Gauge-invariant decomposition of nucleon spin

TL;DR

This paper analyzes various gauge-invariant decompositions of the nucleon spin in QCD, clarifying their relationships and proposing a new decomposition with observable implications for high-energy experiments.

Contribution

It provides a unified framework for understanding different nucleon spin decompositions and introduces a gauge-invariant decomposition closely related to the Ji decomposition with measurable components.

Findings

All known decompositions are gauge-equivalent within a general framework.

A new gauge-invariant decomposition aligns with the Ji decomposition and has observable terms.

Each term in the new decomposition can be extracted from deep-inelastic-scattering data.

Abstract

Based on gauge-invariant decomposition of covariant angular momentum tensor of QCD in an arbitrary Lorentz frame, we investigate the relation between the known decompositions of the nucleon spin into its constituents, thereby clarifying in what respect they are common and in what respect they are different critically. We argue that the decomposition of Bashinsky and Jaffe, that of Chen et al., and that of Jaffe and Manohar are contained in our more general decomposition, after an appropriate gauge-fixing in a suitable Lorentz frame, which means that they all {\it gauge-equivalent}. We however point out that there is another gauge-invariant decomposition of the nucleon spin, which is closer to the Ji decomposition, while allowing the decomposition of the gluon total angular momentum into its spin and orbital parts. An advantage of the latter decomposition is that each of the four terms corresponds to a definite observable, which can be extracted from high-energy deep-inelastic-scattering measurements.