Systematic Uncertainties from Gribov Copies in Lattice Calculation of Parton Distributions in the Coulomb gauge

TL;DR

This study assesses the impact of Gribov copies on Coulomb-gauge-fixed lattice QCD calculations of parton distributions, finding that their effect is negligible compared to statistical noise, thus simplifying future computations.

Contribution

It provides an empirical evaluation showing that Gribov copies do not significantly affect Coulomb gauge-fixed lattice calculations of parton distributions.

Findings

Gribov copies' effect is statistically insignificant.

Statistical errors decrease with more gauge configurations.

Gribov copies can be neglected in practical calculations.

Abstract

Recently, it has been proposed to compute parton distributions from boosted correlators fixed in the Coulomb gauge within the framework of Large-Momentum Effective Theory. This method does not involve Wilson lines and could greatly improve the efficiency and precision of lattice QCD calculations. However, there are concerns about whether the systematic uncertainties from Gribov copies, which correspond to the ambiguity in lattice gauge-fixing, are under control. This work gives an assessment of the Gribov copies' effect in the Coulomb-gauge-fixed quark correlators. We utilize different strategies for the Coulomb-gauge fixing, selecting two different groups of Gribov copies based on the lattice gauge configurations. We test the difference in the resulted spatial quark correlators in the vacuum and a pion state. Our findings indicate that the statistical errors of the matrix elements from both Gribov copies, regardless of the correlation range, decrease proportionally to the square root of the number of gauge configurations. The difference between the strategies does not show statistical significance compared to the gauge noise. This demonstrates that the effect of the Gribov copies can be neglected in the practical lattice calculation of the quark parton distributions.