Horizontal Symmetries $\Delta(150)$ and $\Delta(600)$

TL;DR

This paper explores finite subgroups of SU(3), particularly $ abla(150)$ and $ abla(600)$, to model neutrino mixing angles, providing detailed analysis and proposing models that align with experimental data.

Contribution

It identifies $ abla(150)$ as capable of predicting neutrino mixing angles without free parameters and extends this to $ abla(600)$ for a more comprehensive model.

Findings

$ abla(150)$ predicts $ heta_{13}$ and $ heta_{23}$ consistent with experiments.

A model based on $ abla(600)$ matches the solar angle with experimental data.

Extension from $ abla(150)$ to $ abla(600)$ parallels known symmetry group extensions.

Abstract

Using group theory of mixing to examine all finite subgroups of SU(3) with an order less than 512, we found recently that only the group $\Delta(150)$ can give rise to a correct reactor angle $\th_{13}$ of neutrino mixing without any free parameter. It predicts $\sin^22\th_{13}=0.11$ and a sub-maximal atmospheric angle with $\sin^22\th_{23}=0.94$, in good agreement with experiment. The solar angle $\th_{12}$, the CP phase $\d$, and the neutrino masses $m_i$ are left as free parameters. In this article we provide more details of this case, discuss possible gain and loss by introducing right-handed symmetries, and/or valons to construct dynamical models. A simple model is discussed where the solar angle agrees with experiment, and all its mixing parameters can be obtained from the group $\Delta(600)$ by symmetry alone. The promotion of $\Delta(150)$ to $\Delta(600)$ is on the one hand analogous to the promotion of $S_3$ to $S_4$ in the presence of tribimaximal mixing, and on the other hand similar to the extension from $A_4$ to $S_4$ in that case.