The heavy top quark in the two Higgs doublet model

Constraints on the two Higgs doublet model are presented, assuming a top mass of 174 $\pm$ 17 GeV. We concentrate primarily on the ``type II'' model, where up--type quarks receive their mass from one Higgs doublet, and down--type quarks receive their mass from the second doublet. High energy constraints derived from the $W$ mass, the full width of the $Z$ and the $b \bar b$ partial width of the $Z$ are combined with low energy constraints from $\Gamma(b\to s \gamma)$, $\Gamma(b \to c \tau \bar\nu_\tau)$ and $B^0$-$\bar B^0$ mixing to determine the experimentally favored configurations of the model. This combination of observables rules out small charged Higgs masses and small values of $\tan\beta$, and provides some information about the neutral Higgs masses and the mixing angle $\alpha$. In particular, constraints derived from the $\rho$ parameter rule out configurations where the charged Higgs is much heavier or much lighter than the neutral Higgses. We discuss a scenario where $\Gamma(Z\to b \bar b)$ is enhanced relative to the standard model result, which unfortunately is on the verge of being ruled out by the combination of $\Gamma(b\to s \gamma)$ and $\rho$ parameter constraints. Implications for various extensions of the standard model are briefly discussed.