Abstract
We study the leading-twist quasi parton distribution function (quasi-PDF) and quasigeneralized parton distribution (quasi-GPD) of the pion meson by using a spectator model. We consider the case where the quasifunctions are defined via inserting the matrix ${\ensuremath{\gamma}}_{z}$ in the spacial correlation functions. We obtain the analytical expressions for the quasi-PDF and quasi-GPD. The numerical results of the quasifunctions are calculated from the parameters obtained by fitting the model result to the known parametrization. Particularly, we investigate the hadron momentum dependence of the quasifunctions as well as compare the quasidistributions to the standard functions at different hadron momentum. We find that in the region $x>0.2$, the quasidistribution 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 quasidistributions to obtain standard distributions.
Highlights
The concept of quasi-parton distribution functions (PDFs) for hadrons has been proposed recently in the seminal papers by Ji [1,2] and has received a lot of attention
Different from the standard parton distribution functions (PDFs) which are defined through the light-cone correlation function, quasi-PDFs are defined by the bilocal operator on a spatial interval such that they can be calculated by the lattice QCD in a fourdimensional Euclidian space
Standard PDFs, which are of fundamental importance in haronic physics, describe the density of a parton carrying in hadron a light-cone fraction x of the total momentum, while quasi-PDFs have similar interpretation, but for a parton carrying a fraction x of the finite momentum P⃗ of the hadron
Summary
The concept of quasi-PDFs for hadrons has been proposed recently in the seminal papers by Ji [1,2] and has received a lot of attention. The concept of quasi-PDFs has been extended to the case of generalize parton distributions (GPDs) [30,31,32] It was proposed in parallel with the quasiPDFs in Ref. [33,34,35,36,37,38]) They unify the conventional notions of parton densities, form factors, and distribution amplitudes, which are widely applied in the study of hadron structure. We will investigate both the quasi-PDFs and the quasi-GPDs of the pion meson using a spectatorantiquark model. It largely relies on theoretical studies as well as lattice calculations which are important for obtaining the information on the pion structure.
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