What would it take to determine the neutrino mass hierarchy if $\theta_{13}$ were too small?

Abstract

We discuss the experimental requirements for a mass hierarchy measurement for $\theta_{13}=0$ using muon neutrino disappearance. We find that a specially optimized neutrino factory at $L \simeq 6 \,000 \, \mathrm{km}$ could do this measurement using extreme luminosities. In particular, we do not require charge identification for this purpose. In order to measure the mass hierarchy for more adequate luminosities, we explore the capabilities of low energy narrow band off-axis beams, which have relatively more events at low energies. We find that, in this case, the energy resolution of the detector quickly becomes the limiting factor of the measurement, and significantly affects the baseline optimization for determining the mass hierarchy.