Bilarge Neutrino Mixing and Abelian Flavor Symmetry

Understand

We explore two bilarge neutrino mixing anz$\ddot{a}$tze within the context of Abelian flavor symmetry theories: ($\mathrm{\tt BL_1}$) $\sin\theta_{12}\sim\lambda$, $\sin\theta_{13}\sim\lambda$, $\sin\theta_{23}\sim\lambda$, and ($\mathrm{\tt BL_2}$) $\sin\theta_{12}\sim\lambda$, $\sin\theta_{13}\sim\lambda$, $\sin\theta_{23}\sim 1-\lambda$.

• 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 $U(1)\times Z_2$.