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We investigate the Majorana neutrino mass matrix $M_{ u}$ with one parameter in the context of two texture zeros and its symmetry realization by non-Abelian discrete symmetry. From numerical calculation, we confirm that the textures $(M_{ u})_{11,12}=0$ and $(M_{ u})_{11,13}=0$ are consistent with the current experimental constraints, and show the correlations between non-zero elements of $M_{ u}$. The ratios of non-zero elements of $M_{ u}$ are constrain in small regions, and we find simple examples of $M_{ u}$ with one real mass parameter. We also discuss symmetry realization of the mass matrix by the type-II seesaw mechanism based on the binary icosahedral symmetry $A_5$ .
Using the seesaw mechanism, we construct a model for the light-neutrino Majorana mass matrix which yields trimaximal lepton mixing together with maximal CP violation and maximal atmospheric-neutrino mixing. We demonstrate that, in our model, the ligh
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The residual symmetry approach, along with a complex extension for some flavor invariance, is a powerful tool to uncover the flavor structure of the $3times3$ neutrino Majorana mass matrix $M_ u$ towards gaining insights into neutrino mixing. We util
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