Upper Bound on R_b in Two Higgs Doublet Model from Lepton Universality

It has been known that $R_b$ can be enhanced in the two Higgs doublet model if $\tan \beta$ is large. We point out that a similar enhancement in $\Gamma(Z \to \tau^+ \tau^-)$ is large enough to place a constraint on such a possibility. We obtain a 95% CL upper bound $\mathrm{\Delta }{R}_b\mathrm{/}{R}_b<0.73$ in this model for the $\overline{MS}$ mass $m_b(m_Z)=3.0$ GeV. The 1996 world average is $\mathrm{\Delta }{R}_b\mathrm{/}{R}_b$ = $0.97$. We used the $m_b(m_Z)$ to determine the bottom Yukawa coupling instead of $m_b(m_b)$ unlike in previous analyses, and also an improved experimental test of the lepton universality in $Z$ decay, which made our results qualitatively different.