Neutrino oscillation physics at an upgraded CNGS with large next generation liquid Argon TPC detectors

The determination of the missing $U_{e3}$ element (magnitude and phase) of the PMNS neutrino mixing matrix is possible via the detection of $\numu\to\nue$ oscillations at a baseline $L$ and energy $E$ given by the atmospheric observations, corresponding to a mass squared difference $E/L \sim \Delta m^2\simeq 2.5\times 10^{-3} eV^2$. While the current optimization of the CNGS beam provides limited sensitivity to this reaction, we discuss in this document the physics potential of an intensity upgraded and energy re-optimized CNGS neutrino beam coupled to an off-axis detector. We show that improvements in sensitivity to $\theta_{13}$ compared to that of T2K and NoVA are possible with a next generation large liquid Argon TPC detector located at an off-axis position (position rather distant from LNGS, possibly at shallow depth). We also address the possibility to discover CP-violation and disentangle the mass hierarchy via matter effects. The considered intensity enhancement of the CERN SPS has strong synergies with the upgrade/replacement of the elements of its injector chain (Linac, PSB, PS) and the refurbishing of its own elements, envisioned for an optimal and/or upgraded LHC luminosity programme.