$b\to s\gamma$ and ${ϵ}_b$ Constraints on Two Higgs Doublet Model

We perform a combined analysis of two stringent constraints on the 2 Higgs doublet model, one coming from the recently announced CLEO II bound on $B(b \rightarrow s \gamma)$andtheotherfromtherecentLEPdataon$\epsilon_b$. We have included one-loop vertex corrections to $Z\to b\bar{b}$ through ${ϵ}_b$ in the model. We find that the new ${ϵ}_b$ constraint excludes most of the less appealing window $\tan \beta \text{lsim}1$ at $90\mathrm{\%}$C.~L. for $m_t=150\text{GeV}$. We also find that although $b\to s\gamma$ constraint is stronger for $\tan \beta >1$, ${ϵ}_b$ constraint is stronger for $\tan \beta \text{lsim}1$, and therefore these two are the strongest and complimentary constraints present in the charged Higgs sector of the model.