Three Flavor Neutrino Oscillations in Matter: Flavor Diagonal Potentials, the Adiabatic Basis and the CP phase

We discuss the three neutrino flavor evolution problem with general, flavor-diagonal, matter potentials and a fully parameterized mixing matrix that includes CP violation, and derive expressions for the eigenvalues, mixing angles and phases. We demonstrate that, in the limit that the mu and tau potentials are equal, the eigenvalues and matter mixing angles theta_12 and theta_13 are independent of the CP phase, although theta_23 does have CP dependence. Since we are interested in developing a framework that can be used for S matrix calculations of neutrino flavor transformation, it is useful to work in a basis that contains only off-diagonal entries in the Hamiltonian. We derive the "non-adiabaticity" parameters that appear in the Hamiltonian in this basis. We then introduce the neutrino S matrix, derive its evolution equation and the integral solution. We find that this new Hamiltonian, and therefore the S matrix, in the limit that the mu and tau neutrino potentials are the same, is independent of both theta_23 and the CP violating phase. In this limit, any CP violation in the flavor basis can only be introduced via the rotation matrices, and so effects which derive from the CP phase are then straightforward to determine. We show explicitly that the electron neutrino and electron antineutrino survival probability is independent of the CP phase in this limit. Conversely, if the CP phase is nonzero and mu and tau matter potentials are not equal, then the electron neutrino survival probability cannot be independent of the CP phase

Oscillation Effects and Time Variation of the Supernova Neutrino Signal

The neutrinos detected from the next Galactic core-collapse supernova will contain valuable information on the internal dynamics of the explosion. One mechanism leading to a temporal evolution of the neutrino signal is the variation of the induced neutrino flavor mixing driven by changes in the density profile. With one and two dimensional hydrodynamical simulations we identify the behavior and properties of prominent features of the explosion. Using these results we demonstrate the time variation of the neutrino crossing probabilities due to changes in the MSW neutrino transformations as the star explodes by using the S-matrix - Monte Carlo - approach to neutrino propagation. After adopting spectra for the neutrinos emitted from the proto-neutron star we calculate for a Galactic supernova the evolution of the positron spectra within a water Cerenkov detector and the ratio of charged current to neutral current event rates for a heavy water - SNO like - detector and find that these detector signals are feasible probes of a number of explosion features

A dynamical collective calculation of supernova neutrino signals

We present the first calculations with three flavors of collective and shock wave effects for neutrino propagation in core-collapse supernovae using hydroynamical density profiles and the S matrix formalism. We explore the interplay between the neutrino-neutrino interaction and the effects of multiple resonances upon the time signal of positrons in supernova observatories. A specific signature is found for the inverted hierarchy and a large third neutrino mixing angle and we predict, in this case, a dearth of lower energy positrons in Cherenkov detectors midway through the neutrino signal and the simultaneous revelation of valuable information about the original fluxes. We show that this feature is also observable with current generation neutrino detectors at the level of several sigmas.Comment: 4 pages, 5 figure

Stimulated Neutrino Transformation with Sinusoidal Density Profiles

Large amplitude oscillations between the states of a quantum system can be stimulated by sinusoidal external potentials with frequencies that are similar to the energy level splitting of the states or a fraction thereof. Situations when the applied frequency is equal to an integer fraction of the energy level splittings are known as parametric resonances. We investigate this effect for neutrinos both analytically and numerically for the case of arbitrary numbers of neutrino flavors. We look for environments where the effect may be observed and find that supernova are the one realistic possibility due to the necessity of both large densities and large amplitude fluctuations. The comparison of numerical and analytic results of neutrino propagation through a model supernova reveals it is possible to predict the locations and strengths of the stimulated transitions that occur.Comment: 14 pages, 6 figure

Monte Carlo Neutrino Oscillations

We demonstrate that the effects of matter upon neutrino propagation may be recast as the scattering of the initial neutrino wavefunction. Exchanging the differential, Schrodinger equation for an integral equation for the scattering matrix S permits a Monte Carlo method for the computation of S that removes many of the numerical difficulties associated with direct integration techniques