Mathematics – Probability
Scientific paper
Sep 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvd..36.1625n&link_type=abstract
Physical Review D (Particles and Fields), Volume 36, Issue 6, 15 September 1987, pp.1625-1633
Mathematics
Probability
30
Quark And Lepton Masses And Mixing
Scientific paper
An exact formula for the transition probability in level-crossing phenomena is derived for a general case, ranging from adiabatic to sudden crossings. This is done in the context of neutrino flavor oscillations for the Mikheyev-Smirnov-Wolfenstein (MSW) effect, where hitherto only numerical or approximate solutions were obtained. The matter density or level splitting is assumed to be governed by a hyperbolic-tangent function which, however, can change arbitrarily fast between two constant values. For example, in context of the MSW effect this furnishes a nice fit to the solar density determining the level crossing of solar neutrinos. In the quasiadiabatic limit the exact Landau-Zener factor can be read off, correcting some expressions obtained so far. Even in the opposite limit of a sudden level crossing a conversion is found, which can have far-reaching consequences for neutrino detection on Earth.
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