Light Gluino, Light Bottom Squark Scenario, and LEP Predictions

The scenario of light gluinos and light sbottoms was advocated to explain the discrepancy between the measured and theoretical production of $b$ quarks at the Tevatron. This scenario will have model-independent predictions for $Z\to q\bar q \tilde{g} \tilde{g}$atthe$Z^0$-pole,and$e^+ e^- \to q\bar q \tilde{g} \tilde{g}$atLEPII\mathrm{.}Weshowthatthedatafor$Z\to q \bar q g^* \to q\bar q b \bar b$atLEPIcannotconstrainthescenario,becausetheratio$\Gamma(Z \to q\bar q \tilde{g} \tilde{g})/ \Gamma(Z \to q \bar q g^* \to q\bar q b \bar b) = 0.15 - 0.04$for$m_{\tilde{g}}= 12-16$ GeV is smaller than the uncertainty of the data. However, at LEPII the ratio $\sigma(e^+ e^- \to q\bar q \tilde{g} \tilde{g})/ \sigma(e^+ e^- \to q \bar q g^* \to q\bar q b \bar b) \simeq 0.4 - 0.2$for$m_{\tilde{g}}= 12-16$ GeV, which may give an observable excess in $q\bar{q}b\bar{b}$ events; especially, the $4b$ events.