The Continuum and Leading Twist Limits of Parton Distribution Functions in Lattice QCD

TL;DR

This paper presents the first continuum limit results for the nucleon unpolarized parton distribution function in lattice QCD using the pseudo-PDF approach, employing novel error parameterization techniques and excited state control methods.

Contribution

It introduces a new continuum limit calculation of parton distribution functions in lattice QCD with innovative systematic error modeling and excited state contamination control.

Findings

First continuum limit results for nucleon PDFs in lattice QCD

Implementation of Jacobi polynomial parameterization for systematic errors

Use of sGEVP technique to reduce excited state contamination

Abstract

In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD. This study is the first continuum limit using the pseudo-PDF approach with Short Distance Factorization for factorizing lattice QCD calculable matrix elements. Our findings are also compared with the pertinent phenomenological determinations. Inter alia, we are employing the summation Generalized Eigenvalue Problem (sGEVP) technique in order to optimize our control over the excited state contamination which can be one of the most serious systematic errors in this type of calculations. A crucial novel ingredient of our analysis is the parameterization of systematic errors using Jacobi polynomials to characterize and remove both lattice spacing and higher twist contaminations, as well as the leading twist distribution. This method can be expanded in further studies to remove all other systematic errors.