| The origin of fermion masses and mixing and CP violation is the least understood aspect of the Standard Model (SM) of particle physics. In SM the fermion masses and mixing and CP violation are represented by three arbitrary 3 x 3 complex Yukawa matrices. Another relevant aspect is that the neutrinos are massless in the framework of SM, but recent experiments strongly indicate that they do have small but non-vanishing masses. Incorporating these into theory leads to an increase in the number of parameters. The aim of this dissertation is to reduce the number of parameters in the framework of a grand unified theory (GUT) combined with supersymmetry (SUSY) and family symmetry, and to gain a better understanding of the issues involved. This is realized in a realistic model based on supersymmetric SO(10) combined with a family symmetry SU(2). The symmetries in the model gives rise to various constraints on the Yukawa sector, and the number of parameters is reduced greatly. Neutrino masses are generated naturally due to the presence of three new particles, the right-handed neutrinos, each of which, along with the fermions of the SM, appears as a member of the 16-dimensional representation of SO(10). Higgs fields in the 126-dimensional representation are utilized to construct the Yukawa sector. As a consequence, R-parity is preserved at low energies, and symmetric mass textures arise from the left-right symmetry breaking chain of SO(10). With 11 input parameters, our model predicts 22 physical observable quantities, in good agreement with experimental observation. In the neutrino sector, we propose a new texture for the mass matrix, and our predictions are in good agreement with results from atmospheric neutrino experiments. Our model favors the LOW solution to the solar neutrino anomaly; the matrix element for neutrinoless double beta decay is highly suppressed. The leptonic analogue of the Jarlskog invariant is predicted to be of O(10-2). The observed mass hierarchy and mixing are explained by the two-step breaking of SU(2) family symmetry. |
