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

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.