Lattice continuum-limit study of nucleon quasi-PDFs

TL;DR

This study investigates the continuum limit of lattice QCD calculations of nucleon quasi-PDFs, demonstrating the importance of controlling lattice artifacts for accurate PDF extraction.

Contribution

It provides the first detailed continuum extrapolation of nucleon quasi-PDFs using multiple lattice spacings with Wilson twisted mass fermions.

Findings

Continuum extrapolation improves agreement with phenomenology.

Lattice artifacts significantly affect the small-x antiquark distribution.

Extrapolation changes the sign of the antiquark distribution at small x.

Abstract

The quasi-PDF approach provides a path to computing parton distribution functions (PDFs) using lattice QCD. This approach requires matrix elements of a power-divergent operator in a nucleon at high momentum and one generically expects discretization effects starting at first order in the lattice spacing $a$. Therefore, it is important to demonstrate that the continuum limit can be reliably taken and to understand the size and shape of lattice artifacts. In this work, we report a calculation of isovector unpolarized and helicity PDFs using lattice ensembles with $N_f=2+1+1$ Wilson twisted mass fermions, a pion mass of approximately 370 MeV, and three different lattice spacings. Our results show a significant dependence on $a$, and the continuum extrapolation produces a better agreement with phenomenology. The latter is particularly true for the antiquark distribution at small momentum fraction $x$, where the extrapolation changes its sign.