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Quark orbital motions from Wigner distributions

We investigate quark Wigner distributions in a light-cone spectator model. Both the scalar and the axial-vector spectators are included. The light-cone wave functions are derived from effective quark-spectator-nucleon vertex and then generalized by adjusting the power of energy denominators. The gauge link is taken into account by introducing relative phases to the light-cone amplitudes, and the phases are estimated from one gluon exchange interactions. The mixing distributions, which describe the correlation between transverse coordinate and transverse momentum and represent quark orbital motions, are calculated from the Wigner distributions. We find both $u$ quark and $d$ quark have positive orbital angular momentum in a polarized proton at small $x$ region, but a sign change is observed at large $x$ region for the $d$ quark. Besides, some model relations between Wigner distributions with different polarization configurations are found.