Triple Higgs coupling effect on $h^0 \to b \bar b$ and $h^0 \to \tau^+ \tau^-$ in the 2HDM

We study the one loop electroweak radiative corrections to $h^0\to b\bar{b}$ and $h^0\to \tau^+\tau^-$ in the framework of two Higgs doublet Model(2HDM). We evaluate the deviation of these couplings from their Standard Model (SM) values. $h^0\to b\bar{b}$ and $h^0\to \tau^+\tau^-$ may receives large contribution from triple couplings $h^0H^0H^0$, $H^0h^0h^0$, $h^0A^0A^0$ and $h^0H^+H^-$ which are absent in the Standard Model. It is found that in 2HDM, these corrections could be significant and may reach more than 20\% for not tow heavy $H^0$ or $A^0$ or $H^\pm$. We also study the ratio of branching ratios $R=BR(h^0\to b\bar{b})/BR(h^0\to \tau^+\tau^-)$ of Higgs boson decays which could be used to disentangle SM from other models such as 2HDM.