Atmospheric neutrino oscillations, θ13 and neutrino mass hierarchy Original Research Article

We derive predictions for the Nadir angle (θn) dependence of the ratio Nμ/Ne of the rates of the μ-like and e-like multi-GeV events measured in water-Čerenkov detectors in the case of 3-neutrino oscillations of the atmospheric νe (ν̄e) and νμ (ν̄μ), driven by one neutrino mass squared difference, |Δm231|∼(2.5–3.0)×10−3 eV2⪢Δm221. This ratio is 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 CHOOZ and Palo Verde experiments and that responsible for the dominant atmospheric νμ→ντ (ν̄μ→ν̄τ) oscillations. It is also sensitive to the type of neutrino mass spectrum which can be with normal (Δm231>0) or with inverted (Δm231<0) hierarchy. We show that for sin2θ13≳0.01, sin2θ23≳0.5 and at cosθn≳0.4, the Earth matter effects modify substantially the θn-dependence of the ratio Nμ/Ne and in a way which cannot be reproduced with sin2θ13=0 and a different value of sin2θ23. For normal hierarchy the effects can be as large as ∼25% for cosθn∼(0.5–0.8), can reach ∼35% in the Earth core bin cosθn∼(0.84–1.0), and might be observable. They are typically by ∼10% smaller in the inverted hierarchy case. An observation of the Earth matter effects in the Nadir angle distribution of the ratio Nμ/Ne would clearly indicate that sin2θ13≳0.01 and sin2θ23≳0.50.