Neutrino Propagation When Mass Eigenstates and Decay Eigenstates Mismatch.

We point out that the Hermitian and anti-Hermitian components of the effective Hamiltonian for decaying neutrinos cannot be simultaneously diagonalized by unitary transformations for all matter densities. We develop a formalism for the two-flavor neutrino propagation through matter of uniform density, for neutrino decay to invisible states. Employing a resummation of the Zassenhaus expansion, we obtain compact analytic expressions for neutrino survival and conversion probabilities, to first and second order in the "mismatch parameter" γ[over ¯].

2540 km: bimagic baseline for neutrino oscillation parameters.

We show that a source-to-detector distance of 2540 km, motivated recently [S. K. Raut, R.

Multiple spectral splits of supernova neutrinos.

Collective oscillations of supernova neutrinos swap the spectra f(nu(e))(E) and f(nu[over ](e))(E) with those of another flavor in certain energy intervals bounded by sharp spectral splits. This phenomenon is far more general than previously appreciated: typically one finds one or more swaps and accompanying splits in the nu and nu[over ] channels for both inverted and normal neutrino mass hierarchies. Depending on an instability condition, swaps develop around spectral crossings (energies where f(nu(e))=f(nu(x)), f(nu[over ](e))=f(nu[over ](x)) as well as E-->infinity where all fluxes vanish), and the widths of swaps are determined by the spectra and fluxes.

Identifying neutrino mass hierarchy at extremely small theta13 through earth matter effects in a supernova signal.

Collective neutrino flavor transformations deep inside a supernova are sensitive to the neutrino mass hierarchy even at extremely small values of theta_(13). Exploiting this effect, we show that comparison of the antineutrino signals from a galactic supernova in two megaton class water Cherenkov detectors, one of which is shadowed by Earth, will enable us to distinguish between the hierarchies if sin(2)theta_(13) < or approximately 10(-5), where long baseline neutrino experiments would be ineffectual.