Abstract
Quasi parton distributions (quasi-PDFs) are currently under intense investigation. Quasi-PDFs are defined through spatial correlation functions and are thus accessible in lattice QCD. They gradually approach their corresponding standard (light-cone) PDFs as the hadron momentum increases. Recently, we investigated the concept of quasi-distributions in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator model. In the present work, we extend this study to the remaining six leading-twist GPDs. For large hadron momenta, all quasi-GPDs analytically reduce to the corresponding standard GPDs. We also study the numerical mismatch between quasi-GPDs and standard GPDs for finite hadron momenta. Furthermore, we present results for quasi-PDFs, and explore higher-twist effects associated with the parton momentum and the longitudinal momentum transfer to the target. We study the dependence of our results on the model parameters as well as the type of diquark. Finally, we discuss the lowest moments of quasi distributions, and elaborate on the relation between quasi-GPDs and the total angular momentum of quarks. The moment analysis suggests a preferred definition of several quasi-distributions.
Highlights
Parton distribution functions (PDFs) are important objects encoding information about the quark and gluon structure of hadrons [1]. They can be extracted from data for a large class of hard scattering processes, where the key underlying tool is factorization theorems in quantum chromodynamics (QCD) that separate the perturbatively calculable short distance part of a cross section from the long-distance part described by PDFs and other potential non-perturbative quantities [2]
In the past almost all related studies in lattice QCD focused on moments of PDFs which are defined through time-independent local operators, while the full dependence of PDFs on the parton momentum fraction x remained elusive
The recently proposed quasiparton distributions offer a way to directly access the x-dependence of the PDFs in lattice QCD [3,4]
Summary
Parton distribution functions (PDFs) are important objects encoding information about the quark and gluon structure of hadrons [1]. The first lattice QCD results for quasi-PDFs and related quantities can be considered milestones in this field [15,24,25,28,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82]. We study two sources of higher-twist effects— those related with the average longitudinal momentum fractions of the quark, and those associated with the skewness variable of GPDs. In general, we have tried to extract robust numerical results of the SDM.
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