Obtaining nonvanishing $θ_{13}$ with constrained neutrino Yukawa matrix and implications for flavor model buildings

Abstract

Assuming a diagonal Majorana neutrino mass matrix, we investigate the neutrino Yukawa textures which lead to a non-zero reactor mixing angle $θ_{13}$. The neutrino effective coupling matrix $κ^{eff}$ is pre-diagonalized by a constant mixing pattern $V_ν$ with a vanishing $θ^ν_{13}$. The resulting pre-diagonal symmetrical matrix $κ$ is set to be four texture zeros with two types of off-diagonal elements nonzero, which is $κ_{13}$ and $κ_{23}$, respectively. With the expectation of simple textures we thoroughly classify the linear combinations, $α_{i}$, $β_{i}$ and $γ_{i}$ of Yukawa elements $λ_{ij}$ in a same row, according to the values vanishing or not. Each set of the classifications can lead to a Yukawa texture which may have implications for the discrete flavor model buildings. We also present a model based on $A_{4}$ according to one set of the constraints on the three combinations with a specific choice of a coefficient in Yukawa texture.