We numerically study the effects of gauge smearing on the nucleon and meson gluon-PDF matrix elements, considering hypercubic smearing, stout smearing, and Wilson flow.
The lattice calculations are carried out with $N_\text{f} = 2 + 1 + 1$ highly improved staggered quarks in ensembles generated by the MILC Collaboration.
We use clover fermions for the valence action on one lattice spacing $a \approx 0.12$ fm and two pion masses $M_\pi \approx 310$ and $690$~MeV.
We probe the effects of gluon matrix elements with different smearing methods at various steps. We compute and compare the resulting nucleon and meson gluon PDFs using the pseudo-PDF method when using different smearing methods.