Parton Transverse Momentum and Orbital Angular Momentum Distributions

TL;DR

This paper links two definitions of quark orbital angular momentum in the proton, connecting experimental and lattice QCD approaches through their dependence on partonic transverse momentum, enhancing understanding of proton spin structure.

Contribution

It explicitly connects the Wigner distribution and twist-three GPD definitions of quark orbital angular momentum in QCD, clarifying their relationship via intrinsic transverse momentum.

Findings

Established a formal link between two definitions of $L_q$

Facilitated experimental and lattice QCD comparisons

Showed orbital angular momentum can be observed with longitudinal polarization

Abstract

The quark orbital angular momentum component of proton spin, $L_q$, can be defined in QCD as the integral of a Wigner phase space distribution weighting the cross product of the quark's transverse position and momentum. It can also be independently defined from the operator product expansion for the off-forward Compton amplitude in terms of a twist-three generalized parton distribution. We provide an explicit link between the two definitions, connecting them through their dependence on partonic intrinsic transverse momentum. Connecting the definitions provides the key for correlating direct experimental determinations of $L_q$, and evaluations through Lattice QCD calculations. The direct observation of quark orbital angular momentum does not require transverse spin polarization, but can occur using longitudinally polarized targets.