Mass hierarchy, 2-3 mixing and CP-phase with Huge Atmospheric Neutrino Detectors

We explore the physics potential of multi-megaton scale ice or water Cherenkov detectors with low ($\sim 1$ GeV) threshold. Using some proposed characteristics of the PINGU detector setup we compute the distributions of events versus neutrino energy $E_\nu$ and zenith angle $\theta_z$, and study their dependence on yet unknown neutrino parameters. The $(E_\nu - \theta_z)$ regions are identified where the distributions have the highest sensitivity to the neutrino mass hierarchy, to the deviation of the 2-3 mixing from the maximal one and to the CP-phase. We evaluate significance of the measurements of the neutrino parameters and explore dependence of this significance on the accuracy of reconstruction of the neutrino energy and direction. The effect of degeneracy of the parameters on the sensitivities is also discussed. We estimate the characteristics of future detectors (energy and angle resolution, volume, etc.) required for establishing the neutrino mass hierarchy with high confidence level. We find that the hierarchy can be identified at $3\sigma$ -- $10\sigma$ level (depending on the reconstruction accuracies) after 5 years of PINGU operation.