Higgs bosons decay into bottom-strange in two Higgs Doublets Models

We analyze the decays $\{h^0,H^0,A^0\}\to \bar{s}b$ within two Higgs Doublet Models with Natural Flavor Conservation (2HDM) type I and II. It is found that the Higgs bosons decay into bottom-strange can lead to a branching ratio in the range $10^{-5}\to 10^{-3}$ for small $\tan\beta \approx 0.1\to 0.5$ and rather light charged Higgs in the 2HDM type I. When $\tan\beta \ga 1$, one can easily reach a branching ratio of the order $10^{-5}$. In 2HDM type II, without imposing $b\to s\gamma$ constraint, the situation is the same as in 2HDM type I. If $b\to s\gamma$ constraint on charged Higgs mass ($M_{H\pm}\geq 350$ GeV) is imposed, we obtain $Br(h^0 \to \bar{s}b)$ in the range $10^{-5}$--$10^{-6}$. A comparison between the rates of $h^0\to \bar{s}b$ and $h^0\to \gamma \gamma$ is made. It is found that in the fermiophobic scenario, $h^0\to \gamma \gamma$ is still the dominant decay mode.