We show that by combining high precision measurements of the atmospheric δm² in both the electron and muon neutrino (or antineutrino) disappearance channels one can determine the neutrino mass hierarchy. The required precision is a very challenging fraction of one per cent for both measurements. At even higher precision, sensitivity to the cosine of the $CP$ violating phase is also possible. This method for determining the mass hierarchy of the neutrino sector does not depend on matter effects.
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Nunokawa et al. (2005) studied this question.
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