(Z ₂) ³ symmetry of the nontribimaximal pattern for the neutrino mass matrix

In view of the recent neutrino oscillation data pointing to a nonvanishing value for the smallest mixing angle (θ _z), we derive and find explicit realizations of the (Z ₂) ³ flavor symmetry which characterizes, for the neutrino mass matrix, uniquely a variant of the tripartite form, originally conceived to lead to the tribimaximal mixing with θ _z=0, so as to allow now for a nontribimaximal pattern with nonzero θ _z. We impose this flavor symmetry in a setting including the charged leptons and we see that it can make room, through higher-order terms involving new standard model singlet scalars, for the mass hierarchy of charged leptons. Moreover, within a type-I seesaw mechanism augmented with the flavor symmetry, certain patterns occurring in both the Dirac and the Majorana neutrino mass matrices can accommodate all types of mass hierarchies in the effective neutrino mass matrix, but no lepton/baryon asymmetry can be generated. Finally, we discuss how type-II seesaw mechanism, when supplemented with the flavor symmetry, could be used to interpret the observed baryon asymmetry through leptogenesis.