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

We derive predictions for the Nadir angle (theta(n)) dependence of the ratio N-mu-/N-mu+ of the rates of the mu(-) and mu(+) multi-GeV events, and for the mu(-)-mu(+) event rate asymmetry, A(mu)--(mu)+ = [N(mu(-)) - N(mu(+))]/[N(mu(-)) + N(mu(+))], in iron-magnetized calorimeter detectors (MINOS, INO, etc.) in the case of 3-neutrino oscillations of the atmospheric v(mu) and v(mu), driven by one neutrino mass squared difference, vertical bar Delta m(31)(2)vertical bar similar to (2.0-3.0) x 10(-3) eV(2) >> Delta m(21)(2). The asynunetry A(mu)-(mu)+ (the ratio N-mu-/N-mu+) is shown to be 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 the CHOOZ and Palo Verde experiments and that responsible for the dominant atmospheric v(mu) -> v(tau) (v(mu) -> v(tau)) oscillations. It is also very sensitive to the type of neutrino mass spectrum which can be with normal (Delta m(31)(2) > 0) or with inverted (Delta m(31)(2) < 0) hierarchy. We find that for sin(2) theta(23) >= 0.50, sin(2) 2 theta(13) >= 0.06 and vertical bar Delta m(31)(2)vertical bar = (2-3) x 10(-3) eV(2), the Earth matter effects produce a relative difference between the integrated asymmetries A(mu)-(mu)+ and A(mu)-(mu)+(-2v) in the mantle (cos theta(n) = 0.30-0.84) and core (cos theta(n) = 0.84-1.0) bins, which is bigger in absolute value than approximately similar to 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 Delta m(31)(2). An observation of the Earth matter effects in the Nadir angle distribution of the asymmetry A(mu)-(mu)+ (ratio N-mu-/N-mu+) would clearly indicate that sin(2) 2 theta(13) >= 0.06 and sin(2) theta(23) >= 0.50, and would lead to the determination of the sign of Delta m(31)(2). (c) 2005 Elsevier B.V. All rights reserved.