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The determination of the missing $U_{e3}$ element (magnitude and phase) ofthe PMNS neutrino mixing matrix is possible via the detection of $\numu\to\nue$oscillations at a baseline $L$ and energy $E$ given by the atmosphericobservations, corresponding to a mass squared difference $E/L \sim \Deltam^2\simeq 2.5\times 10^{-3} eV^2$. While the current optimization of the CNGSbeam provides limited sensitivity to this reaction, we discuss in this documentthe physics potential of an intensity upgraded and energy re-optimized CNGSneutrino beam coupled to an off-axis detector. We show that improvements insensitivity to $\theta_{13}$ compared to that of T2K and NoVA are possible witha next generation large liquid Argon TPC detector located at an off-axisposition (position rather distant from LNGS, possibly at shallow depth). Wealso address the possibility to discover CP-violation and disentangle the masshierarchy via matter effects. The considered intensity enhancement of the CERNSPS has strong synergies with the upgrade/replacement of the elements of itsinjector chain (Linac, PSB, PS) and the refurbishing of its own elements,envisioned for an optimal and/or upgraded LHC luminosity programme.Comment: 37 pages, 20 figure

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