Four-neutrino mass spectra and the Super-Kamiokande atmospheric up-down asymmetry

In the framework of schemes with mixing of four massive neutrinos, which can accommodate the atmospheric, solar and LSND ranges of Delta m(2) and contain three active neutrinos and a sterile one, we show that, in the whole region of Delta m(LSND)(2) allowed by LSND, the Super-Kamiokande up-down asymmetry excludes all mass spectra with a group of three close neutrino masses separated from the fourth mass by the LSND gap of order 1 eV. Only two schemes with mass spectra in which two pairs of close masses ore separated by the LSND gap can describe the Super-Kamiokande up-down asymmetry and all other existing neutrino oscillation data. [S0556-2821(99)03419-0].