Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order

Using the worldline quantum field theory formalism, we compute conservative contributions to the scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian and second self-force order. This four-loop calculation involves nonplanar Feynman integrals and requires advanced integration-by-parts reduction, novel differential-equation strategies, and efficient boundary-integral algorithms to solve a system of hundreds of master integrals in four integral families on high-performance computing systems. The resulting function space includes multiple polylogarithms as well as iterated integrals with a K3 period, which generate a spurious velocity divergence at v/c=sqrt[8]/3, γ=3. This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularization pole should cancel against the radiative tail region. As the standard use of Feynman propagators fails to ensure this cancellation, we instead propose a "(γ-3)" conservative prescription that realizes both cancellations, leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied.