Three-Neutrino Oscillations of Atmospheric Neutrinos, θ13, Neutrino Mass Hierarchy and Iron Magnetized Detectors

We derive predictions for the Nadir angle (θn) dependence of the ratio Nμ−/Nμ+ of the rates of the μ− and μ+ multi-GeV events, and for the μ−−μ+ event rate asymmetry, Aμ−μ+ = [N(μ −)−N(μ+)]/[N(μ−)+N(μ+)], in iron-magnetized calorimeter detectors (MINOS, INO, etc.) in the case of 3-neutrino oscillations of the atmospheric νμ and ν̄μ, driven by one neutrino mass squared difference, |∆m31| ∼ (2.0−3.0)×10−3 eV2 ≫ ∆m21. The asymmetry Aμ−μ+ (the ratio Nμ−/Nμ+) is shown to be 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. It is also very sensitive to the type of neutrino mass spectrum which can be with normal (∆m31 > 0) or with inverted (∆m31 < 0) hierarchy. We find that for sin 2 θ23 >∼ 0.50, sin 2θ13 >∼ 0.06 and |∆m31| = (2−3)×10−3 eV2, the Earth matter effects produce a relative difference between the integrated asymmetries Āμ−μ+ and Ā 2ν μ−μ+ in the mantle (cos θn = 0.30−0.84) and core (cos θn = 0.84−1.0) bins, which is bigger in absolute value than approximately ∼ 15%, can reach the values of (30− 35)%, and thus can be sufficiently large to be observable. The sign of the indicated asymmetry difference is anticorrelated with the sign of ∆m31. An observation of the Earth matter effects in the Nadir angle distribution of the asymmetry Aμ−μ+ (ratio Nμ−/Nμ+) would clearly indicate that sin 2 2θ13 >∼ 0.06 and sin θ23 >∼ 0.50, and would lead to the determination of the sign of ∆m31. ∗Also at: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria.