The role of orbital angular momentum in the proton spin

TL;DR

This paper estimates the orbital angular momenta of up and down quarks in the proton across energy scales, revealing a significant negative difference at low energies and discussing foundational issues in defining quark orbital angular momentum in QCD.

Contribution

It provides a model-independent estimation of quark orbital angular momenta in the proton and explores the discrepancy with previous models, addressing fundamental QCD questions.

Findings

$L^u - L^d$ is large and negative at low energy scales

Discrepancy with the cloudy bag model analysis

Highlights issues in defining quark orbital angular momentum in QCD

Abstract

The orbital angular momenta $L^u$ and $L^d$ of up and down quarks in the proton are estimated as functions of the energy scale as model-independently as possible, on the basis of Ji's angular momentum sum rule. This analysis indicates that $L^u - L^d$ is large and negative even at low energy scale of nonperturbative QCD, in contrast to Thomas' similar analysis based on the refined cloudy bag model. We pursuit the origin of this apparent discrepancy and suggest that it may have a connection with the fundamental question of how to define quark orbital angular momenta in QCD.