Non-local Nucleon Matrix Elements in the Rest Frame

TL;DR

This paper investigates the UV renormalization effects on nucleon matrix elements in lattice QCD, demonstrating that NLO perturbative calculations accurately describe the $z_3$ dependence up to 0.6 fm, with residuals linked to nucleon structure.

Contribution

It provides a perturbative renormalization approach to analyze nucleon matrix elements in the rest frame, improving understanding of UV effects in lattice QCD calculations.

Findings

NLO perturbative calculations describe the matrix element logarithm within a few percent.

The $z_3$ dependence can be modeled by nucleon structure effects.

Accurate description up to 0.6 fm separations across multiple lattice spacings.

Abstract

Extracting parton structure from lattice quantum chromodynamics (QCD) calculations requires studying the coordinate scale $z_3$ dependence of the matrix elements of bilocal operators. The most significant contribution comes from the $z_3$ dependence induced by ultraviolet (UV) renormalization of the Wilson line. We demonstrate that the next-to-leading order perturbative calculations of the renormalization factor can describe, to a few percent accuracy, the logarithm of the lattice QCD rest frame matrix elements with separations up to distances of 0.6~fm on multiple lattice spacings. The residual discrepancies can be modeled by a leading effect from the structure of the nucleon.