Mass hierarchy determination via future atmospheric neutrino detectors

We study the problem of determination of the sign of Δm₃₁², or the neutrino mass hierarchy, through observations of atmospheric neutrinos in future detectors. We consider two proposed detector types: (a) Megaton sized water C {} {}{}erenkov detectors, which can measure the event rates of ν_μ+ν_μ and νₑ+νₑ and (b) 100 kton sized magnetized iron detectors, which can measure the event rates of ν_μ and ν_μ. For energies and path lengths relevant to atmospheric neutrinos, these rates obtain significant matter contributions from P_μe, P_μμ and Pₑₑ, leading to an appreciable sensitivity to the hierarchy. We do a binned χ² analysis of simulated data in these two types of detectors which includes the effect of smearing in neutrino energy and direction and incorporates detector efficiencies and relevant statistical, theoretical and systematic errors. We also marginalize the χ² over the allowed ranges of neutrino parameters in order to accurately account for their uncertainties. Finally, we compare the performance of both types of detectors vis a vis the hierarchy determination.