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

• Received 27 July 2006

DOI:https://doi.org/10.1103/PhysRevD.74.053008