Supernova neutrinos: Difference of v_μ-v_τ fluxes and conversion effects

The formalism of flavor conversion of supernova neutrinos is generalized to include possible differences in the fluxes of the muon and tau neutrinos produced in the star. In this case the radiatively induced difference of the v_μ and v_τ potentials in matter becomes important. The v_μ and v_τ flux differences can manifest themselves in the effects of the Earth matter on the observed v_e (v̄_e) signal if: (i) the neutrino mass hierarchy is normal (inverted); (ii) the solution of the solar neutrino problem is in the LMA region; (iii) the mixing U_e3 is relatively large: U_e3 ² ≳ 10^-3. We find that for differences in the v_μ-v_τ (v̄_μ-v̄_τ) average energies and/or integrated luminosities ≲ 20%, the relative deviation of the observed v_e (v̄_e) energy spectrum at E ≳ 50 MeV from that in the case of the equal fluxes can reach ∼ 20-30% (∼ 10-15%) for neutrinos crossing the Earth. It could be detected in future if large detectors sensitive to the v_e (v̄_e) energy spectrum become available. The study of this effect would allow one to test the predictions of the v_μ, v_τ, v̄_μ, v̄_τ fluxes from supernova models and therefore give an important insight into the properties of matter at extreme conditions. It should be taken into account in the reconstruction of the neutrino mass spectrum and mixing matrix from the supernova neutrino observations. We show that even for unequal v_μ and v_τ fluxes, effects of leptonic CP violation cannot be studied in the supernova neutrino experiments.