The role of orbital angular momentum in the proton spin

Understand

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.