formalism developed here does notinvolve taking the classical limit of a quantum amplitude, neither integralswith internal massive fields, nor additional matching calculations, norspurious ('super-classical') infrared singularities. By construction, the EFTapproach can be automatized to all PM orders.

Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics