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

TL;DR

This paper explores specific neutrino Yukawa matrix textures that produce a non-zero reactor angle, classifies these textures, and discusses their implications for flavor model building, including an $A_4$-based model.

Contribution

It introduces a classification scheme for neutrino Yukawa textures with four zeros and non-zero off-diagonal elements, and constructs an $A_4$ flavor model based on these textures.

Findings

Identified textures that generate non-zero $ heta_{13}$

Classified Yukawa textures based on zero and non-zero elements

Developed an $A_4$ flavor model consistent with the textures

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 $\theta^{\nu}_{13}$. 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.