Quasi parton distribution function and quasi generalized parton distribution of the pion meson in a spectator model

TL;DR

This paper investigates the quasi parton distribution functions and generalized parton distributions of the pion meson using a spectator model, analyzing their dependence on hadron momentum and comparing them to standard distributions.

Contribution

It provides analytical expressions and numerical analysis of quasi distributions of the pion, supporting their use in extracting standard distributions at high hadron momentum.

Findings

Quasi distributions resemble standard distributions for x>0.2 at hadron momentum > 2 GeV.

Analytical expressions for quasi-PDF and quasi-GPD derived in the spectator model.

Quasi functions show hadron momentum dependence and are consistent with standard functions at high momentum.

Abstract

We study the leading-twist quasi parton distribution function (quasi-PDF) and quasi generalize parton distribution (quasi-GPD) of the pion meson by using a spectator model. We consider the case the quasi functions are defined via inserting the matrix $\gamma^3$ in the spacial correlation functions. We obtain the analytical expressions for the quasi-PDF and quasi-GPD. The numerical results for them are calculated from the parameters obtained by fitting the model results to the known parametrization. Particularly, we investigate the hadron momentum dependence of the quasi functions as well as compare the quasi distributions to the standard functions at different hadron momentum. We find that in the region $x>0.2$, the quasi distribution are similar to the standard distributions in size and shape when the hadron momentum is larger than $2$ GeV. Our study thus supports the idea of using quasi distributions to obtain standard distributions.