Abstract
The Wigner distributions for u and d quarks in a proton are calculated using the light front wave functions (LFWFs) of the scalar quark-diquark model for nucleon constructed from the soft-wall AdS/QCD correspondence. We present a detail study of the quark orbital angular momentum(OAM) and its correlation with quark spin and proton spin. The quark density distributions, considering the different polarizations of quarks and proton, in transverse momentum plane as well as in transverse impact parameter plane are presented for both u and d quarks.
Highlights
Wigner distributions are six-dimensional distributions containing more general informations about the nucleon structure
Wigner distributions integrated over transverse momentum give the generalized parton distributions (GPDs) at zero skewness, the transverse momentum dependent distributions (TMDs) are obtained by integrating over transverse impact parameters with zero momentum transfer and the integration over transverse momentum and transverse positions provide the parton distribution function (PDF)
The Wigner distributions after integrating over the light-cone energy of the parton are interpreted as a Fourier transform of the corresponding generalized transverse momentum dependent distributions (GTMDs), which are functions of the light-cone threemomentum of the parton as well as the momentum transfer to the nucleon
Summary
Wigner distributions are six-dimensional distributions containing more general informations about the nucleon structure. In [11], five-dimensional Wigner distributions were proposed in the light-front formalism with three momentum and two position components of a parton. The angular momentum of a quark is extracted from the Wigner distributions taking the phase space average. The spin–spin and spin–orbital angular momentum (OAM) correlations between a nucleon and a quark inside the nucleon can be described from a phase space average of Wigner distributions. We investigate the Wigner distributions for unpolarized and polarized proton and the orbital angular momentum (OAM) and spin–spin and spin–OAM correlations in a scalar diquark model of the proton [26] with. We first introduce the light-front scalar diquark model in Sect. 4. The different definitions of the orbital angular momentum are discussed in Sect.
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