Notes on the orbital angular momentum of quarks in the nucleon

TL;DR

This paper explores the decomposition of quark orbital angular momentum within a polarized proton, highlighting gauge-invariant operators and recent theoretical frameworks for understanding nucleon spin structure.

Contribution

It introduces a detailed analysis of Ji's quark orbital angular momentum, decomposing it into canonical and potential parts using gauge-invariant operators, advancing the theoretical understanding of nucleon spin.

Findings

Decomposition of Ji's orbital angular momentum into canonical and potential components.

Representation of these components as matrix elements of gauge-invariant operators.

Clarification of the theoretical framework for spin decomposition in nucleons.

Abstract

We discuss the orbital angular momentum of partons inside a longitudinally polarized proton in the recently proposed framework of spin decomposition. The quark orbital angular momentum defined by Ji can be decomposed into the `canonical' and the `potential' angular momentum parts, both of which are represented as the matrix element of a manifestly gauge invariant operator.