New precision electroweak tests of SU(5) x U(1) supergravity

We explore the one-loop electroweak radiative corrections in $SU(5)\times U(1)$ supergravity via explicit calculation of vacuum-polarization and vertex-correction contributions to the $\epsilon_1$ and $\epsilon_b$ parameters. Experimentally, these parameters are obtained from a global fit to the set of observables $\Gamma_{l}, \Gamma_{b}, A^{l}_{FB}$, and $M_W/M_Z$. We include $q^2$-dependent effects, which induce a large systematic negative shift on $\epsilon_{1}$ for light chargino masses ($m_{\chi^\pm_1}\lsim70\GeV$). The (non-oblique) supersymmetric vertex corrections to $\Zbb$, which define the $\epsilon_b$ parameter, show a significant positive shift for light chargino masses, which for $\tan\beta\approx2$ can be nearly compensated by a negative shift from the charged Higgs contribution. We conclude that at the 90\%CL, for $m_t\lsim160\GeV$ the present experimental values of $\epsilon_1$ and $\epsilon_b$ do not constrain in any way $SU(5)\times U(1)$ supergravity in both no-scale and dilaton scenarios. On the other hand, for $m_t\gsim160\GeV$ the constraints on the parameter space become increasingly stricter. We demonstrate this trend with a study of the $m_t=170\GeV$ case, where only a small region of parameter space, with $\tan\beta\gsim4$, remains allowed and corresponds to light chargino masses ($m_{\chi^\pm_1}\lsim70\GeV$). Thus $SU(5)\times U(1)$ supergravity combined with high-precision LEP data would suggest the presence of light charginos if the top quark is not detected at the Tevatron.