Zero textures and vanishing minor in neutrino mass models and their minimal symmetry realization.

We have made a systematical texture study on some neutrino mass models (Singh¹ et al., 2002; Singh² et al., 2002) which are based on diagonal charged lepton mass matrices (M_l) and Dirac neutrino mass matrices (M_D). We investigate the zero textures of the Majorana mass matrix (M_R). Interestingly we find that all the M_R’s corresponds to only one zero textures. We also observe that the one zero texture of M_R propagate to the left-handed neutrino mass matrices as their vanishing minors. We perform a minimal realization of the textures under the context of an Abelian symmetric group. However in doing so, we have extended the SM to include some SU(2) singlet scalar.