Magnus Expansion and Three-Neutrino Oscillations in Matter

Abstract

We present a semi-analytical derivation of the survival probability of solar neutrinos in the three generation scheme, based on the Magnus approximation of the evolution operator of a three level system, and assuming a mass hierarchy among neutrino mass eigenstates. We have used an exponential profile for the solar electron density in our approximation. The different interesting density regions that appear throughout the propagation are analyzed. Finally, some comments on the allowed regions in the solar neutrino parameter space are addressed.Comment: RevTex4 style, 5 pages including 5 figures. Presented at Mexican School of Astrophysics 2002, Guanajuato, Mexico, 31 Jul - 7 Aug 2002. Final version to appear in the Proceedings of IX Mexican Workshop on Particles and Fields Physics Beyond the Standard Model, Colima Col. Mexico, November 17-22, 200