# On ${\bf Q}_{6}$ flavor symmetry and the breaking of $\mu \leftrightarrow \tau$ symmetry

## TL;DR

This paper explores how a ${f Q}_{6}$ flavor symmetry model with broken $ au
ightarrow au$ symmetry can explain neutrino masses and mixing angles, favoring an inverted or degenerate hierarchy and making testable predictions for neutrinoless double beta decay.

## Contribution

It introduces a ${f Q}_{6}$ flavored supersymmetric model with a specific symmetry breaking mechanism affecting neutrino mixing, providing predictions consistent with experimental data.

## Key findings

- Normal hierarchy is discarded in this model.
- Inverted and degenerate hierarchies fit the data well.
- Predictions for neutrino mass scale and neutrinoless double beta decay are made.

## Abstract

In the simplest version of a $\mathbf{Q}_{6}$ flavored supersymmetric model, we analyze the leptonic masses and mixings in the framework of a soft breaking of the $\mu \leftrightarrow \tau$ symmetry. This breaking is controlled by the inequality $m_{e\tau}\neq m_{e\mu}$ in the effective neutrino mass. As a consequence of this breaking, the reactor and atmospheric angle are deviate from $0^{\circ}$ and $45^{\circ}$, respectively. Such deviations can be enhanced or suppressed by the CP parities in the Majorana phases, so that an analytic study is carried out to remark their importance to constrain the free parameters that accommodate the mixing angles. The normal hierarchy is completely discarded in this model, the inverted hierarchy is less favored than the degenerate one where the reactor and atmospheric angles are in good agreement with the experimental data. Additionally, the model predicts defined regions for the effective neutrino mass decay, the neutrino mass scale and the sum of the neutrino mass in the inverted and degenerate mass spectrum. Thus, this model may be testable by future experiments that focus in neutrinoless double beta decay.