Atmospheric neutrino oscillations, θ13 and neutrino mass hierarchy

Abstract

We derive predictions for the Nadir angle ( θ n ) dependence of the ratio N μ / N e 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 ν e ( ν ̄ e ) and ν μ ( ν ̄ μ ), driven by one neutrino mass squared difference, |Δ m 2 31|∼(2.5–3.0)×10 −3 eV 2⪢Δ m 2 21. This ratio is particularly sensitive to the Earth matter effects in the atmospheric neutrino oscillations, and thus to the values of sin 2 θ 13 and sin 2 θ 23, θ 13 and θ 23 being the neutrino mixing angle limited by CHOOZ and Palo Verde experiments and that responsible for the dominant atmospheric ν μ → ν τ ( ν ̄ μ→ ν ̄ τ ) oscillations. It is also sensitive to the type of neutrino mass spectrum which can be with normal (Δ m 2 31>0) or with inverted (Δ m 2 31<0) hierarchy. We show that for sin 2 θ 13≳0.01, sin 2 θ 23≳0.5 and at cos θ n ≳0.4, the Earth matter effects modify substantially the θ n -dependence of the ratio N μ / N e and in a way which cannot be reproduced with sin 2 θ 13=0 and a different value of sin 2 θ 23. For normal hierarchy the effects can be as large as ∼25% for cos θ n ∼(0.5–0.8), can reach ∼35% in the Earth core bin cos θ n ∼(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 N μ / N e would clearly indicate that sin 2 θ 13≳0.01 and sin 2 θ 23≳0.50.