On Gauge-Invariant Decomposition of Nucleon Spin

TL;DR

This paper analyzes various gauge-invariant decompositions of the nucleon spin, clarifying their differences, similarities, and experimental implications, and introduces a new decomposition closer to the Ji decomposition.

Contribution

It clarifies the relations among different gauge-invariant nucleon spin decompositions and proposes a new decomposition closer to the Ji approach.

Findings

The Chen et al. decomposition generalizes the Jaffe-Manohar decomposition to be gauge-invariant.

There exists an alternative gauge-invariant decomposition similar to Ji's, allowing gluon spin and orbital separation.

The gauge-invariant decomposition of nucleon spin is not unique, affecting experimental interpretations.

Abstract

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 essentially. The decomposition recently proposed by Chen et al. can be thought of as a nontrivial generalization of the gauge-variant Jaffe-Manohar decomposition so as to meet the gauge-invariance requirement of each term of the decomposition. 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 the spin and orbital parts. After clarifying the reason why the gauge-invariant decomposition of the nucleon spin is not unique, we discuss which decomposition is more preferable from the experimental viewpoint.