Quark Wigner distribution of the pion meson in light-cone quark model

TL;DR

This paper calculates the quark Wigner distributions of the pion meson using a light-cone quark model, providing insights into the phase-space structure of quarks within the pion.

Contribution

It introduces a method to compute the Wigner distributions of the pion meson based on light-cone wavefunctions, including analytical results for generalized transverse momentum dependent distributions.

Findings

Numerical results for transverse Wigner distributions are presented.

Mixed Wigner distributions as functions of $b_y$ and $k_x$ are shown.

Analytic expressions for generalized transverse momentum dependent distributions are provided.

Abstract

We study the quark Wigner distributions of the pion meson which are the phase-space distributions containing the most general one-parton information.Using the pion wavefunctions deduced from a light-cone quark model, we calculate the Wigner distributions of the unpolarized, longitudinally polarized and transversely polarized quarks inside the pion meson via the Fock-state overlap representation, respectively.We present the numerical results of the transverse Wigner distributions in which the longitudinal momentum fraction is integrated out. The mixed Wigner distributions as functions of $b_y$ and $k_x$ are also presented.As a intermediate step, we provide the analytic results for the generalized transverse momentum dependent distributions of the pion meson in the same model.