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$b\to sγ$ and $ε_1$ 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 $b\rightarrow sγ$ and the precision measurements at LEP in the form of $ε_{1}$. It turns out that even without including the most devastating constraint from $\Zbb$ measurement at LEP in the form of $R_b$ directly or $ε_b$ indirectly, the combined constraint from $b\rightarrow sγ$ and $ε_1$ 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 $ε_1$ and $ε_b$ constraints and also combining $b\rightarrow sγ$ and $ε_b $ constraints in the previous analysis.