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

TL;DR

This study uses lattice QCD with large momentum effective theory to compute the unpolarized isovector quark PDF, carefully analyzing renormalization and matching procedures, and finds results consistent with phenomenological data.

Contribution

It provides a systematic lattice QCD analysis of the isovector quark PDF including nonperturbative renormalization and one-loop matching, addressing key systematic uncertainties.

Findings

Results agree with recent phenomenological PDFs

Controlled excited state contamination through multiple source-sink separations

Detailed analysis of renormalization and matching systematic errors

Abstract

We present a detailed Lattice QCD study of the unpolarized isovector quark Parton Distribution Function (PDF) using 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 $M_\pi=356$ MeV and $P_z \in \{1.8,2.3\}$ 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 $\bar{\rm MS}$ 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 lightcone PDF are in reasonable agreement with the latest phenomenological analysis.