Isovector parton distribution functions of the proton on a superfine lattice

We study isovector unpolarized and helicity parton distribution functions (PDF) of proton within the framework of Large Momentum Effective Theory. We use a gauge ensemble, generated by the MILC collaboration, with a superfine lattice spacing of $0.042$ fm and a pion mass of $310$ MeV, enabling us to simultaneously reach sub-fermi spatial separations and larger nucleon momenta. We compare the spatial dependence of quasi-PDF matrix elements in different renormalization schemes with the corresponding results of the global fits, obtained using 1-loop perturbative matching. We present determinations of first four moments of the unpolarized and helicity PDFs of proton from the Ioffe-time dependence of the isovector matrix elements, obtained employing a ratio-based renormalization scheme.