The status of hot dark matter after SNO

While the combined SNO-SuperKamiokande solar results require only the three known active neutrinos, adding the atmospheric neutrino and LSND input would require a fourth, sterile neutrino, νs. The LSND results, which alone force appreciable hot dark matter, are unlikely to be accommodated by a 3+1 neutrino scheme, so it is important to know if the 2+2 scheme survives. For the latter, if the fraction of sterile neutrinos is denoted by ηS for the solar flux and ηA for the atmospheric flux, we show that 1) for νμ purely in the atmospheric neutrino pair and νe purely in the solar pair, ηS + ηA ≥ 1 for any arbitrary number of neutrinos, and 2) there is considerable deviation from that sum rule if a small fraction of the νμ and νe mix into the opposite pairs of mass states. Thus 2+2, sterile neutrinos, and hot dark matter can survive