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

TL;DR

This paper explores the Wigner distributions and GTMDs of u and d quarks in the proton using a light-front quark-diquark model, analyzing various polarization states and their relations to momentum transfer and skewness.

Contribution

It introduces a detailed calculation of Wigner distributions and GTMDs in a light-front quark-diquark model considering scalar and axial-vector diquarks, including polarization effects and momentum transfer dependencies.

Findings

Wigner distributions analyzed in impact-parameter, momentum, and mixed spaces.

GTMDs related to longitudinal momentum fraction and skewness.

Results show the dependence of GTMDs on transverse momentum and momentum transfer.

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 $\textbf{p}_\perp$ as well as at different values of total momentum transferred to the proton ${\bf \Delta}_\perp$.