Copositivity criteria, scalar mass eigenstates, and custodial symmetry parameter $\Delta \rho$ for the $S_3 \otimes \mathbb{Z}_2$ model

TL;DR

This paper derives stability criteria, analyzes scalar mass eigenstates, and calculates the custodial symmetry parameter $ ho$ in an $S_3  \u2297 _Z_2$ scalar model, connecting theoretical conditions with phenomenological implications.

Contribution

It provides the copositivity conditions for the scalar potential, identifies the Higgs among scalar eigenstates, and computes the $ ho$ parameter within this specific model.

Findings

Copositivity criteria for the scalar potential established.

Scalar mass eigenstates identified, including the SM Higgs.

Calculated the $ ho$ parameter related to custodial symmetry.

Abstract

We present the copositivity criteria for the scalar sector of our $S_3 \otimes \mathbb{Z}_2$ model, which ensures that it is bounded from below. We also show the scalar mass eigenstates, and identify the Standard Model Higgs boson among these by imposing that its Yukawa couplings are the same in our model and the Standard Model. The $\Delta \rho$ parameter, related to the custodial symmetry, is calculated as well.