Nonzero $\theta_{13}$ and Neutrino Masses from Modified Neutrino Mixing Matrix

TL;DR

This paper modifies traditional neutrino mixing matrices to accommodate the observed nonzero $ heta_{13}$ angle and explores resulting neutrino mass textures, finding some models compatible with experimental data while others are not.

Contribution

It introduces modified neutrino mixing matrices that can explain the nonzero $ heta_{13}$ and investigates their implications for neutrino mass textures and hierarchies.

Findings

Modified BM and DC matrices fit experimental $ heta_{13}$ data.

Modified TB matrix predicts too large $ heta_{13}$.

Certain two-zero textures can produce realistic neutrino mass differences.

Abstract

The nonzero and relatively large $\theta_{13}$ have been reported by Daya Bay, T2K, MINOS, and Double Chooz Collaborations. In order to accommodate the nonzero $\theta_{13}$, we modified the tribimaximal (TB), bimaxima (BM), and democratic (DC) neutrino mixing matrices. From three modified neutrino mixing matrices, two of them (the modified BM and DC mixing matrices) can give nonzero $\theta_{13}$ which is compatible with the result of the Daya Bay and T2K experiments. The modified TB neutrino mixing matrix predicts the value of $\theta_{13}$ greater than the upper bound value of the latest experimental results. By using the modified neutrino mixing matrices and impose an additional assumption that neutrino mass matrices have two zeros texture, we then obtain the neutrino mass in normal hierarchy when $(M_{\nu})_{22}=(M_{\nu})_{33}=0$ for the neutrino mass matrix from the modified TB neutrino mixing matrix and $(M_{\nu})_{11}=(M_{\nu})_{13}=0$ for the neutrino mass matrix from the modified DC neutrino mixing matrix. For these two patterns of neutrino mass matrices, either the atmospheric mass squared difference or the solar mass squared difference can be obtained, but not both of them simultaneously. From four patterns of two zeros texture to be considered on the obtained neutrino mass matrix from the modified BM neutrino mixing matrix, none of them can predict correctly neutrino mass spectrum (normal or inverted hierarchy).