Improving the robustness of the $\delta_{CP}$ determination with $\nu$SCOPE

The determination of leptonic CP violation is a primary goal of future long-baseline neutrino experiments such as DUNE and T2HK. The extraction of $\delta_{\mathrm{CP}}$ relies on the near-to-far extrapolation and on the assumed knowledge of the cross-section ratios $\sigma_{\nu_e}/\sigma_{\nu_\mu}$ and $\sigma_{\bar{\nu}_e}/\sigma_{\bar{\nu}_\mu}$, which are typically inferred under theoretical assumptions such as lepton universality and depend on nuclear modeling. In this work, we quantify how much of the sensitivity of DUNE and T2HK arises from these assumptions by performing a model-agnostic, data-driven estimation of systematic uncertainties in $\nu_e$ and $\bar{\nu}_e$ cross sections. We find that adopting such an agnostic approach can substantially degrade the CP-violation sensitivity, reducing it by nearly $3\sigma$ at maximal CP violation for DUNE, and $4\sigma$ for T2HK. We then assess the impact of the proposed $\nu$SCOPE experiment, which, through a combination of neutrino tagging and the Narrow-Band Off-Axis technique, can provide percent-level measurements of $\sigma_{\nu_\mu}$ and $\sigma_{\bar{\nu}_\mu}$ and constrain the ratio $\sigma_{\nu_e}/\sigma_{\nu_\mu}$ at the $\sim 2\%$ level. We show that including prospective $\nu$SCOPE measurements largely restores the lost sensitivity, highlighting that precise external cross-section measurements may be essential for a fully robust determination of $\delta_{\mathrm{CP}}$ and for breaking its degeneracy with nuclear mis-modeling or possible new physics affecting neutrino detection.