Long-baseline (LBL) neutrino oscillation experiments search for Charge-Parity (CP) violation in the leptonic sector by precisely measuring the $\nu_\mu\to\nu_e$ and $\overline{\nu}_\mu\to\overline{\nu}_e$ appearance probabilities.
One of the dominant systematic uncertainties on the measurements of CP violation, comes from our modeling of the $\nu_e/\overline{\nu}_e$ cross-section ratio, which is subject to a range of uncertainties related to poorly-constrained nuclear physics processes.
Whilst tight constraints on the $\nu_\mu/\overline{\nu}_\mu$ cross-section can be achieved using LBL experiment's near detector data, the lepton mass differences mean that the extrapolation to the $\nu_e/\overline{\nu}_e$ is not trivial.

Currently running LBL experiments reach a sensitivity to exclude the CP conserving hypothesis of about three standard deviations for a relatively large range of $\delta_{CP}$ values, hence a more accurate evaluation of the $\nu_e/\overline{\nu}_e$ related uncertainties becomes increasingly crucial.
Following up on work by Nikolakopoulos et al.~\cite{Nik}, we present the analysis from \cite{UncertaintiesOTDi}, quantifying the potential for miss-modelling of the $\nu_\mu/\nu_e, \ \overline{\nu}_\mu / \overline{\nu}_e$ and $\nu_e/\overline{\nu}_e$ cross sections due to nuclear effects as a model spread in the full kinematic phase space for CCQE interactions.
This impact is then propagated to simulated experimental configurations based on the Hyper-K and ESS$\nu$SB experiments.

Significant differences between the theoretical models are found, which largely lie in regions of phase space that contribute only a small portion of the flux integrated cross sections.
Overall, a systematic uncertainty on the oscillated flux-averaged $\nu_e/\overline{\nu}_e$ cross section of $\sim 2$\% and $\sim4$\% is found for the simulated Hyper-K and ESS$\nu$SB experiments respectively.