The Eikonal Phase and Spinning Observables

TL;DR

This paper develops a formalism to compute next-to-leading order spin effects in scattering, providing a unified approach that agrees with previous quantum field theory and worldline results, applicable to multiple spinning particles.

Contribution

It extends the Kosower, Maybee, O'Connell formalism to generic spin and derives a next-to-leading order eikonal formula for spin-dependent momentum and spin transfer.

Findings

Formalism matches previous QFT and worldline results for electrodynamics.

Handles multiple spins with allowed transitions without imposing spin supplementary conditions.

Provides explicit expressions for spin effects at next-to-leading order.

Abstract

We set up the Kosower, Maybee, O'Connell formalism for generic spin following a previous field theory construction and use it to extract a next-to-leading order eikonal formula for the linear-in-spin momentum impulse, $\Delta p^{\mu}$, and spin kick, $\Delta S^{\mu \nu}$. We explicitly test the formalism for the case of electrodynamics and find agreement with previous QFT and worldline results. This includes the case where multiple spins propagate with allowed spin transitions, or equivalently where no spin supplementary condition is imposed on the worldline equations of motion.