But there was no good evidence of just what sort these other neutrinos might be. Now, at last, the Super-Kamiokande collaboration has published the results of its assault on this experimentally difficult question. Suppose you have oscillation between two neutrino flavors, labeled i and j .
Neutrino oscillation implies unequal neutrino masses.
Because the measured oscillation parameters of the three observational regimes are so different, it is presumed that each involves a different pairing of neutrino species. But if there are only three species, one confronts an obvious algebraic constraint. That's orders of magnitude bigger than the mass-squared differences indicated by the solar and atmospheric neutrino oscillation data, making it impossible to satisfy the algebraic identity. A way out might be to suggest that the data are actually describing messy three-way rather than simple pairwise oscillations. Finally, one could call the data into question.