Updated sensitivities for the discovery of the neutrino mass hierarchy and of CP-violation in the leptonic sector of a very-long baseline neutrino oscillation experiment at 2300 km from CERN

In this addendum to our Expression of Interest (CERN-SPSC-2012-021 (SPSC-EOI-007)),\nwe present an updated study of the sensitivity \nof the LBNO setup, and discuss the impact of \nsystematic errors and of the {\it a priori} knowledge of oscillation parameters. \nFollowing the realistic and incremental approach,\nthe initial phase of LBNO foresees an underground $\sim$20~kton\nfiducial mass double-phase liquid Argon TPC complemented by a magnetised muon detector\nat 2300~km from a conventional neutrino beam from the CERN SPS, monitored by \na magnetised near detector system. We update our results\npresented in the EOI, and show that this first realistic phase already provides \nconclusive and well-motivated physics opportunities.\nWe employ a Monte-Carlo technique simulating a very large number\nof toy experiments to estimate the confidence level of the MH and CPV measurements.\nWith the capability of reversing the horn focusing polarity, and\neven under pessimistic assumptions on systematic errors, a few years of running at\nthe CERN SPS suffice for\nLBNO alone to produce a direct and\nguaranteed discovery of MH ($>5\sigma$~C.L.) over the full phase space\nof oscillation parameters, \nand a unique sensitivity to CPV through the exploration of the \nfirst and second oscillation maxima.\nNeglecting any systematic error, LBNO in its first phase, has the power to reach\na CPV discovery level $> 5\sigma$'s C.L., the actual significance depending on how far from\nzero and $\pi$ the true value\nof $\delta_{CP}$ is.\nThe actually attainable CPV reach is sensitive to the prior knowledge of the oscillation parameters\nand to the achievable systematic errors on fluxes, cross-sections and detector-related effects. \nWith conservative assumptions on\nthe systematic errors and after\n$\sim$12~years of running at the CERN SPS,\na significance for CPV above $> 3\sigma$'s C.L. will be reached for $\sim25(40)$\% of the $\delta_{CP}$ \nvalues, under the expectation that $\sin^22\theta_{13}$ will be known from reactor experiments with a precision\nof $\pm10(2.5)$\%. Several sources of systematic effects need to be addressed, in order to reduce the overall error\nbalance and reach a discovery level. In particular, improvements in\nthe present knowledge of the neutrino interaction differential cross-sections could increase \nthe expected CPV discovery reach. Alternatively, a second phase of LBNO with\nan increased exposure with far more detector mass and beam power, aimed at\nreducing the statistical error around the 2nd oscillation maximum, \nwould allow to reach a $> 5\sigma$ CPV discovery level over\na wide range of $\delta_{CP}$ values, even under the present conservative assumptions\non systematic errors, thanks to the increased dependence on $\delta_{CP}$ at the 2nd maximum.