The minimum width condition for neutrino conversion in matter

We find that for small vacuum mixing angle $\theta$ and low energies ($s\ll M^2_Z$) the width of matter, $d_{1/2}$, needed to have conversion probability $P\geq 1/2$ should be larger than $d_{min}= \pi/(2\sqrt{2} G_{F} \tan 2 \theta)$: $d_{1/2}\geq d_{min}$. Here $G_F$ is the Fermi constant, $s$ is the total energy squared in the center of mass and $M_Z$ is the mass of the $Z$ boson. The absolute minimum $d_{1/2}=d_{min}$ is realized for oscillations in a uniform medium with resonance density. For all the other density distributions (monotonically varying density, castle wall profile, etc.) the required width $d_{1/2}$ is larger than $d_{min}$. The width $d_{min}$ depends on $s$, and for $Z$-resonance channels at $s\sim M^2_Z$ we get that $d_{min}(s)$ is 20 times smaller than the low energy value. We apply the minimum width condition, $d\geq d_{min}$, to high energy neutrinos in matter as well as in neutrino background. Using this condition, we conclude that the matter effect is negligible for neutrinos propagating in AGN and GRBs environments. Significant conversion can be expected for neutrinos crossing dark matter halos of clusters of galaxies and for neutrinos produced by cosmologically distant sources and propagating in the universe.Comment: 35 pages, latex, 5 figures, structure of the paper is slightly changed, typos correcte

Signatures of supernova neutrino oscillations in the Earth mantle and core

The Earth matter effects on supernova (SN) neutrinos can be identified at a single detector through peaks in the Fourier transform of their ``inverse energy'' spectrum. The positions of these peaks are independent of the SN models and therefore the peaks can be used as a robust signature of the Earth matter effects, which in turn can distinguish between different neutrino mixing scenarios. Whereas only one genuine peak is observable when the neutrinos traverse only the Earth mantle, traversing also the core gives rise to multiple peaks. We calculate the strengths and positions of these peaks analytically and explore their features at a large scintillation detector as well as at a megaton water Cherenkov detector through Monte Carlo simulations. We propose a simple algorithm to identify the peaks in the actual data and quantify the chances of a peak identification as a function of the location of the SN in the sky.Comment: 17 pages, 9 figure

A test of tau neutrino interactions with atmospheric neutrinos and K2K

The presence of a tau component in the flux of atmospheric neutrinos inside the Earth, due to flavor oscillations, makes these neutrinos a valuable probe of interactions of the tau neutrino with matter. We study -- analytically and numerically -- the effects of nonstandard interactions in the nu_e-nu_tau sector on atmospheric neutrino oscillations, and calculate the bounds on the exotic couplings that follow from combining the atmospheric neutrino and K2K data. We find very good agreement between numerical results and analytical predictions derived from the underlying oscillation physics. While improving on existing accelerator bounds, our bounds still allow couplings of the size comparable to the standard weak interaction. The inclusion of new interactions expands the allowed region of the vacuum oscillation parameters towards smaller mixing angles, 0.2 ~< sin^2 theta_{23} ~< 0.7, and slightly larger mass squared splitting, 1.5 * 10^{-3} eV^2 ~< |\Delta m^2_{23}| ~< 4.0 * 10^{-3} eV^2, compared to the standard case. The impact of the K2K data on all these results is significant; further important tests of the nu_e-nu_tau exotic couplings will come from neutrino beams experiments such as MINOS and long baseline projects.Comment: 8 figures, some typos corrected, minor editing in the reference

Neutrino oscillation signatures of oxygen-neon-magnesium supernovae

We discuss the flavor conversion of neutrinos from core collapse supernovae that have oxygen-neon-magnesium (ONeMg) cores. Using the numerically calculated evolution of the star up to 650 ms post bounce, we find that, for the normal mass hierarchy, the electron neutrino flux in a detector shows signatures of two typical features of an ONeMg-core supernova: a sharp step in the density profile at the base of the He shell and a faster shock wave propagation compared to iron core supernovae. Before the shock hits the density step (t ~ 150 ms), the survival probability of electron neutrinos is about 0.68, in contrast to values of 0.32 or less for an iron core supernova. The passage of the shock through the step and its subsequent propagation cause a decrease of the survival probability and a decrease of the amplitude of oscillations in the Earth, reflecting the transition to a more adiabatic propagation inside the star. These changes affect the lower energy neutrinos first; they are faster and more sizable for larger theta_13. They are unique of ONeMg-core supernovae, and give the possibility to test the speed of the shock wave. The time modulation of the Earth effect and its negative sign at the neutronization peak are the most robust signatures in a detector.Comment: 14 pages, 10 figures (16 figure files). Text and graphics added for illustration and clarification; Results unchanged. Version accepted for publication in Physical Review