Neutrino masses and oscillations

"Submitted in partial fulfillment of the requirement for the Doctor of Philosophy degree in the Department of Physics and Astronomy at the College of Science, King Saud University", May. 2008In the standard model neutrinos are massless and lepton numbers are conserved. But current observations, based on neutrino oscillations, have provided strong evidence that they are massive and mixed. These findings suggest the necessity of going beyond the standard model. The available observations are, however, insufficient to provide full information about their masses and mixing parameters. This lack of information, and in the absence of a complete acceptable model, motivated proposing phenomenological mass matrices based on available data. There are several proposed mass matrices, in the literature, that attempt to fill out this gap. In this thesis several patterns of Majorana neutrino mass matrix consistent with present available observed data are proposed. These patterns are based on textures possessing two 2x2 submatrices with vanishing trace. This proposed condition can be considered as a non trivial generalization of the 1x1 zero texture condition proposed by Frampton, Glashow and Marfatia. Taking these matrices in pairs we obtain as they have obtained fifteen independent possibilities. Of these we find eight of them are phenomenologically acceptable on the base of the present available observed data. Analytical as well as numerical calculations are carried out for all these patterns. Estimates of neutrino masses and the effective electron neutrino mass as well as the effective mass factor of neutrinoless double beta decay are explicitly calculated. In this thesis we have made use of advanced computational computer programmes including Mathematica, Maple and Origin (10) to perform numerical calculations