Quark phase-space distributions and orbital angular momentum

TL;DR

This paper explores the Wigner functions of the nucleon to visualize quark distributions in phase space, linking GPDs and TMDs, and discusses how to extract quark orbital angular momentum from these distributions.

Contribution

It introduces a comprehensive analysis of nucleon Wigner functions, connecting phase space distributions with GPDs and TMDs, and presents a method to extract quark orbital angular momentum.

Findings

Wigner functions provide multi-dimensional images of quark distributions.

Quark orbital angular momentum can be extracted from phase space distributions.

Comparison of orbital angular momentum from Wigner functions with GPD and TMD based definitions.

Abstract

We discuss the Wigner functions of the nucleon which provide multi-dimensional images of the quark distributions in phase space. They combine in a single picture all the information contained in the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs). In particular, we present results for the distribution of unpolarized quarks in a longitudinally polarized nucleon obtained in a light-cone constituent quark model. We show how quark orbital angular momentum can be extracted from these distributions and compare it with alternative definitions given in terms of the GPDs and the TMDs.