Unpolarized isovector quark distribution function from lattice QCD: A systematic analysis of renormalization and matching

Abstract

We present a detailed lattice QCD study of the unpolarized isovector quark parton distribution function (PDF) using a large-momentum effective theory framework. We choose a quasi-PDF defined by a spatial correlator which is free from mixing with other operators of the same dimension. In the lattice simulation, we use a Gaussian-momentum-smeared source at ${M}_{\ensuremath{\pi}}=356\text{ }\text{ }\mathrm{MeV}$ and ${P}_{z}\ensuremath{\in}{1.8,2.3}\text{ }\text{ }\mathrm{GeV}$. To control the systematics associated with the excited states, we explore five different source-sink separations. The nonperturbative renormalization is conducted in a regularization-independent momentum subtraction scheme, and the matching between the renormalized quasi-PDF and $\overline{\mathrm{MS}}$ PDF is calculated based on perturbative QCD up to one-loop order. Systematic errors due to renormalization and perturbative matching are also analyzed in detail. Our results for light-cone PDF are in reasonable agreement with the latest phenomenological analysis.