Wigner distributions and GTMDs in a proton using light-front quark-diquark model

Abstract

We investigate the Wigner distributions and generalized transverse momentum-dependent distributions (GTMDs) for $u$ and $d$ quarks in the proton by using light-front quark-diquark model. We consider the contribution of scalar and axial-vector diquark having spin-0 and spin-1 respectively. We take different polarization configurations of quark and proton to calculate the Wigner distributions. The Wigner distributions are studied in the impact-parameter space, momentum space and mixed space for $u$ and $d$ quarks in the proton. We also study the relation of GTMDs with longitudinal momentum fraction carried by the active quark $x$ for different values of $\zeta$ (skewness) which is defined as the longitudinal momentum transferred to the proton. Further, we study the GTMDs in the relation with $x$ for zero skewness $(\zeta =0)$ at different values of quark transverse momentum ${\text{p}}_{\perp }$ as well as at different values of total momentum transferred to the proton ${\mathbf{\Delta }}_{\perp }$.

40 pages, 17 figures. To appear in Nucl. Phys. B

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• Quark Wigner Distributions and GTMDs of Pion in the Light-Front Holographic Model
• Quark generalized TMDs at skewness and Wigner Distribution in boost invariant longitudinal space
• Gluon Generalized TMDs and Wigner Distributions in boost invariant longitudinal space