Minimal modifications to the Tri-Bimaximal neutrino mixing

TL;DR

This paper proposes a minimal modification to the Tri-Bimaximal neutrino mixing model to account for the observed large 3, introducing a new flavon field and flavor symmetries to realize the TM2 mixing with CP violation.

Contribution

It introduces a minimal extension of the TBM model by adding one flavon field and flavor symmetries to achieve TM2 mixing with CP violation.

Findings

A neutrino mass matrix for TM2 mixing is derived.

A flavor symmetry model realizing TM2 mixing with CP violation is constructed.

The model supports leptogenesis and can be extended to TM1 mixing.

Abstract

In light of the observation of a relatively large $\theta_{13}$, the ever popular Tri-Bimaximal (TBM) neutrino mixing which predicts a vanishing $\theta_{13}$ needs modifications. In this paper, we shall discuss the possibility of modifying it in a minimal way to fulfil this task. In the first part, a neutrino mass matrix with three independent parameters, which leads to the TM2 mixing, is obtained by analogy with that for the TBM mixing. In the second part, a model that can realize the TM2 mixing is constructed with flavor symmetries $A_4 \times U(1) \times Z_2 \times Z_2 \times Z_2$. It is the variant of a model that gives the TBM mixing, with only one more flavon field included. Furthermore, the imaginary vacuum expectation value (VEV) of this flavon breaks the imposed CP symmetry and results in $\theta_{23}=45^\circ$ and the maximal CP violation. This VEV is also helpful for providing a large enough CP asymmetry required by the leptogenesis mechanism. Besides, this model building approach can be generalized to the TM1 mixing in a straightforward way.