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

Quantum Poisson-Lie T-duality and WZNW model

A pair of conformal sigma models related by Poisson-Lie T-duality is constructed by starting with the O(2,2) Drinfeld double. The duality relates the standard SL(2,R) WZNW model to a constrained sigma model defined on SL(2,R) group space. The quantum equivalence of the models is established by using a path integral argument.Comment: 19 pages, late

Magnetic Monopole and the Finite Photon Mass: Are They Compatible?

We analyze the role played by the gauge invariance for the existence of Dirac monopole. To this end, we consider the electrodynamics with massive photon and ask if the magnetic charge can be introduced there. We show that the derivation of the Dirac quantization condition based on the angular momentum algebra cannot be generalized to the case of massive electrodynamics. Possible implications of this result are briefly discussed.Comment: 12 pages, revtex, no figure

The Charged Neutrino: A New Approach to the Solar Neutrino Problem

We have considered the effect of the reduction of the solar neutrino flux on earth due to the deflection of the charged neutrino by the magnetic field of the solar convective zone. The antisymmetry of this magnetic field about the plane of the solar equator induces the anisotropy of the solar neutrino flux thus creating the deficit of the neutrino flux on the earth. The deficit has been estimated in terms of solar and neutrino parameters and the condition of a 50 \% deficit has been obtained: Q_{\nu} gradH \agt 10^{-18} eG/cm where $Q_{\nu}$ is the neutrino electric charge, $gradH$ is the gradient of the solar toroidal magnetic field, e is the electron charge. Some attractive experimental consequences of this scenario are qualitatively discussed.Comment: 15 pages, UM-P/94-26, in REVTE

On pattern classification algorithms - Introduction and survey

Pattern recognition algorithms, and mathematical techniques of estimation, decision making, and optimization theor