spectrum of neutrino masses: a chance for LSND?

If active to active neutrino transitions are dominant modes of the atmospheric ( ν μ →ν τ ) and the solar neutrino oscillations ( ν e →ν μ /ν τ ), as is indicated by recent data, the favoured scheme which accommodates the LSND result — the so-called (2+2) -scheme — should be discarded. We introduce the parameters η s atm and η s sun which quantify an involvement of the sterile component in the solar and atmospheric neutrino oscillations. The (2+2) -scheme predicts η s atm +η s sun =1 and the experimental proof of deviation from this equality will discriminate the scheme. In this connection the (3+1) -scheme is revisited in which the fourth (predominantly sterile) neutrino is isolated from a block of three flavour neutrinos by the mass gap Δm 2 LSND ∼(0.4 – 10) eV2. We find that in the (3+1) -scheme the LSND result can be reconciled with existing bounds on ν e - and ν μ -disappearance at 95–99% C.L. The generic prediction of the scheme is the ν e - and ν μ -disappearance probabilities at the level of present experimental bounds. The possibility to strengthen the bound on ν μ -disappearance in the KEK — front detector experiment is studied. We consider phenomenology of the (3+1) -scheme, in particular, its implications for the atmospheric neutrinos, neutrinoless double beta decay searches, supernova neutrinos and primordial nucleosynthesis.