Three Dimensional Imaging of the Nucleon

TL;DR

This paper analytically calculates and numerically analyzes the Wigner distributions of quarks and gluons within a dressed quark model using light-front wave functions, providing insights into the three-dimensional structure of the nucleon.

Contribution

It introduces an analytical framework for Wigner distributions of quarks and gluons in a dressed quark model using LFWFs and improves numerical techniques for Fourier transforms.

Findings

Wigner distributions of quarks and gluons are characterized in the model.

Contour plots reveal the spatial and momentum structure of partons.

Numerical methods effectively remove cutoff dependence in Fourier transforms.

Abstract

We study the Wigner distributions of quarks and gluons in light-front dressed quark model using the overlap of light front wave functions (LFWFs). We take the target to be a dressed quark, this is a composite spin $-1/2$ state of quark dressed with a gluon. This state allows us to calculate the quark and gluon Wigner distributions analytically in terms of LFWFs using Hamiltonian perturbation theory. We analyze numerically the Wigner distributions of quark and gluon and report their nature in the contour plots. We use an improved numerical technique to remove the cutoff dependence of the Fourier transformed integral over ${\bf \Delta}_\perp$.