We find that for small vacuum mixing angle ΞΈ and low energies (sβͺMZ2β) the width of matter, d1/2β, needed to have conversion probability
Pβ₯1/2 should be larger than dminβ=Ο/(22βGFβtan2ΞΈ): d1/2ββ₯dminβ. Here GFβ is the Fermi constant, s is the
total energy squared in the center of mass and MZβ is the mass of the Z
boson. The absolute minimum d1/2β=dminβ 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
d1/2β is larger than dminβ. The width dminβ depends on s, and for
Z-resonance channels at sβΌMZ2β we get that dminβ(s) is 20 times
smaller than the low energy value. We apply the minimum width condition, dβ₯dminβ, 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