Systematic improvement of $x$-dependent unpolarized nucleon generalized parton distributions in lattice-QCD calculation

We present a first study of the effects of renormalization-group resummation (RGR) and leading-renormalon resummation (LRR) on the systematic errors of the unpolarized isovector nucleon generalized parton distribution in the framework of large-momentum effective theory. This work is done using lattice gauge ensembles generated by the MILC Collaboration, consisting of $2+1+1$ flavors of highly improved staggered quarks with a physical pion mass at lattice spacing $a\approx 0.09\mathrm{fm}$ and a box width $L\approx 5.76\mathrm{fm}$. We present results for the nucleon $H$ and $E$ generalized parton distributions (GPDs) with average boost momentum $P_z\approx 2\mathrm{GeV}$ at momentum transfers $Q^2=[0,0.97]{\mathrm{GeV}}^2$ at skewness $\xi =0$ as well as $Q^2\in 0.23{\mathrm{GeV}}^2$ at $\xi =0.1$, renormalized in the modified minimal subtraction ($\overline{\mathrm{MS}}$) scheme at scale $\mu =2.0\mathrm{GeV}$, with two- and one-loop matching, respectively. We demonstrate that the simultaneous application of RGR and LRR significantly reduces the systematic errors in renormalized matrix elements and distributions for both the zero and nonzero skewness GPDs, and that it is necessary to include both RGR and LRR at higher orders in the matching and renormalization processes.