A comparison of the sensitivities of the parameters with atmospheric neutrinos for different analysis methods

In the atmospheric neutrino experiments the primary problems are the huge uncertainties of flux, very rapid fall of flux with increase of energy, the energy dependent wide resolutions of energy and zenith angle between true neutrinos and reconstructed neutrinos. These all in together make the choice of binning of the data for chi-square analysis complicated. The large iron calorimeter has the ability to measure the energy and the direction of the muon with high resolution. From the bending of the track in the magnetic field it can also distinguish its charge. We have analyzed the atmospheric neutrino oscillation generating events by Nuance and then considering the muons produced in the charge current interactions as the reconstructed neutrinos. This practically takes into account the major problem of wide resolutions. We have binned the data in three ways: i) in the grids of $\log E -\log L$ plane, ii) in the grids of $\log E -\cos\theta_{\rm zenith}$ plane, and iii) in the bins of $\log (L/E)$. We have performed a marginalized $\chi^2$ study over $\Delta m_{32}^2, ~\theta_{13}$ and $\theta_{23}$ for neutrinos and anti-neutrinos separately for each method and finally compared the results.