We employ the “KMOC” formalism of [1] to compute classical momentum
deflections of spinning bodies with arbitrary spin orientations up to
next-to-leading order (one loop). We do this in electrodynamics and gravity.
The final result, valid for generic masses, is true for all spins at tree level
and up to second (fourth) spin order for the electromagnetic (gravity) case at
one loop. Furthermore, emphasis is given to the probe limit scenario where our
results extend to all spin orders in the heavy source, even at next-to-leading
order. We carry out our computations both using a unitarity based framework and
Feynman diagrammatic approach which relies on scattering amplitudes computed on
fixed backgrounds.

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