Towards Systematic Control of the Nucleon Gluon PDF with the Pseudo-PDF Method

We present updated lattice quantum chromodynamics (QCD) results for the unpolarized nucleon gluon parton distribution function (PDF) using the pseudo-PDF methodology. The calculation is performed at valence pion masses $M_π\approx 310$ and $690$ MeV on an $a \approx 0.06$ fm ensemble with $2+1+1$ flavors of highly improved staggered quarks (HISQ) generated by the MILC Collaboration. This lattice spacing is finer than those used in previous gluon pseudo-PDF studies, providing access to multiple short-distance separations and nucleon boost momenta as high as $4.4$ GeV. To control excited-state contamination and reduce model dependence, we employ the recently developed Lanczos method, finding good agreement with our previous two-state fit approach. Higher-twist contributions and discretization effects are accounted for through explicit parameterizations in fits to the renormalized short-distance matrix elements. Together, these advances represent important steps toward systematically controlled, high-precision extractions of the gluon PDF. The resulting PDFs exhibit no statistically significant dependence on the valence pion mass and indicate a strongly suppressed gluon distribution at large $x$, consistent with a subset of phenomenological PDF extractions. These results demonstrate progress toward providing systematically controlled lattice-QCD constraints for future global PDF analyses.