Neutrino Mass Hierarchy, Vacuum Oscillations, and Vanishing U_e3

Abstract

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 |U_e3| nor the presence of significant matter effects. 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.