Reconstructing parton densities at large fractional momenta

TL;DR

This paper introduces a new method to improve the reconstruction of parton distribution functions (PDFs) by combining quasi-PDFs and Mellin moments, aiming to enhance lattice QCD calculations at high fractional momenta.

Contribution

It proposes a novel approach that integrates quasi-PDFs with Mellin moments to better reconstruct PDFs from lattice QCD data.

Findings

Method successfully tested on diquark spectator model

Improves PDF reconstruction at high fractional momenta

Potential to produce PDFs solely from lattice QCD results

Abstract

Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to compute moments of PDFs, which are matrix elements of local operators. Recently, an alternative approach has been proposed, based on the introduction of quasi-parton distribution functions (quasi-PDFs), which are matrix elements of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs approach standard PDFs in the limit of very large longitudinal proton momenta $P^z$. This limit is not attainable in lattice simulations, and quasi-PDFs fail to reproduce PDFs at high fractional longitudinal momenta. In this paper, we propose a method to improve the reconstruction of PDFs by combining information from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method using the diquark spectator model for up and down valence distributions of both unpolarized and helicity PDFs. In the future, the method can be used to produce PDFs entirely based on lattice QCD results.