Classical Spin Transitions and Absorptive Scattering

Abstract

We describe an on-shell, amplitudes-based approach to incorporating radiation absorption effects in the post-Minkowskian scattering of generic, compact, spinning bodies. Classical spinning observables are recovered by extrapolating to large spin, results calculated with finite quantum spin-$s$ particles using the properties of spin universality and Casimir interpolation. At leading-order our results give a completely general and non-redundant parametrization of absorptive observables in terms of a finite number of Wilson coefficients associated with 3-particle mass and spin-magnitude changing on-shell amplitudes. We denote these semi-fictitious microscopic processes: \textit{classical spin transitions}. Explicit results for the leading-order impulse due to the absorption of scalar, electromagnetic and gravitational radiation, for spin transitions $\Delta s = 0,\pm 1, \pm 2$ are given in a fully interpolated form up to $\mathcal{O}\left(S^2\right)$, and Casimir independent contributions given up to $\mathcal{O}\left(S^4\right)$. Our explicit results reveal some surprising universal patterns. We find that, up to identification of Wilson coefficients, the Casimir independent contributions to the impulse for spinning-up and spinning-down by the same magnitude $|\Delta s|$ are identical. For processes where the quantum $\Delta s<0$ transition is forbidden, the corresponding classical observable is suppressed in powers of $S$ by a predictable amount. Additionally we find that, while for generic non-aligned spin configurations there is a non-zero scattering angle at leading-order, for aligned spin, similar to non-spinning absorption, the scattering angle vanishes and the impulse is purely longitudinal.