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

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.