Phenomenology of the Discrete Symmetry Approach to Neutrino Mixing and Leptonic CP Violation

The discovery of neutrino oscillations caused by non-zero neutrino masses and neutrino mixing opened new field of research in particle physics. The impressive experimental progress made in the last two decades allowed to measure neutrino oscillation parameters with a relatively high precision. However, in spite of the experimental progress, the mechanism of neutrino mass generation as well as the dynamics behind the peculiar pattern of neutrino mixing which emerged from the experimental data remain currently unknown. The present PhD thesis is devoted to the problem of understanding the origin of the observed pattern of neutrino mixing and, more generally, the origin of (lepton) flavour. Our particular focus is on predictions for leptonic CP violation, since the status of CP symmetry in the lepton sector is also unknown at the moment. Driven by the measured values of the neutrino mixing parameters, we adopt symmetry approach to neutrino mixing, based on the assumption of existence of a (lepton) flavour symmetry described by a non-Abelian finite (discrete) group. At low energies this symmetry is broken down to residual symmetries of the charged lepton and neutrino mass matrices. The residual symmetries correspond to Abelian subgroups of the original flavour symmetry group. The most distinct feature of the discrete symmetry approach is correlations between the neutrino mixing angles and the CP violation phases present in the neutrino mixing matrix. These correlations are referred to as neutrino mixing sum rules. We first consider all types of the residual symmetries for which such correlations are expected and derive the corresponding sum rules for the Dirac CP violation phase. Using the derived sum rules, we obtain predictions for the Dirac phase in the cases of several discrete flavour symmetries. Further, we concentrate on a scenario in which the main contribution to neutrino mixing comes from the neutrino sector and explore in a systematic way possible charged lepton corrections. These corrections are required to reconstitute compatibility of highly symmetric mixing patterns, such as, for instance, tri-bimaximal mixing, with the experimental data. Again, our main focus is on leptonic Dirac CP violation. In a number of phenomenologically interesting cases, we perform a statistical analysis of the predictions for the Dirac phase, using (i) the results of the global analysis of neutrino oscillation data and (ii) the prospective uncertainties on the neutrino mixing angles. Next, we derive sum rules for the Majorana phases, which are present in the neutrino mixing matrix if massive neutrinos are Majorana particles. We demonstrate how generalised CP invariance of the neutrino Majorana mass term constrains the Majorana phases and obtain predictions for the effective Majorana mass in neutrinoless double beta decay. Finally, we investigate the impact of renormalisation group corrections on the sum rule predictions for the Dirac phase in the cases of the neutrino Majorana mass term generated by the Weinberg (dimension 5) operator added to (i) the Standard Model and (ii) the Minimal Supersymmetric Standard Model