Determining neutrino mass hierarchy by precision measurements in electron and muon neutrino disappearance experiments

Recently a new method for determining the neutrino mass hierarchy by comparing the effective values of the atmospheric Δm² measured in the electron neutrino disappearance channel, Δm²(ee), with the one measured in the muon neutrino disappearance channel, Δm²(μμ), was proposed. If Δm²(ee) is larger (smaller) than Δm²(μμ) the hierarchy is of the normal (inverted) type. We reexamine this proposition in the light of two very high precision measurements: Δm²(μμ) that may be accomplished by the phase II of the Tokai-to-Kamioka (T2K) experiment, for example, and Δm²(ee) that can be envisaged using the novel M\"ossbauer enhanced resonant νₑ absorption technique. Under optimistic assumptions for the systematic uncertainties of both measurements, we estimate the parameter region of (θ₁₃, δ) in which the mass hierarchy can be determined. If θ₁₃ is relatively large, sin²2θ₁₃0.05, and both of Δm²(ee) and Δm²(μμ) can be measured with the precision of ~0.5% it is possible to determine the neutrino mass hierarchy at $>95%$ CL for 0.3πδ1.7π for the current best fit values of all the other oscillation parameters.