Orbital Angular Momentum and Generalized Transverse Momentum Distribution

TL;DR

This paper establishes a theoretical connection between orbital angular momentum operators in nucleons and generalized transverse momentum distributions, linking fundamental operators to measurable quantities and discussing lattice QCD calculations.

Contribution

It demonstrates that orbital angular momentum operators in the nucleon spin sum rule are equivalent to those derived from generalized transverse momentum distributions in the infinite momentum frame.

Findings

Orbital angular momentum operators match in the infinite momentum frame.

Connection established between sum rule terms and experimental observables.

Discussion on local definitions and lattice QCD calculations.

Abstract

We show that, when boosted to the infinite momentum frame, the quark and gluon orbital angular momentum operators defined in the nucleon spin sum rule of X. S. Chen et al. are the same as those derived from generalized transverse momentum distributions. This completes the connection between the infinite momentum limit of each term in that sum rule and experimentally measurable observables. We also show that these orbital angular momentum operators can be defined locally, and discuss the strategies of calculating them in lattice QCD.