Bilarge Neutrino Mixing and Abelian Flavor Symmetry

Abstract

We explore two bilarge neutrino mixing anz$\ddot{a}$tze within the context of Abelian flavor symmetry theories: ($\mathrm{\tt BL_1}$) $\sinθ_{12}\simλ$, $\sinθ_{13}\simλ$, $\sinθ_{23}\simλ$, and ($\mathrm{\tt BL_2}$) $\sinθ_{12}\simλ$, $\sinθ_{13}\simλ$, $\sinθ_{23}\sim 1-λ$. The first pattern is proposed by two of us and is favored if the atmospheric mixing angle $θ_{23}$ lies in the first octant, while the second one is preferred for the second octant of $θ_{23}$. 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.