Measurement of the $\nu_e-$Nucleus Charged-Current Double-Differential Cross Section at $\left< E_{\nu} \right> = $ 2.4 GeV using NOvA

The inclusive electron neutrino charged-current cross section is measured in the NOvA near detector using $8.02\times10^{20}$ protons-on-target (POT) in the NuMI beam. The sample of GeV electron neutrino interactions is the largest analyzed to date and is limited by $\simeq$ 17\% systematic rather than the $\simeq$ 7.4\% statistical uncertainties. The double-differential cross section in final-state electron energy and angle is presented for the first time, together with the single-differential dependence on $Q^{2}$ (squared four-momentum transfer) and energy, in the range 1 GeV $ \leq E_{\nu} < $6 GeV. Detailed comparisons are made to the predictions of the GENIE, GiBUU, NEUT, and NuWro neutrino event generators. The data do not strongly favor a model over the others consistently across all three cross sections measured, though some models have especially good or poor agreement in the single differential cross section vs. $Q^{2}$.