Conservative and Radiative Dynamics of Spinning Bodies at Third Post-Minkowskian Order Using Worldline Quantum Field Theory

Using the spinning worldline quantum field theory formalism we calculate the quadratic-in-spin momentum impulse Δ p_i^μ and spin kick Δ a_i^μ from a scattering of two arbitrarily oriented spinning massive bodies (black holes or neutron stars) in a weak gravitational background up to third post-Minkowskian (PM) order (G³). Two-loop Feynman integrals are performed in the potential region, yielding conservative results. For spins aligned to the orbital angular momentum we find a conservative scattering angle that is fully consistent with state-of-the-art post-Newtonian results. Using the 2PM radiated angular momentum previously obtained by Plefka, Steinhoff, and the present authors, we generalize the angle to include radiation-reaction effects, in which case it avoids divergences in the high-energy limit.