Three-neutrino oscillations of atmospheric neutrinos, [formula omitted], neutrino mass hierarchy and iron magnetized detectors

Abstract

We derive predictions for the Nadir angle ( θ n ) dependence of the ratio N μ − / N μ + of the rates of the μ − and μ + multi-GeV events, and for the μ − – μ + event rate asymmetry, A μ − 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 ν μ and ν ¯ μ , driven by one neutrino mass squared difference, | Δ m 31 2 | ∼ ( 2.0 – 3.0 ) × 10 −3 eV 2 ≫ Δ m 21 2 . The asymmetry A μ − μ + (the ratio N μ − / N μ + ) is shown to be 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 the CHOOZ and Palo Verde experiments and that responsible for the dominant atmospheric ν μ → ν τ ( ν ¯ μ → ν ¯ τ ) oscillations. It is also very sensitive to the type of neutrino mass spectrum which can be with normal ( Δ m 31 2 > 0 ) or with inverted ( Δ m 31 2 < 0 ) hierarchy. We find that for sin 2 θ 23 ≳ 0.50 , sin 2 2 θ 13 ≳ 0.06 and | Δ m 31 2 | = ( 2 – 3 ) × 10 −3 eV 2 , the Earth matter effects produce a relative difference between the integrated asymmetries A ¯ μ − μ + and A ¯ μ − μ + 2 ν in the mantle ( cos θ n = 0.30 – 0.84 ) and core ( cos θ n = 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 Δ m 31 2 . An observation of the Earth matter effects in the Nadir angle distribution of the asymmetry A μ − μ + (ratio N μ − / N μ + ) would clearly indicate that sin 2 2 θ 13 ≳ 0.06 and sin 2 θ 23 ≳ 0.50 , and would lead to the determination of the sign of Δ m 31 2 .