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

TL;DR

This paper employs worldline quantum field theory to compute third post-Minkowskian order scattering dynamics of spinning bodies, including conservative and radiation-reaction effects, with results consistent with existing post-Newtonian data.

Contribution

It introduces a novel calculation of spin-dependent scattering at third PM order using worldline QFT, extending previous work to include radiation-reaction effects.

Findings

Conservative scattering angle matches post-Newtonian results for aligned spins.

Generalization of scattering angle to include radiation-reaction effects.

Avoidance of divergences in high-energy limit with radiation effects.

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.