conditions of vacuum stability and perturbative unitarity. Notice that couplings of $H$ are similar to those of $A$ for $\sin(\alpha-\beta)=-1$ where there are no $HVV$ couplings. Hence we show the results only for the LFV decays of $H$ below. In a general case, the branching ratio of $H \to \tau^\pm \mu^\mp$ tends to be smaller than that of $A \to \tau^\pm \mu^\mp$ due to the contribution from the modes $H \to VV$.

(7.8,7) (0,1)[![ Contour plots of ${\rm Br}(H \rightarrow \tau^{\pm} \mu^{\mp})_{\text{max}}$ are shown in the $\tan\beta$-$m_{\Phi}^{}$ plane ($m_\Phi^{}\equiv m_H^{}=m_A^{}=m_{H^\pm}^{}$) for $m_h^{}=120$ GeV and $\sin(\alpha-\beta)=-1$ with (a) $M=m_\Phi^{}$, (b) $M=m_\Phi^{}/\sqrt{2}$, and (c) $M=0$. The dark (light) shaded area indicates the excluded region by the theoretical requirements of vacuum stability and perturbative unitarity with $\xi=1$ ($\xi=1/2$). []{data-label="Fig:Br-Htm"}](BrHunit.eps "fig:"){width="5.14cm"}]{} (2,0.5)[(a)]{} (0,4.6)[$m_{\Phi}^{}$ \[GeV\]]{} (4,0.7)[$\tan\beta$]{}

(7.8,7) (0.24,1)[![ Contour plots of ${\rm Br}(H \rightarrow \tau^{\pm} \mu^{\mp})_{\text{max}}$ are shown in the $\tan\beta$-$m_{\Phi}^{}$ plane ($m_\Phi^{}\equiv m_H^{}=m_A^{}=m_{H^\pm}^{}$) for $m_h^{}=120$ GeV and $\sin(\alpha-\beta)=-1$ with (a) $M=m_\Phi^{}$, (b) $M=m_\Phi^{}/\sqrt{2}$, and (c) $M=0$. The dark (light) shaded area indicates the excluded region by the theoretical requirements of vacuum stability and perturbative unitarity with $\xi=1$ ($\xi=1/2$). []{data-label="Fig:Br-Htm"}](BrHsqrt2.eps "fig:"){width="4.58cm"}]{} (2,0.5)[(b)]{} (4,0.7)[$\tan\beta$]{}

(7.8,7) (0,1)[![ Contour plots of ${\rm Br}(H \rightarrow \tau^{\pm} \mu^{\mp})_{\text{max}}$ are shown 