On the Atmospheric Neutrino Oscillations, θ13 and Neutrino Mass Hierarchy

We give predictions for the up-down asymmetry in the Nadir angle dependence of the ratio Nμ/Ne of the rates of the μ−like and e−like multi-GeV events measured in water-Čerenkov detectors (Super-Kamiokande, etc.) in the case of 3-neutrino oscillations of the atmospheric νe (ν̄e) and νμ (ν̄μ), driven by one neutrino mass squared difference, |∆matm | ≡ |∆m 2 31| ∼ (2.0 − 3.0) × 10 −3 eV2 ≫ ∆m21 ≡ ∆m 2 ⊙ . This ratio is particularly sensitive to the Earth matter effects in the atmospheric neutrino oscillations, and thus to the values of sin θ13 and sin 2 θ23, θ13 and θ23 being the neutrino mixing angle limited by the CHOOZ and Palo Verde experiments and that responsible for the dominant atmospheric νμ → ντ (ν̄μ → ν̄τ ) oscillations, respectively. It is also sensitive to the type of neutrino mass spectrum which can be with normal (∆matm > 0) or with inverted (∆m 2 atm < 0) hierarchy. Based on the invited talk by S. T. Petcov at the NOON2004 International Workshop, February 11 15, 2004, Tokyo, Japan (to be published in the Proceedings of the Workshop). Also at: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria.