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

Abstract

We consider in detail the effects of the 13-mixing(sin2θ13) and of the type of mass hierarchy/ordering(sign[Δm213]) on neutrino signals from thegravitational collapses of stars. The observables (characteristics of the energy spectra of νe andν̄e events) sensitive to sin2θ13 and sign[Δm213] have been calculated. They include theratio of average energies of the spectra, rE≡⟨E⟩/⟨Ē⟩, the ratio of widths of theenergy distributions, rΓ≡Γ/Γ̄,the ratios of total numbers of νe and ν̄e events at low energies, S, and in the high energy tails, Rtail. Weconstruct and analyse scatter plots which show the predictionsfor the observables for different intervals of sin2θ13and signs of Δm213, taking into account uncertaintiesin the original neutrino spectra, the star density profile, etc.Regions in the space of observables rE, rΓ, S, Rtail exist in which certain mass hierarchy and intervals of sin2θ13 can be identified or discriminated. We elaborateon the method of the high energy tails in the spectra of events.The conditions are formulated for which sin2θ13 can be(i) measured, (ii) restricted from below, (iii) restricted fromabove. We comment on the possibility to determinesin2θ13 using the time dependence of the signals dueto the propagation of the shock wave through the resonancelayers of the star. We show that the appearance of the delayed Earth matter effect in one of the channels(νe or ν̄e) in combination with the undelayed effect in the other channel will allow us to identify the shock wave appeareance and determine the mass hierarchy.