Gluon Parton Distribution of the Nucleon from 2+1+1-Flavor Lattice QCD in the Physical-Continuum Limit

We present the first physical-continuum limit $x$-dependent nucleon gluon distribution from lattice QCD using the pseudo-PDF approach, on lattice ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. We use clover fermions for the valence action on three lattice spacings $a\approx 0.9$, 0.12 and 0.15~fm and three pion masses $M_{\pi }\approx 220$, 310 and 690~MeV, with nucleon two-point measurements numbering up to $O({10}^6)$ and nucleon boost momenta up to 3~GeV. We study the lattice-spacing and pion-mass dependence of the reduced pseudo-ITD matrix elements obtained from the lattice calculation, then extrapolate them to the continuum-physical limit before extracting $xg(x)\mathrm{/}⟨x{⟩}_g$. We use the gluon momentum fraction $⟨x{⟩}_g$ calculated from the same ensembles to determine the nucleon gluon unpolarized PDF $xg(x)$ for the first time entirely through lattice-QCD simulation. We compare our results with previous single-ensemble lattice calculations, as well as selected global fits.