Reduction of $SU_f(3)\supset SO(3)\supset A_4$ -- The scalar potential

TL;DR

This paper explores embedding the discrete symmetry A_4 within an SU_f(3) flavor symmetry, constructing scalar potentials to analyze spontaneous symmetry breaking along the full symmetry chain.

Contribution

It provides a detailed construction of quadratic and quartic scalar potentials respecting the SU_f(3) to A_4 symmetry chain and analyzes the resulting spontaneous symmetry breaking patterns.

Findings

Constructed scalar potentials consistent with the symmetry chain

Analyzed spontaneous symmetry breaking involving SU(3) octet scalars

Elucidated the embedding of A_4 within SU_f(3) symmetry

Abstract

We examine the possibility of the flavor symmetry being $SU_f(3)$ in which the phenomenologically successful discreet symmetry $A_4$ is embedded. The allowed quadratic and quartic potentials are constructed exploiting the full symmetry chain $SU(3)\supset SO(4)\supset A_4$. The spontaneous symmetry breaking involving the $SU(3)$ octet scalar fields is analyzed.