Abstract
We obtain a conservative Hamiltonian describing the interactions of two charged bodies in Yang-Mills through mathcal{O}left({alpha}^2right) 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.
Highlights
Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory (EFT) to consider color-charged objects
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, extending the domain of applicability of a formula originally proposed in the context of spinning particles
A further relation between amplitudes and classical observables is given through the eikonal phase, which is obtained as the Fourier transform to impact parameter space of the scattering amplitude [64]
Summary
We introduce the KMOC approach for color and introduce our notation and conventions. The classical scattering of two color-charged scalar particles of masses m1 and m2 can be modeled by the action. The color charge operators, obtained from the Noether procedure, satisfy the usual Lie algebra modified by a factor of [Ca, Cb] = i f abcCc,. The color factors (Ca)ij are rescalings of the usual generators (TRa)ij. The classical color charges are defined by ca ≡ ψ| Ca |ψ ,. Where the states |ψ are coherent states for SU(N ), whose explicit form will not be relevant for our purposes.4 These states ensure the correct behavior of color charges in the classical. The divergence of the color impulse is the familiar divergence due to the long-range nature of 1/r2 forces in four-dimensions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
