Phenomenology of the discrete symmetry approach to neutrino mixing and leptonic CP violation
The problem of understanding the origin of the observed pattern of neutrino mixing and, more generally, the origin of (lepton) flavour is among the biggest problems in particle physics. 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. 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 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 to highly symmetric mixing patterns. These corrections are required to reconstitute compatibility of these patterns with experimental data. 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 matrix 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.