Exploring twist-2 GPDs through quasidistributions in a diquark spectator 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 as the type of diquark. Finally, we discuss the lowest moments of quasidistributions, and elaborate on the relation between quasi-GPDs and the total angular momentum of quarks. The moment analysis suggests a preferred definition of several quasidistributions.

Generalized parton distributions of the proton from lattice QCD

“…We also notice that, at this accuracy, 𝐸 𝑇 and H𝑇 do not show asymmetry between quarks (𝑥 > 0) and antiquarks (𝑥 < 0). We also find that H𝑇 is negative and a similar qualitative conclusion was found within the scalar diquark model [35]. In fact, a reduction in magnitude the momentum transfer is also observed in standard form factors, that are just integrals over 𝑥 of the GPDs.…”

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

“…In the latter, the GPDs are further suppressed. Note, however, that the observed discontinuity at the border between the regions is a manifestation of enhanced HTE, expected from model calculations [54,55]. The ETMC work was very recently extended to the chiral-odd transversity case with four GPDs [56], using the same lattice setup.…”

“…their enhancement both at small-and large-. It is worth to emphasize that the former translate to enhanced corrections at = ± in quasi-GPDs [54,55].…”

Transversity GPDs of the proton from lattice QCD

“…In the ERBL region, there is a significant decrease of the distribution as −t increases. However, the distribution in the DGLAP region shows less sensitivity in t. We note that the discontinuity at x = ±ξ is not physical, as twist-2 GPDs are continuous functions at the boundaries of the ERBL region [47,96]. The observed effect is due to uncontrolled higher-twist contamination, which cannot be treated by the matching formalism as it contains only the leading twist.…”

“…Since we are using positive and negative values for the momentum transfer, one has to be careful with the signs in the decomposition. In addition to the signs of the kinematic factors, one also has to consider that H T q , E T q , and H T q are even functions of ξ, while E T q is odd [94,95], which also holds for the quasi-GPDs [96] and F G . For example, F E T (z, −ξ, t, P 3 ) = −F E T (z, ξ, t, P 3 ), which is taken into account in the decomposition for the negative value of ξ.…”