Searching for non-diagonal Mass varying mechanism in the   $\nu_{\mu}$-$\nu_{\tau}$ system
  We use atmospheric neutrino data and MINOS data to constrain the MaVaN (Mass Varying Neutrinos) mechanism. The MaVaN model was largely studied in cosmology scenarios and comes from the coupling of the neutrinos with a neutral scalar depending on the local matter density. For atmospheric neutrinos, this new interaction affects the neutrino propagation inside the Earth, and as consequence, induces modifications in their oscillation pattern. To perform such test for a non-standard oscillation mechanism with a non-diagonal neutrino coupling in the mass basis, we analyze the angular distribution of atmospheric neutrino events as seen by the Super-Kamiokande experiment for the events in the Sub-GeV and multi-GeV range and muon neutrinos (anti-neutrinos) in MINOS experiment. From the combined analysis of these two sets of data we obtain the best fit for $\Delta m^{2}_{32}=2.45 \times 10^{-3}$ eV$^{2}$, $sin^{2}(\theta_{23})=0.42 $ and MaVaN parameter $\alpha_{32}=0.28$ with modest improvement, $\Delta \chi^{2}= 1.8$, over the standard oscillation scenario. The combination of MINOS data and Super-Kamiokande data prefers small values of MaVaN parameter $\alpha_{32} < 0.31 $ at $90 \%$ C. L.. 
D. R. Gratieri and O. L. G. Peres
hep-ph