Probing the neutrino mass hierarchy and the 13-mixing with supernovae

We consider in details the effects of the 13-mixing (sin^2 theta_{13}) and of the type of mass hierarchy/ordering (sign[ Delta m^2_{13}]) on neutrino signals from the gravitational collapses of stars. The observables (characteristics of the energy spectra of nu_e and antinu_e events) sensitive to sin^2 theta_{13} and sign[Delta m^2_{13}] have been calculated. They include the ratio of average energies of the spectra, r_E = /, the ratio of widths of the energy distributions, r_Gamma, the ratios of total numbers of nu_e and antinu_e events at low energies, S, and in the high energy tails, R_{tail}. We construct and analyze scatter plots which show the predictions for the observables for different intervals of sin^2 theta_{13} and signs of Delta m^2_{13}, taking into account uncertainties in the original neutrino spectra, the star density profile, etc.. Regions in the space of observables r_E, r_Gamma, S, R_{tail} exist in which certain mass hierarchy and intervals of sin^2 theta_{13} can be identified or discriminated. We elaborate on the method of the high energy tails in the spectra of events. The conditions are formulated for which sin^2 theta_{13} can be (i) measured, (ii) restricted from below, (iii) restricted from above. We comment on the possibility to determine sin^2 theta_{13} using the time dependence of the signals due to the propagation of the shock wave through the resonance layers of the star. We show that the appearance of the delayed Earth matter effect in one of the channels (nu_e or antinu_e) in combination with the undelayed effect in the other channel will allow to identify the shock wave appeareance and determine the mass hierarchy.Comment: LaTeX, 56 pages, 12 figures; a few clarifications added; typos corrected. Version to appear in JCA

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.Comment: LaTeX, 34 pages, 10 figures; minor changes to text and figures, references and acknowledgements adde