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 $Z\to q\bar q \tilde{g} \tilde{g}$ at the $Z^0$-pole, and $e^+ e^- \to q\bar q \tilde{g} \tilde{g}$ at LEPII. We show that the data for $Z\to q \bar q g^* \to q\bar q b \bar b$ at LEPI cannot constrain the scenario, because the ratio $\Gamma(Z \to q\bar q \tilde{g} \tilde{g})/ \Gamma(Z \to q \bar q g^* \to q\bar q b \bar b) = 0.15 - 0.04$ 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.Comment: to match the published version in PR

Bottomed Analog of Z+(4433)

The newly observed $Z^+ (4433)$ resonance by BELLE is believed to be a tetraquark bound state made up of $(cu)(\bar c \bar d)$. We propose the bottomed analog of this bound state, namely, by replacing one of the charm quarks by a bottom quark, thus forming $Z_{bc}^{0, \pm, \pm\pm}$. One of the $Z_{bc}$ is doubly charged. The predicted mass of $Z_{bc}$ is around 7.6 GeV. This doubly-charged bound state can be detected by its decay into $B_c^\pm \pi^\pm$. Similarly, we can also replace both charm quark and antiquark of the $Z^+ (4433)$ by bottom quark and antiquark, respectively, thus forming $Z_{bb}$ the bottomonium analog of $Z^+ (4433)$. The predicted mass of $Z_{bb}$ is about 10.7 GeV.Comment: 5 page

CPCP violating mode of the stoponium decay into ZhZh

We show that a novel decay mode $Zh$ of the bound state of stop-anti-stop pair in the ground state $^1S_0(\widetilde t_1\widetilde t_1^*)$ may have a significant branching ratio if the $CP$ violating mixing appears in the stop sector, even after we apply the stringent constraint from the measurement of the electric dipole moment (EDM) of the electron. We show that the branching ratio can be as large as 10% in some parameter space that it may be detectable at the LHC.Comment: 16 pages, 4 figure