# Valence parton distribution function of pion from fine lattice

## TL;DR

This paper uses lattice QCD with Large Momentum Effective Theory to compute the valence parton distribution function of the pion, providing a first-principles determination with non-perturbative renormalization and matching.

## Contribution

It introduces a lattice QCD approach with mixed action and RI-MOM scheme to extract the pion's valence PDF, testing the validity of 1-loop matching in this context.

## Key findings

- Valence PDF of pion obtained from lattice QCD.
- Validation of 1-loop matching procedure.
- Consistent results across different lattice spacings.

## Abstract

We present a lattice QCD study of valence parton distribution inside the pion within the framework of Large Momentum Effective Theory. We use a mixed action approach with 1-HYP smeared valence Wilson clover quarks on 2+1 flavor HISQ sea with the valence quark mass tuned to 300 MeV pion mass. We use $48^3 \times 64$ lattice at a fine lattice spacing $a=0.06$ fm for this computation. We renormalize the quasi-PDF matrix element in the non-perturbative RI-MOM scheme. As a byproduct, we test the validity of 1-loop matching procedure by comparing the RI-MOM renormalized quasi-PDF matrix element with off-shell quark external states as computed in the continuum 1-loop perturbation theory with the lattice results at $a=0.04$ and 0.06 fm. By applying the RI-MOM to ${\bar{\rm MS}}$ one-loop matching, implemented through a fit to phenomenologically motivated PDFs, we obtain the valence PDF of pion.