The minimal extension of the SM and the neutrino oscillation data

We study the simplest Standard Model extension with only one extra right-ha nded neutrino. In this case there are two massless m(1,2) and two massive m (3,4) neutrinos, and in principle both solar and atmospheric anomalies can be described in two different scenarios, m(3) much less than m(4) (scheme I ) and m(3) similar or equal to m(4) (scheme II). However, neither bi-maxima l mixing nor the dark matter problem are explained in this minimal extensio n. Only scheme II can accommodate simultaneously maximal mixing for atmosph eric neutrinos and the small mixing angle MSW solution for the solar anomal y. This scenario can be tested in the BOREXINO experiment.