# Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD

## TL;DR

This paper demonstrates a novel lattice QCD method to directly extract the pion valence quark distribution from coordinate space current-current correlations, offering a complementary approach to experimental global analyses.

## Contribution

It introduces a new lattice QCD technique using antisymmetric vector and axial-vector currents to determine the pion valence quark distribution.

## Key findings

- First exploratory lattice QCD calculation of pion valence distribution
- Validation of the method with controllable systematics
- Potential to complement experimental global analyses

## Abstract

We present the first exploratory lattice QCD calculation of the pion valence quark distribution extracted from spatially separated current-current correlations in coordinate space. We show that an antisymmetric combination of vector and axial-vector currents provides direct information on the pion valence quark distribution. Using the collinear factorization approach, we calculate the perturbative tree-level kernel for this current combination and extract the pion valence distribution. The main goal of this article is to demonstrate the efficacy of this general lattice QCD approach in the reliable extraction of parton distributions. With controllable power corrections and a good understanding of the lattice systematics, this method has the potential to serve as a complementary to the many efforts to extract parton distributions in global analyses from experimentally measured cross sections. We perform our calculation on an ensemble of 2+1 flavor QCD using the isotropic-clover fermion action, with lattice dimensions $32^3\times 96$ at a lattice spacing \mbox{$a=0.127$ fm} and the quark mass equivalent to a pion mass $m_\pi \simeq 416$ MeV.