and (b) $m_{h}^{} =120$ GeV and $m_{H}^{} = m_{A} = m_{H^{\pm}} = 350$ GeV. The remaining parameter $M$ is scanned from 0 to 1,000 GeV. 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:allowed-kappa"}](kappa350mA.eps "fig:"){width="8cm"}]{} (0,5.5)[$m_{A}^{}$ \[GeV\]]{} (6.8,1)[$\tan\beta$]{} (3,0.5)[(a)]{}

(7.8,6) (0,1)[![ Contours of $|\kappa^{\text{max}}_{32}|^{2}$, the possible maximal value of $|\kappa_{32}|^{2}$ from the rare tau decay results, are shown (a) in the $\tan\beta$-$m_{A}$ plane and (b) in the $\tan\beta$-$\sin^{2}(\alpha-\beta)$ plane. The parameters are taken to be (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. The remaining parameter $M$ is scanned from 0 to 1,000 GeV. 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:allowed-kappa"}](kappa350SinSq.eps "fig:"){width="7.8cm"}]{} (0,5.6)[$\sin^{2}(\alpha-\beta)$]{} (7,1)[$\tan\beta$]{} (3,0.5)[(b)]{}

In Figs. \[Fig:allowed-kappa\]-(a) and \[Fig:allowed-kappa\]-(b), contour plots for $|\kappa_{32}^{\text{max}}|^{2}$ are shown under the rare tau decay results in the $\tan\beta$-$m_{A}$ plane and the $\tan\beta$-$\sin^{2}(\alpha-\beta)$ plane, respectively. The combined excluded region from the theoretical conditions of vacuum stability and pertrbative unitarity is indicated by the 