Physical-Continuum Limit of the Nucleon Gluon Parton Distribution from Lattice QCD

We present the key results from the first study of the $x$-dependent nucleon gluon distribution from lattice QCD extrapolated to the physical-continuum limit. We use ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ) generated by the MILC Collaboration with clover fermions for the valence action on three different lattice spacings and three different pion masses. We took up to $O(10^6)$ measurements of two-point correlators, obtaining good signal at boost momenta up to 3~GeV. We extrapolated the reduced pseudo-ITD matrix elements to the physical-continuum limit before extracting $xg(x)/\langle x \rangle_g$. Then using the gluon momentum fraction $\langle x \rangle_g$ calculated on the same configurations, we determine the unpolarized nucleon gluon PDF $xg(x)$ and compare results with other lattice and selected global fits.