Possibility of $m_t < M_W + m_b$ for SUSY-type of Two Higgs Doublet Model

Abstract

Allowing for realistic uncertainties in input parameters, we demonstrate that the present CLEO limit of $5.4\times 10^{-4}$ for inclusive $b\to s\gamma$ decay does not yet fully exclude the $t\to bH^+$ decay possibility in supersymmetric type of two Higgs doublet models. Combined with direct search for $t\to bH^+$ via $H^+\to \tau^+\nu$ at the Tevatron, we conclude that $\tan\beta \sim 1$ is the ``allowed" window for $m_{H^+} < m_t < M_W$. The possibility becomes excluded, however, {\it if} the CLEO limit is pushed below $4\times 10^{-4}$.