Mu-tau neutrino refraction and collective three-flavour transformations in supernovae

We study three-flavor collective neutrino transformations in the dense-neutrino region above the neutrino sphere of a supernova core. We find that two-flavor conversions driven by the atmospheric mass difference and the 13-mixing angle capture the full effect if one neglects the second-order difference between the muon and tau neutrino refractive index. Including this 'mu-tau matter term' provides a resonance at a density of approximately 3 x 10^7 g/cm3 that typically causes significant modifications of the overall electron neutrino and antineutrino survival probabilities. This effect is surprisingly sensitive to deviations from maximal 23-mixing, being different for each octant