Phenomenological analysis of the nucleon spin contents and their scale dependence

TL;DR

This paper explores how the distribution of spin and orbital angular momentum among nucleon constituents depends on the energy scale, clarifying apparent discrepancies in experimental and theoretical findings.

Contribution

It provides a phenomenological analysis emphasizing the importance of scale dependence in understanding nucleon spin decomposition.

Findings

Gluon polarization is small at low scales.

Quark orbital angular momentum is nearly zero according to lattice QCD.

Scale dependence is crucial for resolving nucleon spin sum rule issues.

Abstract

In the past few years, a lot of evidences have been accumulated, which indicate that the gluon polarization inside the nucleon is likely to be small at least at the low renormalization scales. On the other hand, the recent lattice QCD analyses suggest that the net orbital angular momentum carried by the quarks is nearly zero. There is also some indication noticed by Brodsky and Gardner based on the COMPASS observation of small single-spin asymmetry on the isoscalar deuteron target, that the gluon orbital angular momentum inside the nucleon is likely to be small. Naively combining all these observations, we are led to a rather embarrassing conclusion that the nucleon constituents altogether do not carry enough amount of angular momentum saturating the total nucleon spin. We show that this somewhat confused state of affairs can be cleared up only by paying careful attention to the scale dependencies of the nucleon spin decomposition.