Notes on the orbital angular momentum of quarks in the nucleon

TL;DR

This work addresses how to define and separate the quark orbital angular momentum (OAM) in the nucleon within a gauge-invariant spin decomposition framework. It adopts the Chen–Hatta approach to split the gauge field into physical and pure-gauge parts, enabling a gauge-invariant canonical OAM $L_{can}$ and its relation to Ji’s $L_{Ji} = L_{can} + L_{pot}$, with $L_{pot}$ governed by twist-three quark-gluon dynamics and soft-gluon poles. By linking $L_{can}$ to the Wigner distribution and transverse-momentum dependent (TMD) formalisms, the paper provides a concrete, lattice-accessible operator expression for the canonical OAM and shows how it can be measured or computed alongside the Ji and potential contributions. The results offer a path to disentangle quark OAM in practice, discuss measurability through lattice QCD and twist-three GPDs, and clarify frame- and path-dependence issues inherent in gauge-invariant decompositions.

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.