Valence parton distribution of pion from lattice QCD: Approaching continuum

TL;DR

This paper provides a high-precision lattice QCD calculation of the pion's valence parton distribution function, exploring continuum limit approaches and analyzing the large-x behavior with various renormalization schemes.

Contribution

It introduces a detailed lattice QCD methodology for determining the pion's valence PDF at multiple lattice spacings, including continuum extrapolation and analysis of high-x behavior.

Findings

Valence PDF reconstructed with high precision

First moments inferred using perturbative matching

Large-x behavior analyzed with multiple schemes

Abstract

We present a high-statistics lattice QCD determination of the valence parton distribution function (PDF) of the pion, with a mass of 300 MeV, using two very fine lattice spacings of $a=0.06$ fm and 0.04 fm. We reconstruct the $x$-dependent PDF, as well as infer the first few even moments of the PDF using leading-twist 1-loop perturbative matching framework. Our analyses use both RI-MOM and ratio-based schemes to renormalize the equal-time bi-local quark-bilinear matrix elements of pions boosted up to 2.4 GeV momenta. We use various model-independent and model-dependent analyses to infer the large-$x$ behavior of the valence PDF. We also present technical studies on lattice spacing and higher-twist corrections present in the boosted pion matrix elements.