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

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 ζ (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 $p_{\perp }$ as well as at different values of total momentum transferred to the proton ${\Delta }_{\perp }$.