Atmospheric neutrino oscillations, θ13 and neutrino mass hierarchy

We derive predictions for the Nadir angle (theta(n)) dependence of the ratio N-mu/N-e of the rates of the mu-like and e-like multi-GeV events measured in water-Cerenkov detectors in the case of 3-neutrino oscillations of the atmospheric nu(e) (nu(e)) and nu(mu) (nu(mu)), driven by one neutrino mass squared difference, \Deltam(31)(2)\ similar to (2.5-3.0) x 10(-3) eV(2) much greater than Deltam(21)(2). This ratio is particularly sensitive to the Earth matter effects in the atmospheric neutrino oscillations, and thus to the values of sin(2) theta(13) and sin(2) theta(23), theta(13) and theta(23) being the neutrino mixing angle limited by CHOOZ and Palo Verde experiments and that responsible for the dominant atmospheric nu(mu) --> nu(tau) (nu(mu) --> nu(tau)) oscillations. It is also sensitive to the type of neutrino mass spectrum which can be with normal (Deltam(31)(2) > 0) or with inverted (Deltam(31)(2) < 0) hierarchy. We show that for sin(2) theta(13) greater than or similar to 0.01, sin(2) theta(23) greater than or similar to 0.5 and at cos theta(n) greater than or similar to 0.4, the Earth matter effects modify substantially the theta(n)-dependence of the ratio N-mu/N-e and in a way which cannot be reproduced with sin(2) theta(13) = 0 and a different value of sin(2) theta(23). For normal hierarchy the effects can be as large as similar to25% for cos theta(n) similar to (0.5-0.8), can reach similar to35% in the Earth core bin cos theta(n) similar to (0.84-1.0), and might be observable. They are typically by similar to10% smaller in the inverted hierarchy case. An observation of the Earth matter effects in the Nadir angle distribution of the ratio N-mu/N-e would clearly indicate that sin(2) theta(13) greater than or similar to 0.01 and sin(2) theta(23) greater than or similar to 0.50. (C) 2003 Elsevier B.V. All rights reserved.