On Exotic Solutions of the Atmospheric Neutrino Problem

The measurements of the fluxes of atmospheric neutrinos give evidence for the disappearance of muon neutrinos. The determination of the dependence of the disappearance probability on the neutrino energy and trajectory allows in principle to establish unambiguosly the existence of neutrino oscillations. Alternative mechanisms for the disappearance of the neutrinos have been proposed, but do not provide a viable description of the data, if one includes both events where the neutrinos interact in the detector and $\nu$-induced upward going muons. The proposed mechanisms differ in the energy dependence of the disappearance probability and the upward going muon data that are produced by high energy neutrinos give a crucial constraint.