Unpolarized and helicity generalized parton distributions of the proton within lattice QCD

TL;DR

This paper presents the first lattice QCD calculation of the x-dependence of proton generalized parton distributions, providing new insights into proton structure through non-local operator matrix elements at various momenta.

Contribution

It introduces a novel lattice QCD approach to compute the x-dependent GPDs of the proton, including unpolarized and helicity distributions, at multiple momenta and momentum transfers.

Findings

First lattice QCD results for x-dependent proton GPDs.

Results obtained at multiple proton momenta and momentum transfers.

GPDs matched to light-cone distributions in the MS scheme at 2 GeV.

Abstract

We present the first calculation of the $x$-dependence of the proton generalized parton distributions (GPDs) within lattice QCD. Results are obtained for the isovector unpolarized and helicity GPDs. We compute the appropriate matrix elements of fast-moving protons coupled to non-local operators containing a Wilson line. We present results for proton momenta $0.83,\,1.25,\,1.67$ GeV, and momentum transfer squared $0.69,\,1.38$ GeV$^2$. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate mass light, a strange and a charm quark of maximally twisted mass fermions with a clover term. The lattice results are matched to the light-cone GPDs using one-loop perturbation theory within the framework of large momentum effective theory. The final GPDs are given in the $\overline{\rm MS}$ scheme at a scale of 2 GeV.