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Using the spinning worldline quantum field theory formalism we calculate thequadratic-in-spin momentum impulse $\Delta p_i^\mu$ and spin kick $\Deltaa_i^\mu$ from a scattering of two arbitrarily oriented spinning massive bodies(black holes or neutron stars) in a weak gravitational background up to thirdpost-Minkowskian (PM) order ($G^3$). Two-loop Feynman integrals are performedin the potential region, yielding conservative results. For spins aligned tothe orbital angular momentum we find a conservative scattering angle that isfully consistent with state-of-the-art post-Newtonian results. Using the 2PMradiated angular momentum previously obtained by Plefka, Steinhoff and thepresent authors we generalize the angle to include radiation-reaction effects,in which case it avoids divergences in the high-energy limit.

Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory