Neutrino Mixing and Discrete Symmetries

In this paper we discuss a new way to derive neutrino mixing patterns, which originates from the idea proposed in a recent article by Hernandez and Smirnov. Its applications to various cases are discussed. We first present the complete set of possible mixing patterns for the minimal case where unbroken residual symmetries of the Majorana neutrino and left-handed charged-lepton mass matrices obey some general assumptions that are also satisfied by many models based on discrete symmetries. We find that they are either well-known mixing patterns or phenomenologically disfavored ones. It shows clearly that, for full-mixing matrices to fit the mixing data with small or negligible corrections, it is necessary to go beyond the minimal scenario. We present an explicit formalism for a rather general nonminimal case. Some applications and phenomenological implications are discussed. Several new mixing patterns are derived.