Fate of the Sterile Neutrino

In light of recent Super-Kamiokande data and global fits that seem to exclude both pure \nu_\mu \to \nu_s oscillations of atmospheric neutrinos and pure \nu_e \to \nu_s oscillations of solar neutrinos (where \nu_s is a sterile neutrino), we reconsider four-neutrino models to explain the LSND, atmospheric, and solar neutrino oscillation indications. We argue that the solar data, with the exception of the ^{37}Cl results, are suggestive of \nu_e \to \nu_s oscillations that average to a probability of approximately 1/2. In this interpretation, with two pairs of nearly degenerate mass eigenstates separated by order 1 eV, the day-night asymmetry, seasonal dependence, and energy dependence for ^8B neutrinos should be small. Alternatively, we find that four-neutrino models with one mass eigenstate widely separated from the others (and with small sterile mixings to active neutrinos) may now be acceptable in light of recently updated LSND results; the ^{37}Cl data can be accommodated in this model. For each scenario, we present simple four-neutrino mixing matrices that fit the stated criterion and discuss future tests.