Precision electroweak tests of the minimal and flipped SU(5) supergravity models

We explore the one-loop electroweak radiative corrections in the minimal SU(5) and the no-scale flipped SU(5) supergravity models via explicit calculation of vacuum polarization contributions to the ${\epsilon }_{1,2,3}$ parameters. Experimentally, ${\epsilon }_{1,2,3}$ are obtained from a global fit to the CERN LEP observables, and $\frac{M_W}{M_Z}$ measurements. We include $q^2$-dependent effects which have been neglected in most previous "model-independent" analyses of this type. These effects induce a large systematic negative shift on ${\epsilon }_{1,2,3}$ for light chargino masses ($m_{{\chi }_1^{\pm }}\lesssim 70$ GeV). In agreement with previous general arguments we find that for increasingly large sparticle masses the heavy sector of both models rapidly decouples; i.e., the values for ${\epsilon }_{1,2,3}$ quickly become asymptotic to the standard model values with a light Higgs boson ($m_{H_{\mathrm{SM}}}\sim 100$ GeV). Specifically, at present the 90% C.L. upper limit on the top-quark mass is $m_t\lesssim 175$ GeV in the no-scale flipped SU(5) supergravity model. These bounds can be strengthened for increasing chargino masses in the 50-100 GeV interval. In particular, for $m_t\gtrsim 160$ GeV, the Fermilab Tevatron may be able to probe through gluino ($\tilde{g}$) and squark ($\tilde{q}$) production up to $m_{\tilde{g}}\approx m_{\tilde{q}}\approx 250$ GeV, exploring at least half of the parameter space in this model.