Breaking Tri-bimaximal Mixing and Large $\theta_{13}$

The long baseline neutrino experiment, T2K, and the reactor experiment, Double Chooz will soon present new data. If we expect $\sin\theta_{13}$ to be 0.1-0.2, which is close to the present experimental upper bound, we should not persist in the paradigm of the tri-bimaximal mixing. We discuss breaking the tri-bimaximal mixing by adding a simple mass matrix, which could be derived from some non-Abelian discrete symmetries. It is found that $\sin\theta_{13}=0.1-0.2$ is expected in our model independent analysis of the generalized mass matrix for the normal or inverted hierarchical neutrino mass spectrum. On the other hand, $\sin^2\theta_{23}$ and $\sin^2\theta_{12}$ are expected to be not far from 1/2 and 1/3, respectively. As a typical example, we also discuss the $A_4$ flavor model with the 1 and 1' flavons, which break the tri-bimaximal mixing considerably. In this modified version of the Altarelli and Feruglio model, $\sin\theta_{13}$ is predicted to be around 0.15 in the case of the normal hierarchical neutrino masses $m_3\gg m_2, m_1$, and 0.2 in the case of the inverted hierarchy $m_3\ll m_2, m_1$. The form of the neutrino mass matrix looks rather interesting --- it is suggestive of other discrete symmetries as well.