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 $\Delta R_b/R_{ b} < 0.73%$ in this model for the $\overline{ MS}$ mass $m_{ b} (m_{ Z}) = 3.0$ GeV. The 1996 world average is $\Delta R_{ b}/R_{ b}$ = $0.97% \pm 0.51%$. 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.
Categories: hep-ph