Obtaining nonvanishing ${\theta }_{13}$ 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 ${\theta }_{13}$. The neutrino effective coupling matrix ${\kappa }^{eff}$ is pre-diagonalized by a constant mixing pattern $V_{\nu }$ with a vanishing ${\theta }_{13}^{\nu }$. The resulting pre-diagonal symmetrical matrix $\kappa$ is set to be four texture zeros with two types of off-diagonal elements nonzero, which is ${\kappa }_{13}$ and ${\kappa }_{23}$, respectively. With the expectation of simple textures we thoroughly classify the linear combinations, ${\alpha }_i$, ${\beta }_i$ and ${\gamma }_i$ of Yukawa elements ${\lambda }_{ij}$ 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.

Comments: 10 pages, 2 tables, no figures