Trimaximal mixing with one texture zero from type II seesaw and $\Delta(54)$ family symmetry

TL;DR

This paper introduces a neutrino model based on $ ext{Δ}(54)$ symmetry and type II seesaw, predicting normal hierarchy, lower octant of atmospheric angles, and CP violation, with testable implications for future experiments.

Contribution

The model uniquely combines $ ext{Δ}(54)$ symmetry with a texture-zero neutrino mass matrix to explain current data and make novel testable predictions.

Findings

Only normal hierarchy is allowed.

CP violation is always present in the model.

Predicted effective Majorana mass $m_{ββ}$ is within reach of upcoming experiments.

Abstract

We propose a neutrino model based on a $\Delta(54)$ flavor symmetry suitable for explaining the current neutrino oscillation data. Neutrino masses arise from the type II seesaw mechanism where the $\Delta(54)$ field assignments has led to a simple neutrino mass matrix with one texture zero and which satisfies the magic symmetry consistent with the well-known trimaximal mixing matrix. We found interesting predictions concerning neutrino masses and mixing. In particular, only the normal neutrino mass hierarchy and the lower octant of the atmospheric angles are allowed in this model. The model predicts as well that the $CP$ conserving values for the Dirac $CP$ phase $\delta _{CP}$ are not allowed and thus, $CP$ is always violated in the neutrino sector. We have also investigated the sum of absolute neutrino masses from cosmological observations, the effective Majorana mass $m_{\beta \beta }$\ from neutrinoless double beta decay experiments, and the electron neutrino mass $m_{\beta }$\ from beta decays where we found that the obtained range of $m_{\beta \beta }$\ can be tested by several experiments in the near future.