Quark Wigner Distributions

TL;DR

This paper explores the Wigner functions of the nucleon to provide a comprehensive phase-space picture of quark distributions, linking GPDs and TMDs, and examines orbital angular momentum in various quark models.

Contribution

It introduces the calculation of quark Wigner distributions for the nucleon and compares orbital angular momentum results across different models and definitions.

Findings

Distribution of unpolarized quark in a longitudinally polarized nucleon analyzed.

Orbital angular momentum values obtained from Wigner functions compared with GPD and TMD approaches.

Results highlight differences and consistencies among various quark model predictions.

Abstract

We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space and 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 quark in a longitudinally polarized nucleon. Treating this distribution as it was a classical distribution, we also obtain the expectation value of the orbital angular momentum operator and compare the corresponding results from different quark models with the values obtained using alternative definitions of the orbital angular momentum, as given in terms of the GPDs and the TMDs.