Mass Matrix Model Broken From A4 To 2 $\leftrightarrow$ 3 Symmetry

TL;DR

This paper explores how breaking the $A_4$ symmetry to a $2\leftrightarrow 3$ symmetry results in specific mass matrix structures with vanishing (1,1) components, relevant for GUT models.

Contribution

It introduces a mass matrix model with $2\leftrightarrow 3$ symmetry derived from $A_4$ breaking, highlighting its group theoretical basis in GUT frameworks.

Findings

Mass matrices exhibit $2\leftrightarrow 3$ symmetry with zero (1,1) component.

Breaking $A_4$ leads to a specific mass matrix form.

The model has implications for GUT symmetry structures.

Abstract

2$\leftrightarrow$3 symmetry is realized by the breaking from alterating group of degree 4 ($A4$) symmetry. $A4$ explains why the generation number is three. However the mass matrices are realized in the form of the breaking to $2\leftrightarrow 3$ symmetry $\times Z_3$, which leads us to $2\leftrightarrow 3$ symmetric mass matrix with vanishing (1,1) component. Thus the $3\times 3$ mass matrix model with $2\leftrightarrow 3$ symmetry and vanishing (1,1) component has the group theoretical background as the symmetry in GUT model.