Toward the First Gluon Parton Distribution from the LaMET

TL;DR

This paper reports progress in calculating the first unpolarized gluon quasi-PDF from lattice QCD, comparing different operators, gauge techniques, and pion masses to identify the best approach for future gluon PDF studies.

Contribution

It introduces the first gluon quasi-PDF calculation using LaMET, compares multiple operators and techniques, and explores gauge fixing to improve signal quality.

Findings

Identifies the optimal operator for gluon quasi-PDF extraction.

Demonstrates the need for higher hadron boost momentum.

Shows Coulomb gauge fixing can improve signal quality.

Abstract

We present progress towards the first unpolarized gluon quasi-PDF from lattice QCD using high-statistics measurement with $a \approx 0.12$ fm and two valence pion masses $M_\pi \approx 310$ and $690$ MeV generated on $2+1+1$-flavors of HISQ ensemble by the MILC collaboration. In this study, we consider two different gluon operators, for which the hybrid-ratio renormalization matching kernels have been recently derived, and a third operator that has been used in prior pseudo-PDF studies of the gluon PDFs. We compare matrix elements for each operators for both nucleon and pseudo-scalar mesons, both pion masses, and two gauge-smearing techniques. Focusing on the more phenomenologically studied nucleon gluon PDF, we compare the ratio and hybrid-ratio renormalized matrix elements at both pion masses and both smearings to those reconstructed from the nucleon gluon PDF from the CT18 global analysis. We identify the best choice of operator to study the gluon PDF through LaMET and present the first gluon quasi-PDF under some caveats. Additionally, we explore the recent idea of Coulomb gauge fixing to improve signal at large Wilson line displacement and found it could be a major help in improving the signal of gluon matrix elements given the perturbative calculation to confirm our results. This work helps identify the best operator for studying the gluon quasi-PDF, shows higher hadron boost momentum is needed to implement hybrid-ratio renormalization reliably, and suggests the need to study more diverse set of operators with their corresponding perturbative calculations for hybrid-ratio renormalization to further gluon quasi-PDF study.