Two-neutrino oscillation model - reason for assumption In a recent paper done by the MiniBooNE experiment at Fermilab, it says in the abstract "If interpreted in a standard two-neutrino oscillation model". I understand they were using a muon neutrino beam that then oscillated occasionally into electron neutrinos, but there are also tau neutrinos. Why was it a reasonable assumption to "cut out" the tau neutrinos? Is it extremely low probability that muon neutrinos or electron neutrinos oscillate to tau neutrinos? Could their detection system not detect tau neutrinos?
 A: I emailed Professor Kerry Whisnant, who does research on neutrinos, and here is the answer he gave:

To detect a tau neutrino, you would have to have an interaction in your detector in which a tau lepton is produced (remember neutrinos couple to charged leptons in the weak interactions), and there is not enough energy in the beam to do that. There have been more energetic neutrino beams where there are oscillations to tau neutrinos, which then are detected by seeing taus, but not MiniBooNE. Tau neutrinos have also been detected in atmospheric neutrinos since some of those are very energetic. So there could have been (and likely were) oscillations to tau neutrinos in MiniBooNE, too, but they would not have been detected.
The reason the MiniBooNE result suggests sterile neutrinos is that oscillations depend on both the distance traveled and the neutrino energy (the exact statement is that it depends on L divided by E). But it also depends on the difference of the squared masses. Solar neutrinos indicate one value for this difference (7.6x10^(-5) eV^2) and atmospheric neutrinos indicate another (2.5x10^(-3) eV^2), but because of their L and E, the LSND and MiniBooNE results indicate a much larger value (more like 1 eV^2). But the only way to have three very different values for the squared mass differences is to have four different neutrino masses. And because it has been known since the 1990's that there are only three active neutrinos (neutrinos that have standard weak interactions), a fourth neutrino must be "sterile," i.e., it does not have the usual weak interactions.
Regarding the two-neutrino model analysis (Fig. 5 in their paper), with four neutrinos, there are actually six different mixing angles. At the particular L and E of MiniBooNE (and LSND), the amplitude of the nu_mu to nu_e oscillation is some combination of those mixing angles, and it can be approximated as a two-neutrino oscillation. But all possible oscillations actually occur (although some may be so unlikely that they are not visible).

