The minimum width condition for neutrino conversion in matter

We find that for small vacuum mixing angle theta and low energies (s much less than M-Z(2)) the width of matter, d(1/2), needed to have conversion probability P greater than or equal to 1/2 should be larger than d(min) = pi/(2 root 2 G(F) tan 2 theta): d(1/2) greater than or equal to d(min). Here G(F) is the Fermi constant, s is the total energy squared in the center of mass and Mt is the mass of the Z boson. The absolute minimum d(1/2) = dmin is realized for oscillations in a uniform medium with resonance density, For realistic 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 similar to M-Z(2) we get that d(min)(s) is 20 times smaller than the low energy value. We apply the minimum width condition, d greater than or equal to 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. (C) 2000 Elsevier Science B.V. All rights reserved.