Derivation of Novel analytic Expression for three Neutrino Oscillations in Matter

Abstract

Neutrino physics has been an active and successful research field in recent years, especially experimentally. As a result of a series of great experimental discoveries neutrino oscillations are today a well established phenomenon indicating non vanishing neutrino masses. If all the existing evidences of oscillation, coming from the atmospheric and the solar neutrino experiments and the laboratory experiment LSND, are described jointly, at least four neutrino flavors are needed. The fourth flavor must be sterile with respect to the Standard Model interactions since experiments show that only three neutrino flavors couple to the Z-boson and we discuss oscillations of atmospheric and solar neutrinos into sterile neutrinos in the 2+2 scheme. To invalidate the 2+2 model, a global fit to data with the small mixing angles included seems to be required. In this thesis various phenomenological aspects of sterile neutrinos have been investigated. The lightness of the sterile neutrino, required by the oscillation data, is a challenging problem for theoretical model building. In this thesis some of the most important present and future neutrino experiments are described.It is shown that neutrino oscillations can exist if the neutrino has mass and mixes. We derive analytic expressions for three flavor neutrino oscillations in the presence of matter in the plane wave approximation using the Cayley Hamilton formalism. Especially, we calculate the time evolution operator in both flavor and mass bases. Furthermore, we find the transition probabilities, matter mass squared differences, and matter mixing angles all expressed in terms of the vacuum mass squared differences, the vacuum mixing angles, and the matter density. The conditions for resonance in the presence of matter are also studied in some examples.