Probing Parton Orbital Angular Momentum in Longitudinally Polarized Nucleon

TL;DR

This paper investigates two definitions of parton orbital angular momentum in polarized nucleons, exploring their theoretical properties and potential measurement methods via twist-three GPDs and phase-space distributions.

Contribution

It introduces and compares two different parton OAM distributions, one gauge-invariant and lattice-calculable, the other canonical and related to experimental observables.

Findings

Gauge-invariant OAM moments are calculable in lattice QCD.

Canonical OAM can be related to twist-three GPDs and Wigner distributions.

Both distributions offer pathways for experimental measurement.

Abstract

While the total orbital angular momentum (OAM) of a definite quark flavor in a longitudinally-polarized nucleon can be obtained through a sum rule involving twist-two generalized parton distribution (GPDs), its distribution as a function of parton momentum in light-front coordinates is more complicated to define and measure because it involves intrinsically twist-three effects. In this paper, we consider two different parton OAM distributions. The first is manifestly gauge invariant, and its moments are local operators and calculable in lattice QCD. We show that it can potentially be measured through twist-three GPDs. The second is the much-debated canonical OAM distribution natural in free-field theory and light-cone gauge. We show the latter in light-cone gauge can also be related to twist-three GPDs as well as quantum phase-space Wigner distributions, both being measurable in high-energy experiments.