General Neutrino Mass Matrix Patterns and Its Underlying Family Symmetries

Based on current experimental results, such as neutrino oscillations and the neutrinoless double beta decays (i.e. data from Super Kamiokande, KamLAND, SNO, etc.), the neutrino mixing matrix can be adequately determined. Though there are still certain parameters that have possibility limits, but based on the current experimental results it is possible to construct a general form of neutrino mass matrix. Starting from this general form of the neutrino mass matrix we put certain conditions in the context of the seesaw mechanism model to determine the possible pattern of the neutrino mass matrix that has a texture zero. From the obtained neutrino mass matrix pattern, there are three class of patterns, where two of the class are known to be realized in literature by the underlying family symmetries of the $D_{4}$ and $A_{4}$ groups, the dihedral and tetrahedral symmetry groups.