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 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 (ζ=0) at different values of quark transverse momentum p⊥ as well as at different values of total momentum transferred to the proton Δ⊥.
Highlights
The major aim of the hadron physics is to expose the relationship between partons and hadrons
The distribution located in the direction transverse to the motion of the hadron is explained through the generalized parton distributions (GPDs) [1,2,3] as a function of longitudinal momentum fraction carried by the parton, the longitudinal momentum transferred to the hadron and the total momentum transferred (x, ζ and t respectively)
The calculations of the Wigner distributions and generalized transverse momentum-dependent parton distributions (GTMDs) involve the inputs for the diquark mass (Ms) and the coupling for the scalar isoscalar diquark, the axial-vector diquark mass (Ma) and the coupling corresponding to ud-system with Iz = 0 as well as the axial-vector diquark mass (Ma) and coupling corresponding to uu-system with Iz = 1
Summary
The major aim of the hadron physics is to expose the relationship between partons (basic degrees of freedom of QCD) and hadrons. Other possible versions of phase-space distributions are: Husimi distribution (smeared version of Wigner distribution) and Kirkwood distribution where the former one is real and positive definite and later is complex [61] It has been introduced in recent times that the gluon GTMDs can be accessible through diffractive di-jet production in deep-inelastic lepton-nucleon scattering [62,63,64] and in virtual photon-nucleus quasi-elastic scattering [65]. Using light-front quark-diquark model, GPDs, TMDs and spin transverse asymmetries for electron and hadron have already been evaluated [6, 74,75,76]. Considering the above developments of the light-front quark-diquark model in studying internal structure of the hadrons through GPDs and TMDs, it becomes desirable to extend this model to investigate the Wigner distributions and GTMDs of the hadrons.
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