Transition Radiation by Standard Model Neutrinos at an Interface

We discuss the transition radiation process $\nu \to \nu \gamma$ at an interface of two media. The medium fulfills the dual purpose of inducing an effective neutrino-photon vertex and of modifying the photon dispersion relation. The transition radiation occurs when at least one of those quantities have different values in different media. We present a result for the probability of the transition radiation which is both accurate and analytic. For $E_\nu =1$MeV neutrino crossing polyethylene-vacuum interface the transition radiation probability is about $10^{-39}$ and the energy intensity (deposition) is about $10^{-34}$eV. At the surface of the neutron stars the transition radiation probability may be $\sim 10^{-20}$. Our result on three orders of magnitude is larger than the results of previous calculations.}Comment: invited talk, to appear in the proceedings of the XLVIth Rencontres de Moriond EW 201

Degenerate Neutrinos and CP Violation

We have studied mixing and masses of three left handed Majorana neutrinos in the model, which assumes exactly degenerate neutrino masses at some "neutrino unification" scale. Such a simple theoretical ansatz naturally leads to quasidegenerate neutrinos. The neutrino mass splittings induced by renormalization effects. In the model we found that the parameters of the neutrino physics (neutrino mass spectrum, mixing angles and CP violation phases) are strongly intercorrelated to each other. From these correlations we got strong bounds on the parameters which could be checked in the oscillation experiments.Comment: 5 pages, latex, presented at CAPP200

Describing neutrino oscillations in matter with Magnus expansion

We present new formalism for description of the neutrino oscillations in matter with varying density. The formalism is based on the Magnus expansion and has a virtue that the unitarity of the S-matrix is maintained in each order of perturbation theory. We show that the Magnus expansion provides better convergence of series: the restoration of unitarity leads to smaller deviations from the exact results especially in the regions of large transition probabilities. Various expansions are obtained depending on a basis of neutrino states and a way one splits the Hamiltonian into the self-commuting and non-commuting parts. In particular, we develop the Magnus expansion for the adiabatic perturbation theory which gives the best approximation. We apply the formalism to the neutrino oscillations in matter of the Earth and show that for the solar oscillation parameters the second order Magnus adiabatic expansion has better than 1% accuracy for all energies and trajectories. For the atmospheric $\Delta m^2$ and small 1-3 mixing the approximation works well ($< 3$ accuracy for $\sin^2 \theta_{13} = 0.01$) outside the resonance region (2.7 - 8) GeV.Comment: Discussions expanded, two figures and references added, the version will appear in Nucl. Phys.

Attenuation effect and neutrino oscillation tomography

Attenuation effect is the effect of weakening of contributions to the oscillation signal from remote structures of matter density profile. The effect is a consequence of integration over the neutrino energy within the energy resolution interval. Structures of a density profile situated at distances larger than the attenuation length, $\lambda_{att}$, are not "seen". We show that the origins of attenuation are (i) averaging of oscillations in certain layer(s) of matter, (ii) smallness of matter effect: $\epsilon \equiv 2EV/\Delta m^2 \ll 1$, where $V$ is the matter potential, and (iii) specific initial and final states on neutrinos. We elaborate on the graphic description of the attenuation which allows us to compute explicitly the effects in the $\epsilon^2$ order for various density profiles and oscillation channels. The attenuation in the case of partial averaging is described. The effect is crucial for interpretation of oscillation data and for the oscillation tomography of the Earth with low energy (solar, supernova, atmospheric, {\it etc.}) neutrinos.Comment: 24 pages, 8 figures, typos corrected, more explanations adde