Quark Wigner Distributions and Orbital Angular Momentum

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.

29 pages, 10 figures, 3 tables

References in corpus (18)

• Relations between generalized and transverse momentum dependent parton distributions
• Generalized parton correlation functions for a spin-1/2 hadron
• Spin Structure of the Nucleon - Status and Recent Results
• The transverse momentum dependent distribution functions in the bag model
• Generalized parton correlation functions for a spin-0 hadron
• Empirical transverse charge densities in the nucleon and the nucleon-to-$\Delta$ transition
• Unified framework for generalized and transverse-momentum dependent parton distributions within a 3Q light-cone picture of the nucleon
• Azimuthal spin asymmetries in light-cone constituent quark models
• Pretzelosity $h_{1T}^{\perp }$ and quark orbital angular momentum
• Nucleon spin densities in a light-front constituent quark model
• Electroweak structure of the nucleon, meson cloud and light-cone wavefunctions
• Drell-Yan processes, transversity and light-cone wavefunctions
• Connection between the Sivers function and the anomalous magnetic moment
• Naive time-reversal odd phenomena in semi-inclusive deep-inelastic scattering from light-cone constituent quark models
• Tensor charges of light baryons in the Infinite Momentum Frame
• Improvement of the Theta+ width estimation method on the Light Cone
• Baryon vector and axial content up to the 7Q component
• Orbital structure of quarks inside the nucleon in the light-cone diquark model

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• Six-dimensional light-front Wigner distributions of the proton
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• T-odd Wigner Distributions in boost-invariant longitudinal position space and Spin-momentum correlation in proton
• Azimuthal asymmetries in lepton and heavy-quark pair production in UPCs
• Wigner Functions and Quark Orbital Angular Momentum
• Relations between generalized parton distributions and transverse momentum dependent parton distributions
• Spin structure of the nucleon on the light front