Neutrino mass hierarchy, vacuum oscillations, and vanishing |Ue3| -: art. no. 113009

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 U-e3 element of the leptonic mixing matrix (parameterized by the unknown theta(13) mixing angle) be sufficiently large, and will utterly fail in the limit theta(13)-> 0. For this reason, we explore alternative oscillation approaches that would still succeed even if theta(13) vanishes. We identify several alternatives that require neither a nonzero vertical bar U-e3 vertical bar 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.