Neutrino mass hierarchy, vacuum oscillations, and vanishing |Ue3|

Is the relatively isolated member of the neutrino mass spectrum heavier or lighter than the two closely-spaced members? This question-the character of the neutrino mass hierarchy-is of great theoretical interest. All previously identified experiments for addressing it via neutrino oscillations require that the currently unknown size of the Ue3 element of the leptonic mixing matrix (parameterized by the unknown θ13 mixing angle) be sufficiently large, and will utterly fail in the limit θ13→0. For this reason, we explore alternative oscillation approaches that would still succeed even if θ13 vanishes. We identify several alternatives that require neither a nonzero |Ue3| nor the presence of significant matter effects (even if the latter are unavoidable in the case of long-baseline, Earth-based experiments). All include multiple percent-level neutrino oscillation measurements, usually involving muon-neutrino (or antineutrino) disappearance and very long baselines. We comment on the degree of promise that these alternative approaches show.