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, |∆m 2 31 | ∼ (2.5 − 3.0) × 10 −3 eV 2 ≫ ∆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 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 sensitive to the type of neutrino mass spectrum which can be with normal (∆m 2 31 > 0) or with inverted (∆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.

Three-neutrino oscillations of atmospheric neutrinos,θ13, neutrino mass hierarchy and iron magnetized detectors

“…It is a natural continuation of our similar study for water-Čerenkov detectors [46]. In the experiments with muon charge identification it will be possible to distinguish between the ν µ andν µ induced events.…”

“…Here P 2ν ≡ P 2ν (∆m 2 31 , θ 13 ; E, θ n ) is the probability of 2-neutrino ν e → ν ′ τ oscillations in the Earth, where ν ′ τ = s 23 ν µ + c 23 ν τ [55], and κ and A 2ν (ν τ → ν τ ) ≡ A 2ν are known phase and 2-neutrino transition probability amplitude [29,30,46].…”

“…This difference can be relatively large and observable in the samples of the multi-GeV µ ± events (E µ ∼ (2 − 10) GeV), in which the muons are produced by atmospheric neutrinos with relatively large path length in the Earth, i.e., by neutrinos crossing deeply the Earth mantle [32,33] or the mantle and the core [29,50,51,52]. These are the neutrinos for which [46] cos θ n > ∼ (0.3 − 0.4), θ n being the Nadir angle characterizing the (atmospheric) neutrino trajectory in the Earth.…”

“…[52,46], which contain also a rather complete list of references to earlier work on the subject). A rather detailed analysis for the MONOLITH detector has been performed in ref.…”

“…In ref. [46], in particular, the magnitude of the Earth matter effects in the Nadir angle distribution of the ratio of the multi-GeV µ−like and e−like events, measured in water-Čerenkov detectors, N µ /N e , has been investigated. This Nadir angle distribution is the observable most sensitive to the matter effects of interest.…”