Type: Article
Publication Date: 2006-09-20
Citations: 39
DOI: https://doi.org/10.1103/physrevd.74.053008
Recently a new method for determining the neutrino mass hierarchy by comparing the effective values of the atmospheric $\ensuremath{\Delta}{m}^{2}$ measured in the electron neutrino disappearance channel, $\ensuremath{\Delta}{m}^{2}(\mathrm{ee})$, with the one measured in the muon neutrino disappearance channel, $\ensuremath{\Delta}{m}^{2}(\ensuremath{\mu}\ensuremath{\mu})$, was proposed. If $\ensuremath{\Delta}{m}^{2}(\mathrm{ee})$ is larger (smaller) than $\ensuremath{\Delta}{m}^{2}(\ensuremath{\mu}\ensuremath{\mu})$ the hierarchy is of the normal (inverted) type. We reexamine this proposition in the light of two very high precision measurements: $\ensuremath{\Delta}{m}^{2}(\ensuremath{\mu}\ensuremath{\mu})$ that may be accomplished by the phase II of the Tokai-to-Kamioka (T2K) experiment, for example, and $\ensuremath{\Delta}{m}^{2}(\mathrm{ee})$ that can be envisaged using the novel M\"ossbauer enhanced resonant ${\overline{\ensuremath{\nu}}}_{e}$ absorption technique. Under optimistic assumptions for the systematic uncertainties of both measurements, we estimate the parameter region of (${\ensuremath{\theta}}_{13}$, $\ensuremath{\delta}$) in which the mass hierarchy can be determined. If ${\ensuremath{\theta}}_{13}$ is relatively large, ${sin}^{2}2{\ensuremath{\theta}}_{13}\ensuremath{\gtrsim}0.05$, and both of $\ensuremath{\Delta}{m}^{2}(\mathrm{ee})$ and $\ensuremath{\Delta}{m}^{2}(\ensuremath{\mu}\ensuremath{\mu})$ can be measured with the precision of $\ensuremath{\sim}0.5%$ it is possible to determine the neutrino mass hierarchy at $>95%$ CL for $0.3\ensuremath{\pi}\ensuremath{\lesssim}\ensuremath{\delta}\ensuremath{\lesssim}1.7\ensuremath{\pi}$ for the current best fit values of all the other oscillation parameters.