Pion Valence Structure from Ioffe Time Pseudo-Distributions

TL;DR

This paper calculates the pion valence quark distribution using lattice QCD with pseudo-PDF formalism, incorporating multiple ensembles and smearing techniques, and compares results with global fits and prior studies.

Contribution

It introduces a lattice QCD calculation of the pion valence distribution using pseudo-PDFs on two ensembles with novel smearing and summation methods, providing new insights into pion structure.

Findings

Consistent pion valence quark distribution obtained from two ensembles.

Calculated the first four moments of the distribution.

Qualitative agreement with global fits and previous lattice results.

Abstract

We present a calculation of the pion valence quark distribution extracted using the formalism of reduced Ioffe time pseudo-distributions or more commonly known as pseudo-PDFs. Our calculation is carried out on two different 2+1 flavor QCD ensembles using the isotropic-clover fermion action, with lattice dimensions $24^3\times 64$ and $32^3\times 96$ at the lattice spacing of $a=0.127$ fm, and with the quark mass equivalent to a pion mass of $m_\pi \simeq 415$ MeV. We incorporate several combinations of smeared-point and smeared-smeared pion source-sink interpolation fields in obtaining the lattice QCD matrix elements using the summation method. After one-loop perturbative matching and combining the pseudo-distributions from these two ensembles, we extract the pion valence quark distribution using a phenomenological functional form motivated by the global fits of parton distribution functions. We also calculate the lowest four moments of the pion quark distribution through the "OPE without OPE". We present a qualitative comparison between our lattice QCD extraction of the pion valence quark distribution with that obtained from global fits and previous lattice QCD calculations.