Studying twist-2 GPDs through quasi-distributions in a scalar diquark model

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. 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. I. INTRODUCTIONParton 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]. On the other hand, first-principles calculations of PDFs using lattice QCD have remained challenging due to their explicit time-dependence. As a result, 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 quasi parton distributions (quasi-PDFs) offer a way to directly access the x-dependence of the PDFs in lattice QCD [3,4]. Quasi-PDFs are defined through spatial equal-time operators that can be computed on four-dimensional Euclidean lattices. They reduce to their corresponding standard (light-cone) PDFs if the hadron momentum P 3 = | P | → ∞, prior to renormalization. However, for lattice calculations one first renormalizes, and P 3 is finite. This leads to two sources of discrepancies between quasi-PDFs and standard PDFs: higher-twist corrections that are suppressed by powers of 1 P 3 , and a different ultraviolet (UV) behavior for these two types of PDFs. The UV disparities can be cured order by order in perturbative QCD through a so-called matching procedure -see for instance . Other approaches for computing the x-dependence of PDFs and related quantities have also been suggested [8][9][10][11][12][13][14][15...

Progress in $x$-dependent partonic distributions from lattice QCD

“…The ℎ function was very recently explored numerically [65], with qualitatively very similar conclusions to the ones for , including the validity of the WW approximation. Even more recently, first results appeared [68] for the twist-3 GPD ˜ 2 ( ), whose combination with the helicity twist-2 GPD ˜ ( ) is the off-forward generalization of ( ).…”

Working Group 6 Summary: Spin and 3D Structure

“…Work was presented on progress in the study of GPDs, including the presentation of new global fits to deeply virtual Compton scattering (DVCS) in a leading order and leading twist formalism [49]. In addition, calculations within models [50,51] addressing aspects needed for their implementation in lattice calculations and a study by A. Amor-Quiroz confirming the appearance of a difference between the Ji and Jaffe-Manohar spin decompositions at two-loop [52], while S. Rodini reported on a breakdown of the lensing relation in a model field theory when the final state involves many partons [53].…”