$\nu_\mu$ disappearance at the SPL, T2K-I, NO$\nu$A and the Neutrino Factory

Abstract

We study the measurement of the atmospheric neutrino oscillation parameters, $\theta_{23}$ and $\Delta m^2_{23}$, at the $\nu_\mu$ disappearance channel at three conventional beam facilities, the SPL, T2K-phase I and NO$\nu$A. These two parameters have been shown to be of crucial importance in the measurement of two of the unknowns of the PMNS mixing matrix, $\theta_{13}$ and the leptonic CP-violating phase $\delta$. In our analyis, the effect of the two discrete ambiguities, ${\rm sign}(\Delta m^2_{23})$ and ${\rm sign}(\tan 2 \theta_{23})$, is explicitly taken into account. We analyse also the $\nu_\mu$ disappearance channel at the Neutrino Factory, and combine it with the ``golden'' $\nu_e \to \nu_\mu$ and ``silver'' $\nu_e \to \nu_\tau$ appearance channels to study its impact on the measurement of $\theta_{13}$ and $\delta$. Eventually, we present the sensitivity of the four facilities to different observables: $\theta_{13}$, $\delta$, maximal $\theta_{23}$, the sign of the atmospheric mass difference, $s_{atm}$, and the $\theta_{23}$-octant, $s_{oct}$.