Pion valence quark distribution from matrix element calculated in lattice QCD

Raza Sabbir Sufian,David G Richards,Jian-Wei Qiu,Colin Egerer,Joseph Karpie,Kostas Orginos

doi:10.1103/physrevd.99.074507

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.

Highlights

In the hard scattering processes involving hadrons, such as in the deep inelastic scattering (DIS) of leptons on hadrons, the experimentally measured cross sections are a combination of short- and long-distance physics
The inclusive DIS cross section can be factorized into a short-distance partonic hard part which is calculable order by order in perturbation theory and a long-distance hadronic part which can be represented by universal and nonperturbative distribution functions, called the parton distribution functions (PDFs), plus corrections suppressed by inverse power of large momentum transfer of the scattering
IV, we present the derivation of the tree-level perturbative kernel for an antisymmetric vector and axial-vector current combination, and show how one can factorize the associated hadronic matrix element to extract pion valence distribution in a lattice QCD calculation

Summary

Introduction

In the hard scattering processes involving hadrons, such as in the deep inelastic scattering (DIS) of leptons on hadrons, the experimentally measured cross sections are a combination of short- and long-distance physics. The inclusive DIS cross section can be factorized into a short-distance partonic hard part which is calculable order by order in perturbation theory and a long-distance hadronic part which can be represented by universal and nonperturbative distribution functions, called the parton distribution functions (PDFs), plus corrections suppressed by inverse power of large momentum transfer of the scattering. It is the QCD factorization theorem [1] which enables us to connect the dynamics of quarks and gluons to the physically measured hard scattering cross sections of identified hadrons.

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