Isovector parton distribution functions of the proton on a superfine lattice

TL;DR

This paper computes isovector proton PDFs using Large Momentum Effective Theory on a superfine lattice, comparing matrix elements across schemes and extracting moments from Ioffe-time data.

Contribution

It introduces a high-precision lattice calculation of isovector PDFs at superfine lattice spacing, employing a ratio-based renormalization scheme and analyzing spatial dependence with perturbative matching.

Findings

Agreement with global fits for spatial dependence of matrix elements

First four moments of PDFs determined from Ioffe-time dependence

Validation of the approach at superfine lattice spacing

Abstract

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 1-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.