with $\xi=1$ ($\xi=1/2$). []{data-label="Fig:Br-htm"}](BRh350mA.eps "fig:"){width="8cm"}]{} (3,0.5)[(a)]{} (0,5.5)[$m_{A}^{}$ \[GeV\]]{} (6.8,1)[$\tan\beta$]{}

(7.8,6) (0,1)[![Contour plots of ${\rm Br}(h \rightarrow \tau^{\pm} \mu^{\mp})_{\text{max}}$, the possible maximal values for the branching ratio under the tau rare decay results, are shown (a) in the $\tan\beta$-$m_{A}$ plane and (b) in the $\tan\beta$-$\sin(\alpha-\beta)$ plane. The parameters are taken as the same as Figs. \[Fig:allowed-kappa\]-(a) and \[Fig:allowed-kappa\]-(b), respectively. 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"}](BRh350SinSq.eps "fig:"){width="7.8cm"}]{} (3,0.5)[(b)]{} (0,5.5)[$\sin^{2}(\alpha-\beta)$]{} (6.8,1)[$\tan\beta$]{}

In Figs. \[Fig:Br-htm\]-(a) and \[Fig:Br-htm\]-(b), contours of ${\rm Br}(h \rightarrow \tau^{\pm}\mu^{\mp})_{\text{max}}$, which is twice of ${\rm Br}(h \rightarrow \tau^{-}\mu^{+})_{\text{max}}$, are shown in the $\tan\beta$-$m_{A}^{}$ plane and in the $\tan\beta$-$\sin^{2}(\alpha-\beta)$ plane, respectively. The parameters are taken to be the same as those for Figs. \[Fig:allowed-kappa\]-(a) and \[Fig:allowed-kappa\]-(b), respectively; i.e., (a) $m_{h}^{} =120$ GeV, $m_{H}^{} = m_{H^{\pm}}^{} = 350$ GeV and $\sin(\alpha -\beta) = -0.9999$, and (b) $m_{h}^{} =120$ GeV and $m_{H}^{} = m_{A}^{} = m_{H^{\pm}}^{} = 350$ GeV, with $M$ to be scanned from 0 to 1000 GeV. We again show the excluded area from requirements of tree-level unitarity and vacuum stability as in the same way as Figs. \[Fig:allowed-kappa\]-(a) and \[Fig:allowed-kappa\]-(b). For low and moderate 