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

Abstract

Using the spinning worldline quantum field theory formalism we calculate the quadratic-in-spin momentum impulse $\Delta p_i^{\mu }$ and spin kick $\Delta a_i^{\mu }$ 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 ($G^3$). 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.

5 pages, 2 figures + appendices

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