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

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• Defining the Proton Radius: a Unified Treatment
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• Probing the Weizsäcker-Williams gluon Wigner distribution in pp collisions
• Hunting the Gluon Orbital Angular Momentum at the Electron-Ion Collider
• Spin-orbit correlations in the nucleon
• The elliptic gluon GTMD inside a large nucleus
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• The light-front gauge-invariant energy-momentum tensor
• A Fixed-Target Programme at the LHC: Physics Case and Projected Performances for Heavy-Ion, Hadron, Spin and Astroparticle Studies
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• Quark Wigner distributions in a light-cone spectator model
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• The relativistic center of mass in field theory with spin
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• Quark orbital dynamics in the proton from Lattice QCD -- from Ji to Jaffe-Manohar orbital angular momentum
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• Angular momentum and generalized parton distributions for the proton with basis light-front quantization
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• Lorentz Invariance and QCD Equation of Motion Relations for Generalized Parton Distributions and the Dynamical Origin of Proton Orbital Angular Momentum
• Wigner Distributions For Gluons
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• Use of the Husimi distribution for nucleon tomography
• Probing the gluon tomography in photoproduction of di-pions
• Electron Structure: Shape, Size and GPDs in QED
• From Ji to Jaffe-Manohar orbital angular momentum in Lattice QCD using a direct derivative method
• Sivers and Boer-Mulders GTMDs in Light-front Holographic Quark-diquark Model
• Twist-three cross-sections in deeply virtual Compton scattering
• Study of kaon structure using the light-cone quark model
• Phase-space distributions of nuclear short-range correlations
• Quark Wigner distribution of the pion meson in light-cone quark model
• Orbital Angular Momentum and Generalized Transverse Momentum Distribution
• Prospects for quarkonium studies at the high-luminosity LHC
• Quark transverse spin-orbit correlations
• Pre-Town Meeting on Spin Physics at an Electron-Ion Collider
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• Inclusive Single-Spin Asymmetries, Quark-Photon, and Quark-Quark Correlations
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• Gauge Invariant Descriptions of Gluon Polarizations
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• Understanding the Valence Quark Structure of the Pion through GTMDs
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• Six-dimensional light-front Wigner distributions of the proton
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• Discrete Wigner-Weyl calculus for the finite lattice
• Partonic Picture of Generalized Transverse Momentum Distributions
• Phase space distributions in information theory
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• Wigner - Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field
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