A4-based see-saw model for realistic neutrino masses and mixing

TL;DR

This paper proposes an $A4$-based neutrino mass model combining see-saw mechanisms, explaining small mixing parameters and mass splittings, and predicting specific neutrino mass orderings and CP-violation scenarios.

Contribution

The model uniquely combines Type-II and Type-I see-saw mechanisms within an $A4$ symmetry framework to naturally produce observed neutrino mixing angles and mass splittings.

Findings

Type-II see-saw dominates, setting $ heta_{23} = rac{ ext{ extpi}}{4}$

Type-I see-saw acts as a perturbation to generate correct $ heta_{12}$ and $ heta_{13}$

Model favors normal mass ordering with large CP-phase $ o ext{ extpi}/2$

Abstract

We present an $A4$-based model where neutrino masses arise from a combination of see-saw mechanisms. The model is motivated by several small mixing and mass parameters indicated by the data. These are $\theta_{13}$, the solar mass splitting, and the small deviation of $\theta_{23}$ from maximal mixing (= $\pi/4$). We take the above as indications that at some level the small quantities are well-approximated by zero. In particular the mixing angles, to a zero order, should be either 0 or $\pi/4$. Accordingly, in this model the Type-II see-saw dominates and generates the larger atmospheric mass splitting and sets $\theta_{23} = \pi/4$. The other mixing angles are vanishing as is the solar splitting. We show how the $A4$ assignment for the lepton doublets leads to this form. We also specify the $A4$ properties of the right-handed neutrinos which result in a smaller Type-I see-saw contribution that acts as a perturbation and shifts the angles $\theta_{12}$ and $\theta_{13}$ into the correct range and the desired value of $\Delta m^2_{solar}$ is produced. The $A4$ symmetry results in relationships between these quantities as well as with a small deviation of $\theta_{23}$ from $\pi/4$. If the right-handed neutrino mass matrix, $M_R$, is chosen real then there is no leptonic CP-violation and only Normal Ordering is admissible. If $M_R$ is complex then Inverted Ordering is also allowed with the proviso that the CP-phase, $\delta$, is large, i.e., $\sim \pi/2$ or $-\pi/2$. The preliminary results from NO$\nu$A favouring Normal Ordering and $\delta$ near $-\pi/2$ imply quasi-degenerate neutrino masses in this model.