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Abstract
We have studied the mass hierarchy with atmospheric neutrinos considering the muon
energy and zenith angle of the event at the magnetized iron calorimeter detector.
For \(\chi^2\) analysis we have migrated the number of events from neutrino energy and
zenith angle bins to muon energy and zenith angle bins using the two-dimensional energy-angle
correlated resolution functions. The binning of data is made in two-dimensional grids
of \(\log_{10} E - L^{0.4}\) plane to get a better reflection of the oscillation pattern
in the \(\chi^2\) analysis. Then the \(\chi^2\) is marginalized considering all possible
systematic uncertainties of the atmospheric neutrino flux and cross section. The effects
of the ranges of oscillation parameters on the marginalization are also studied. The
lower limit of the range of \(\theta_{13}\) for marginalization is found to be very
crucial in determining the sensitivity of hierarchy for a given \(\theta_{13}\). Finally,
we show that one can discriminate atmospheric neutrino mass hierarchy at \(>\)90% C.L.
if the lower limit of \(\theta_{13} \ge 5^\circ\).