matrices, they correspond to two CP-even ($h$ and $H$), a CP-odd ($A$), and a pair of charged ($H^{\pm}$) Higgs bosons. We define such that $h$ is lighter than $H$. The eight real parameters $m_{1-3}^{2}$ and $\lambda_{1-5}$ can be described by the same number of physical parameters; i.e., the vacuum expectation value $v$ $(\simeq 246$ GeV), the Higgs boson masses $m_{h}^{}, m_{H}^{}, m_{A}^{}$ and $m_{H^{\pm}}^{}$, the mixing angle $\alpha$ between the CP-even Higgs bosons, the ratio $\tan \beta$ ($ \equiv \langle \Phi^{0}_{2} \rangle / \langle \Phi^{0}_{1}
\rangle$) of the vacuum expectation values for two Higgs doublets, and the soft-breaking scale $M$ ($\equiv \sqrt{m_{3}^{2}/\sin\beta
\cos\beta}$) for the discrete symmetry. The quartic couplings are expressed in terms of physical parameters in Ref. [@smlike2]

Parameters of the Higgs sector are constrained from requirements of theoretical consistencies and also from the current experimental results. We here take into account two kinds of theoretical conditions; i.e., vacuum stability[@VS] and perturbative unitarity[@PU-1; @PU-2] at the tree level. The condition for tree-level unitarity, which we employ in Refs. [@PU-2; @smlike2], is described as $\left|\langle \phi_{3} \phi_{4}  
| a^{0}  | \phi_{1} \phi_{2} \rangle   \right|
< \xi, $ where $\langle \phi_{3} \phi_{4}  |a^{0}  | \phi_{1} \phi_{2} \rangle $ is the 