Orbital angular momenta of quarks and gluons in the nucleon -- model-dependent versus model-independent extractions

TL;DR

This paper explores two gauge-invariant decompositions of the nucleon spin, distinguishing between model-dependent canonical OAMs and model-independent dynamical OAMs related to measurable observables.

Contribution

It clarifies the physical inequivalence of two nucleon spin decompositions and relates dynamical OAMs to experimental observables, emphasizing the model dependence of canonical OAMs.

Findings

Dynamical OAMs are related to deep-inelastic scattering observables.

Canonical OAMs are model-dependent and not directly measurable.

Two gauge-invariant decompositions of nucleon spin are physically inequivalent.

Abstract

We demonstrate that there exist two kinds of gauge-invariant decompositions of the nucleon spin, which are physically inequivalent. The quark and gluon orbital angular momenta (OAMs) appearing in one decomposition are basically the canonical OAMs, while the quark and gluon OAMs appearing in another decomposition are called the dynamical OAMs. It is shown that the dynamical OAMs of quarks and gluons in the nucleon can be related to definite high-energy deep-inelastic-scattering observables. On the other hand, we conjecture that the canonical OAMs of quarks and gluon in the nucleon are model-dependent quantities, which is meaningful only within a specific theoretical model of the nucleon.