Deviations from Tribimaximal Neutrino Mixing using a Model with $\Delta(27)$ Symmetry

TL;DR

This paper proposes a neutrino mixing model based on the $ ext{Δ}(27)$ symmetry that naturally explains the non-zero reactor angle and predicts an inverted mass hierarchy with potential observable CP violation effects.

Contribution

The model introduces a circulant-plus-diagonal mass matrix structure within the $ ext{Δ}(27)$ symmetry framework, accounting for deviations from tribimaximal mixing and predicting specific neutrino mass and CP phase values.

Findings

Predicts inverted neutrino mass hierarchy.

Identifies two solutions with different CP phases and lightest neutrino masses.

Suggests large CP violation effects are observable in future experiments.

Abstract

We present a model of neutrino mixing based on the flavour group $\Delta(27)$ in order to account for the observation of a non-zero reactor mixing angle ($\theta_{13}$). The model provides a common flavour structure for the charged-lepton and the neutrino sectors, giving their mass matrices a `circulant-plus-diagonal' form. Mass matrices of this form readily lead to mixing patterns with realistic deviations from tribimaximal mixing, including non-zero $\theta_{13}$. With the parameters constrained by existing measurements, our model predicts an inverted neutrino mass hierarchy. We obtain two distinct sets of solutions in which the atmospheric mixing angle lies in the first and the second octants. The first (second) octant solution predicts the lightest neutrino mass, $m_3 \sim 29~\text{meV}$ ($m_3 \sim 65~\text{meV}$) and the $CP$ phase, $\delta_{CP} \sim -\frac{\pi}{4}$ ($\delta_{CP} \sim \frac{\pi}{2}$), offering the possibility of large observable $CP$ violating effects in future experiments.