Resonance refraction and neutrino oscillations

The refraction index and matter potential depend on neutrino energy and this dependence has a resonance character associated to the production of the mediator in the $s-$channel. For light mediators and light particles of medium (background) the resonance can be realized at energies accessible to laboratory experiments. We study properties of the energy dependence of the potential for different C-asymmetries of background. Interplay of the background potential and the vacuum term leads to (i) bump in the oscillation probability in the resonance region, (ii) dip related to the MSW resonance in the background, (iii) substantial deviation of the effective $\Delta m^2$ above the resonance from the low energy value, etc. We considered generation of mixing in the background. Interactions with background shifts the energy of usual MSW resonance and produces new MSW resonances. Searches of the background effects allow us to put bounds on new interactions of neutrinos and properties of the background. We show that explanation of the MiniBooNE excess, as the bump due to resonance refraction, is excluded.