Supernova neutrinos: difference of nu_mu - nu_tau 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 nu_mu and nu_tau potentials in matter becomes important. The nu_mu and nu_tau flux differences can manifest themselves in the effects of the Earth matter on the observed nu_e (antinu_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}|>10^{-3}. We find that for differences in the nu_mu - nu_tau (antinu_mu - antinu_tau) average energies and/or integrated luminosities < 20 %, the relative deviation of the observed nu_e (antinu_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 nu_e (antinu_e) energy spectrum become available. The study of this effect would allow one to test the predictions of the nu_mu, nu_tau, antinu_mu, antinu_tau 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 nu_mu and nu_tau fluxes, effects of leptonic CP violation can not be studied in the supernova neutrino experiments.