Search for Matter-Dependent Atmospheric Neutrino Oscillations in   Super-Kamiokande
  We consider muon neutrino to tau neutrino oscillations in the context of the Mass Varying Neutrino (MaVaN) model, where the neutrino mass can vary depending on the electron density along the flight path of the neutrino. Our analysis assumes a mechanism with dependence only upon the electron density, hence ordinary matter density, of the medium through which the neutrino travels. Fully-contained, partially-contained and upward-going muon atmospheric neutrino data from the Super--Kamiokande detector, taken from the entire SK--I period of 1489 live days, are compared to MaVaN model predictions. We find that, for the case of 2-flavor oscillations, and for the specific models tested, oscillation independent of electron density is favored over density dependence. Assuming maximal mixing, the best-fit case and the density-independent case do not differ significantly. 
The Super-Kamiokande Collaboration, K. Abe, et al