# Parton distributions from lattice data: the nonsinglet case

## TL;DR

This paper develops a new framework to extract nonsinglet parton distribution functions from lattice QCD data using the qPDF approach, integrating it with the NNPDF methodology to assess its potential in constraining PDFs.

## Contribution

It introduces a novel method to relate lattice QCD matrix elements to PDFs and incorporates this into the NNPDF framework for improved PDF determination.

## Key findings

- Successfully extracted nonsinglet distributions from lattice data.
- Demonstrated the potential of lattice data to constrain PDFs.
- Assessed systematic uncertainties in the extraction process.

## Abstract

We revise the relation between Parton Distribution Functions (PDFs) and matrix elements computable from lattice QCD, focusing on the quasi-Parton Distribution Functions (qPDFs) approach. We exploit the relation between PDFs and qPDFs in the case of the unpolarized isovector parton distribution to obtain a factorization formula relating the real and imaginary part of qPDFs matrix elements to specific nonsinglet distributions, and we propose a general framework to extract PDFs from the available lattice data, treating them on the same footing as experimental data. We implement the proposed approach within the NNPDF framework, and we study the potentiality of such lattice data in constraining PDFs, assuming some plausible scenarios to assess the unknown systematic uncertainties. We finally extract the two nonsinglet distributions involved in our analysis from a selection of the available lattice data.