  We investigate a minimal extension of the standard model in which the only
new ingredient is the sterile neutrinos. We do not introduce extra Higgs
multiplets or high dimensional effective operators to induce mass terms for the
active neutrinos, and the model is renormalizable in itself. We show for
arbitrary numbers of generations and sterile neutrinos that the independent
physical parameters in the leptonic sector are much less than previously
anticipated. For instance, with three active and two sterile neutrinos, there
are four mixing angles and three CP phases in addition to four non-vanishing
neutrino masses. We study phenomenological implications for tritium beta decay,
neutrinoless double beta decay and neutrino oscillations. For the most natural
see-saw parameters, we find that it is difficult to accommodate in the model
the best-fit values of masses and mixing parameters from oscillation data no
matter whether we include or not the null short-baseline experiments together
with the LSND result. This implies that if the LSND result is confirmed by
MiniBooNE, the see-saw parameter region of the model with two sterile neutrinos
could be largely excluded.
