Atmospheric neutrino oscillations with three neutrinos and a mass hierarchy

A comprehensive formalism for the description of neutrino oscillations in the Earth in a general scheme with three massive neutrinos and the mass hierarchy m_1<<m_2<<m_3 is presented. Using this formalism, which is valid both in vacuum and in a medium, the matter effect on the oscillations of low-energy neutrinos is discussed, pointing out the existence of very long oscillations which are independent of the neutrino masses and the neutrino energy, and are very sensitive to the matter density along the neutrino trajectory. As an example of application of the formulation, a fit of the Kamiokande atmospheric neutrino data with the matter effect taken into account for neutrinos propagating in the Earth is presented. The results of the fit indicate that 4*10^{-3} eV^2 < m_3^2 nu_e, nu_munu_tau, nu_enu_tau) could be large. Hence, long-baseline experiments with reactor (CHOOZ and Palo Verde) and accelerator (K2K, MINOS and ICARUS) neutrinos could observe neutrino oscillations in all channels with a relatively large statistics.Comment: 42 pages, including 7 figure

ARE THERE STERILE NEUTRINOS IN THE FLUX OF SOLAR NEUTRINOS ON THE EARTH?

It is shown that the future SNO and Super-Kamiokande experiments, in which high energy $^8\mathrm{B}$ neutrinos will be detected through the observation of CC, NC and $\nu$--$e$ elastic scattering processes, could allow to reveal in a model independent way the presence of sterile neutrinos in the flux of solar neutrinos on the earth. Lower bounds for different averaged values of the probability of transition of solar $\nu_e$'s into sterile states and for the total flux of $^8\mathrm{B}$ neutrinos are derived in terms of measurable quantities. The possibilities to reveal the presence of $\nu_\mu$ and/or $\nu_\tau$ in the solar neutrino flux on the earth are also considered and the case of transitions of solar $\nu_e$'s only into sterile states is discussed. Some numerical results for a simple model with $\nu_e$--$\nu_s$ mixing are given.Comment: Revised reference list. Revtex file, 15 pages + 4 figures (included). The postscript file of text and figures is available at ftp://toxd01.to.infn.it/pub/giunti/1995/dftt-12-95/dftt-12-95.ps.

Neutrino mass spectrum from the results of neutrino oscillation experiments

All the possible schemes of neutrino mixing with four massive neutrinos inspired by the existing experimental indications in favor of neutrino mixing are considered in a model independent way. Assuming that in short-baseline experiments only one mass-squared difference is relevant, it is shown that the scheme with a neutrino mass hierarchy is not compatible with the experimental results. Only two schemes with two pairs of neutrinos with close masses separated by a mass difference of the order of 1 eV are in agreement with the results of all experiments. One of these schemes leads to possibly observable effects in Tritium and neutrinoless double-beta decay experiments.Comment: Latex2e file, 13 pages including 2 figures. Postscript also available at http://www.to.infn.it/teorici/giunti/papers.htm