We explore two bilarge neutrino mixing Anzätze within the context of Abelian flavor symmetry theories: (${\mathtt{B}\mathtt{L}}_{\mathtt{1}}$) $\sin {\theta }_{12}\sim \lambda$, $\sin {\theta }_{13}\sim \lambda$, $\sin {\theta }_{23}\sim \lambda$, and (${\mathtt{B}\mathtt{L}}_{\mathtt{2}}$) $\sin {\theta }_{12}\sim \lambda$, $\sin {\theta }_{13}\sim \lambda$, $\sin {\theta }_{23}\sim 1-\lambda$. The first pattern is proposed by two of us and is favored if the atmospheric mixing angle ${\theta }_{23}$ lies in the first octant, while the second one is preferred for the second octant of ${\theta }_{23}$. In order to reproduce the second texture, we find that the flavor symmetry should be $U(1)\times Z_m$, while for the first pattern the flavor symmetry should be extended to $U(1)\times Z_m\times Z_n$ with $m$ and $n$ of different parity. Explicit models for both mixing patterns are constructed based on the flavor symmetries $U(1)\times Z_3\times Z_4$ and $U(1)\times Z_2$. The models are extended to the quark sector within the framework of $SU(5)$ grand unified theory in order to give a successful description of quark and lepton masses and mixing simultaneously. Phenomenological implications are discussed.

• Received 15 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.053013