It must be emphasized that the size of the anomaly being as large as it is, does not permit a subtle problem to be the cause of the anomaly. As we will discuss later, it is true that subtle effects can have significant influence on the parameters measured, but not enough to dismiss the phenomena. We discuss each of these. Summary of alternative hypotheses to explain the atmospheric neutrino anomaly, with new evidence from Super-Kamiokande. Atmospheric flux calculation problems cannot be the source of the anomaly, as was concluded by many who studied the situation over the last 15 years.
Different models give significantly different spectra, but the ratio is robust.
There is some complication at the few hundred MeV energy range due to the lopsided nature of the earth's magnetic field. A mistaken double ratio due to a difference in electron neutrino and muon neutrino cross sections was an idea pursued for a while as an explanation for the anomaly. The well established fact of lepton universality prevents any significant difference, except at energies near the muon mass, where calculable kinematic differences exist. The fact that the anomaly now is seen to persist to energies above a GeV, dismisses this possibility. We have the independent cross check of a sample of events where the muon is observed to stop and decay, which gives completely consistent results in IMB, Kamioka and now Super-Kamiokande.