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) much less than m(2) much less than 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 x 10(-3) eV(2) less than or similar to m(3)(2) less than or similar to 4 x 10(-2) eV(2) and the oscillation amplitudes in all channels (v(u) reversible arrow v(e), v(u) reversible arrow v(tau), v(e) reversible arrow v(tau)) could be large. Hence, long-baseline experiments with reactor (CHOOZ and Pale Verde) and accelerator (K2K, MINOS and ICARUS) neutrinos could observe neutrino oscillations in all channels with a relatively large statistics. (C) 1998 Elsevier Science B.V.