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

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 $\mathrm{\Delta }\rho$ parameter, related to the custodial symmetry, is calculated as well.