Gluon distribution functions in the nucleon from lattice QCD

We report on our calculation of the unpolarized and polarized gluon parton distribution functions (PDFs) in the nucleon using short-distance QCD factorization of lattice QCD matrix elements . The computation is performed on a $32^3 \times 64$ isotropic lattice with a pion mass of 360 MeV and lattice spacing, a = 0.094 fm using 2+1 flavor of Clover-Wilson fermion. In order to reduce the statistical fluctuations, the gluonic operators are smeared using gradient flow and the renormalized matrix elements are extracted by taking the small flow-time limit. Finally the lattice QCD matrix elements are factorized to the $\overline{MS}$ scheme PDFs in the light-cone $z^2\to 0$ limit, using next-to-leading order perturbative matching formula.