$M=0$ (Fig. \[Fig:Br-Htm\]-(c)), the allowed region is limited only the area of around $\tan\beta \sim 1$ and $m_\Phi^{} \lesssim 600$ GeV.

The extra Higgs bosons ($H$, $A$ and $H^\pm$) are expected to be searched at the LHC. The signal of $gg \to H/A \to \tau^\pm \mu^\mp$ may be detectable at LHC with high luminosity (100 ${\rm fb}^{-1}$) when ${\rm Br}(H/A \to \tau^\pm\mu^\mp)$ is greater than $10^{-2}$ for $m_{H/A}^{} \sim 350$ GeV and $\tan\beta=45$[@Assamagan]. However the rate is rapidly reduced for smaller values of $\tan\beta$ and for larger values of $m_{H/A}^{}$. Further feasibility study is necessary.

Search for LFV decays of Higgs bosons at a Linear Collider
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=0.6cm

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=0.6cm

(10,8) (1,1)[(1,3)[1]{}]{} (1,7)[(1,-3)[1]{}]{} (2,4)(0.5,0)[3]{}[ (0,0)(0.125,0.25)(0.25,0) (0.25,0)(0.375,-0.25)(0.5,0)]{} (3.5,4) (4.15,5.4) (4.15,5.4) (3.5,4)(0.5,0)[5]{}[(1,0)[0.3]{}]{} (6,4)[(1,3)[1]{}]{} (6,4)[(1,-3)[1]{}]{} (6.42,5.3) (6.42,5.3) (6.4,2.8) (6.4,2.8) (2,4) (3.5,4) (6,4) (4.15,5.4) (6.4,2.75) (6.47,5.4) (1.5,2.5)[(1,3)[0]{}]{} (1.505,5.5)[(-1,3)[0]{}]{} (6.15,3.5)[(-1,3)[0]{}]{} (6.35,5)[(1,3)[0]{}]{} (4.16,6.5)[(0,-1)[0]{}]{} (4.82,6.5)[(2,3)[0]{}]{} (6.85,6.5)[(1,3)[0]{}]{} (7.4,6.25)[(1,1)[0]{}]{} (7.4,5.75)[(-2,-1)[0]{}]{} (6.655,2)[(-1,3)[0]{}]{} (6.41,1.6)[(0,1)[0]{}]{} (5.8,1.745)[(-2,-3)[0]{}]{} (0.3,0.3)[$e^{-}$]{} (0.3,7.2)[$e^{+}$]{} (2.5,3)[$Z^{*}$]{} (3,4.5)[$Z$]{} (4.5,3)[$h^{0}$]{} (6.8,7.2)[$\nu_{\tau}$]{} (6.5,4.5)[$\tau^{-}$]{} (6.5,3)[$\tau^{+}$]{} (6.85,0.55)[$\mu^{+}$]{} (6,0.35)[$\bar{\nu}_{\mu}$]{} (5,0.5)[$\nu_{\tau}$]{} (8,6.5)[$\tau$-decay]{} (3.5,7.4)[$Z$-decay]{} (3.5,-0.5)[(b)]{}

Let us consider the 