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

Abstract

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 $B(b\to s\gamma )$ and the other from the recent LEP data on ${\epsilon }_b$. We have included one-loop vertex corrections to $Z\to b\overline{b}$ through ${\epsilon }_b$ in the model. We find that the new ${\epsilon }_b$ constraint excludes most of the less appealing window $\tanβ\lsim 1$ at $90\%$C.~L. for $m_t=150\GeV$. We also find that although $b\to s\gamma$ constraint is stronger for $\tan \beta >1$, ${\epsilon }_b$ constraint is stronger for $\tanβ\lsim 1$, and therefore these two are the strongest and complimentary constraints present in the charged Higgs sector of the model.

LATEX, 9 Pages+1 Figure, the Figure available upon request as a Postscript file, CTP-TAMU-69/93

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