Nucleon Gluon Distribution Function from 2+1+1-Flavor Lattice QCD

The parton distribution functions (PDFs) provide process-independent information about the quarks and gluons inside hadrons. Although the gluon PDF can be obtained from a global fit to experimental data, it is not constrained well in the large-$x$ region. Theoretical gluon-PDF studies are much fewer than those of the quark PDFs. In this work, we present the first lattice-QCD results that access the $x$-dependence of the gluon unpolarized PDF of the nucleon. The lattice calculation is carried out with nucleon momenta up to 2.16 GeV, lattice spacing $a\approx0.12$ fm, with valence pion masses of 310 and 690 MeV. We use reduced Ioffe-time distributions to cancel the renormalization and implement a one-loop perturbative pseudo-PDF matching to the lightcone distribution. Our matrix element results in coordinate space are consistent with those obtained from the global PDF fits of CT18 NNLO and NNPDF3.1 NNLO. Our fitted gluon PDF extrapolated to the physical pion mass gives consistent results in the $x > 0.3$ region.