Yang-Mills observables: from KMOC to eikonal through EFT

TL;DR

This paper derives a Hamiltonian for two charged bodies in Yang-Mills theory using scattering amplitudes and EFT, extending previous methods to include color charge and connecting impulses to the eikonal phase.

Contribution

It introduces a Hamiltonian for color-charged interactions in Yang-Mills theory at second order in coupling, extending the amplitude-EFT framework to non-Abelian charges.

Findings

Hamiltonian valid to all orders in velocity at $ ext{O}( ext{α}^2)$

Impulses expressed via eikonal phase for color-charged scattering

Results verified against KMOC formalism

Abstract

We obtain a conservative Hamiltonian describing the interactions of two charged bodies in Yang-Mills through $\mathcal{O}(\alpha^2)$ and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory (EFT) to consider color-charged objects. These results are checked against the direct integration of the observables in the Kosower-Maybee-O'Connell (KMOC) formalism. At the order we consider we find that the linear and color impulses in a scattering event can be concisely described in terms of the eikonal phase, thus extending the domain of applicability of a formula originally proposed in the context of spinning particles.