Generalized Parton Distributions of proton for non zero skewness in transverse and longitudinal position spaces

TL;DR

This paper explores the proton's generalized parton distributions (GPDs) using a simulated model to analyze their behavior in transverse and longitudinal position spaces, revealing diffraction patterns and improving convergence near end points.

Contribution

It introduces a simulated model for GPDs that enhances convergence near end points and provides a detailed analysis of GPDs in both transverse and longitudinal position spaces.

Findings

Fourier transforms reveal diffraction patterns in longitudinal position space.

The model improves convergence of GPDs near end points.

Distribution patterns in transverse and longitudinal spaces are characterized.

Abstract

We investigate the Generalized Parton Distributions(GPDs) of proton by expressing them in terms of overlaps of light front wave functions (LFWFs) using a simulated model which is able to qualitatively improve the convergence near the end points of $x$. We study the spin non-flip $H(x, \zeta, t)$ and spin flip $E(x, \zeta, t)$ part of GPDs for the particle conserving $n \rightarrow n$ overlap in the DGLAP region $(\zeta<x<1)$. The Fourier transform (FT) of the GPDs w.r.t. to the transverse momentum transfer as well the FT of the GPDs w.r.t. $\zeta$ have also been obtained giving the distribution of partons in the transverse position space and the distribution in the longitudinal position space respectively. Diffraction pattern is obtained for both $ \mathcal{H}(x,\sigma,t)$ and $ \mathcal{E}(x,\sigma,t)$ in the longitudinal position space.