One-Loop Observables to Higher Order in Spin

TL;DR

This paper develops formulas for higher-order spin effects in classical scattering of spinning objects at one-loop level, applicable across different theories and conditions, and confirms results in gravity.

Contribution

It derives general formulas for spin kick and momentum impulse at one-loop order, independent of specific theories or spin conditions.

Findings

Formulas agree with previous gravity results after SSC imposition

Method is theory-agnostic and applicable to generic long-range scattering

Extends understanding of spin effects to higher order in classical scattering

Abstract

We study observables in the scattering of classical, spinning objects using the KMOC formalism. In particular, we derive formulas to higher order in spin and one loop $\mathcal{O}(G^2)$ for the spin kick and momentum impulse. Our derivation method is agnostic to the choice of theory or special conditions, such as the spin supplementary condition (SSC); we only rely on the generic structure of long-range scattering amplitudes of non-transverse, massive spinning fields in the classical limit. We check these formulas for the case of gravity and agree with previous results from the eikonal formalism after imposing a SSC.