Article

# Quark Wigner Distributions and Orbital Angular Momentum

06/2011; DOI:10.1103/PhysRevD.84.014015
Source: arXiv

ABSTRACT We study the Wigner functions of the nucleon which provide multidimensional
images of the quark distributions in phase space. These functions can be
obtained through a Fourier transform in the transverse space of the generalized
transverse-momentum dependent parton distributions. They depend on both the
transverse position and the three-momentum of the quark relative to the
nucleon, and therefore combine in a single picture all the information
contained in the generalized parton distributions and the transverse-momentum
dependent parton distributions. We focus the discussion on the distributions of
unpolarized/longitudinally polarized quark in an unpolarized/longitudinally
polarized nucleon. In this way, we can study the role of the orbital angular
momentum of the quark in shaping the nucleon and its correlations with the
quark and nucleon polarizations. The quark orbital angular momentum is also
calculated from its phase-space average weighted with the Wigner distribution
of unpolarized quarks in a longitudinally polarized nucleon. The corresponding
results obtained within different light-cone quark models are compared with
alternative definitions of the quark orbital angular momentum, as given in
terms of generalized parton distributions and transverse-momentum dependent
parton distributions.

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31 Jan 2013

### Keywords

alternative definitions

different light-cone quark models

distributions

Fourier

functions

generalized parton distributions

longitudinally polarized nucleon

phase space

phase-space average weighted

quark

quark distributions

quark orbital angular momentum

single picture

three-momentum

transverse position

transverse space

unpolarized quarks

unpolarized/longitudinally polarized quark

Wigner distribution

Wigner functions