Isovector parton distribution functions of the proton on a superfine lattice

We study isovector unpolarized and helicity parton distribution functions (PDF) of the 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 one-loop perturbative matching. We present determinations of the first four moments of the unpolarized and helicity PDFs of proton from the Ioffe-time dependence of the isovector matrix elements, obtained by employing a ratio-based renormalization scheme.