Classical Spin Transitions and Absorptive Scattering

TL;DR

The paper develops an on-shell, amplitudes-based framework to incorporate absorptive (radiation-absorption) effects into post-Minkowskian scattering of spinning compact objects by extrapolating finite-spin quantum amplitudes to the classical large-spin limit via spin universality and Casimir interpolation. At leading order, absorptive observables are parametrized by a finite set of Wilson coefficients tied to 3-point mass/spin-changing amplitudes $\mathcal{A}_3^{(s,s\pm\Delta s,h)}$, which define classical spin transitions with $\Delta s = 0,\pm 1,\pm 2$. The authors uncover universal structures, including a Casimir-independent equivalence of impulses for spin-up and spin-down by the same $|\Delta s|$, a predictable spin-suppression when floor processes are absent, and a vanishing leading-order scattering angle for aligned spins, highlighting deep kinematic universality beyond specific UV completions. The framework extends the amplitudes-based pipeline for gravitational-wave predictions to include absorptive and dissipative effects, offering a path to EFT parametrizations that connect with Kerr black-hole physics and potential superradiance phenomena, and it outlines future extensions to higher spins, higher orders in spin, and explicit matching to UV completions.

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 $Δs = 0,\pm 1, \pm 2$ 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 $|Δs|$ are identical. For processes where the quantum $Δs<0$ 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.

Figures (3)

• Figure 1: Building blocks of the leading-order absorption calculation: mass/spin-magnitude changing on-shell 3-particle amplitudes. Here parametrized in the all-outgoing convention, an incoming asymptotic state with mass $m^2$ and spin-magnitude $s_1$ absorbs a quantum of radiation (scalar, electromagnetic or gravitational); the resulting body is then in an "excited state" with mass $\mu^2>m^2$ and spin-magnitude $s_2$, which in general differs from $s_1$. After extrapolating to the classical, large-spin regime we refer to such processes as classical spin transitions.
• Figure 2: Schematic representation of contributions to the spectral integral. The mass scale $\mu^2$ is the mass of the "excited" internal state, $m_1^2$ is the mass of the incoming body, $m_{1*}^2$ is the minimal mass that can be reached by spontaneous emission of superradiant modes. Modes with $\mu^2 > \Lambda \sim q$, are always off-shell for scattering at large impact parameter, and so can be consistently integrated out giving a contribution to conservative tidal response operators.
• Figure 3: Unitarity cut required to reconstruct the integrand for the leading-order absorptive impulse. Pinched mediator contributions are scaleless in the soft region of $\ell$-integration and pinched $X$-state contributions are scaleless in the soft region of $x$-integration corresponding to absorptive modes.