Model of leptons from $SO(3) \to A_4$

TL;DR

This paper proposes a model where the $A_4$ symmetry, used to explain lepton masses and mixing, arises from spontaneous symmetry breaking of the continuous group SO(3).

Contribution

It introduces a novel mechanism for deriving $A_4$ symmetry from SO(3) via spontaneous breaking, providing a theoretical foundation for lepton sector models.

Findings

$A_4$ symmetry can originate from SO(3) breaking.

The model explains lepton masses and mixing angles.

Spontaneous symmetry breaking mechanism is demonstrated.

Abstract

The lepton sector masses and mixing angles can be explained in models based on $A_4$ symmetry. $A_4$ is a non-Abelian discrete group. Therefore, one issue in constructing models based on it is explaining the origin of $A_4$. A plausible mechanism is that $A_4$ is an unbroken subgroup of a continuous group that is broken spontaneously. We construct a model of leptons where the $A_4$ symmetry is obtained by spontaneous symmetry breaking of SO(3).