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 ν¯μ, driven by one neutrino mass squared difference, |Δm312|∼(2.0-3.0)×10−3 eV2≫Δm212. 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 sin2θ13 and sin2θ23, 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 (ν¯μ→ν¯τ) oscillations. It is also very sensitive to the type of neutrino mass spectrum which can be with normal (Δm312>0) or with inverted (Δm312<0) hierarchy. We find that for sin2θ23≳0.50, sin22θ13≳0.06 and |Δm312|=(2-3)×10−3 eV2, the Earth matter effects produce a relative difference between the integrated asymmetriesA¯μ−μ+ and A¯μ−μ+2ν in the mantle (cosθn=0.30-0.84) and core (cosθn=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 Δm312. An observation of the Earth matter effects in the Nadir angle distribution of the asymmetry Aμ−μ+ (ratio Nμ−/Nμ+) would clearly indicate that sin22θ13≳0.06 and sin2θ23≳0.50, and would lead to the determination of the sign of Δm312.