$b\to s\gamma$ and $\epsilon_1$ Constraints on Supergravity Models

In the light of the top quark discovered very recently by CDF, we investigate the possibility of narrowing down the allowed top quark masses by combining for the first time only two strongest constraints present in the no-scale $SU(5)\times U(1)$ supergravity model, namely, the ones from the flavor-changing radiative decay $b\rightarrow s\gamma$ and the precision measurements at LEP in the form of $\epsilon_{1}$. It turns out that even without including the most devastating constraint from $\Zbb$ measurement at LEP in the form of $R_b$ directly or $\epsilon_b$ indirectly, the combined constraint from $b\rightarrow s\gamma$ and $\epsilon_1$ alone in fact excludes $m_t(m_t)\gsim 180\GeV$ altogether in the no-scale model, providing a constraint on $m_t$ near the upper end of the CDF values. The resulting upper bound on $m_t$ is stronger and $5 \GeV$ lower than the one from combining $\epsilon_1$ and $\epsilon_b$ constraints and also combining $b\rightarrow s\gamma$ and $\epsilon_b$ constraints in the previous analysis.