Leading Power Accuracy in Lattice Calculations of Parton Distributions

TL;DR

This paper addresses the dominant power correction in lattice-QCD calculations of parton distribution functions and proposes a method to eliminate this uncertainty, significantly improving the accuracy of the matching process.

Contribution

It introduces a consistent mass renormalization scheme aligned with infrared renormalon resummation to reduce leading power correction uncertainties in lattice PDFs.

Findings

Improved matching accuracy by a factor of 3 to 5 at P^z = 1.9 GeV.

Reduction of leading power correction impact in lattice PDF calculations.

Enhanced reliability of lattice QCD results for parton distributions.

Abstract

In lattice-QCD calculations of parton distribution functions (PDFs) via large-momentum effective theory, the leading power (twist-three) correction appears as ${\cal O}(\Lambda_{\rm QCD}/P^z)$ due to the linear-divergent self-energy of Wilson line in quasi-PDF operators. For lattice data with hadron momentum $P^z$ of a few GeV, this correction is dominant in matching, as large as 30\% or more. We show how to eliminate this uncertainty through choosing the mass renormalization parameter consistently with the resummation scheme of the infrared-renormalon series in perturbative matching coefficients. An example on the lattice pion PDF data at $P^z = 1.9$ GeV shows an improvement of matching accuracy by a factor of more than $3\sim 5$ in the expansion region $x= 0.2\sim 0.5$.