$b\bar{b}$ events in the $e^+e^-$ collision at Z resonance

Abstract

We study the some topics on the $b\bar{b}$ events in the $e^+e^-$ collision at Z resonance. According to the Standard Model, b quarks are produced almost completely longitudinally polarized at $\sqrt{s}\simeqM_Z$. Unfortunately, a measurement of $P_b$ is not as much straightforward. This is mainly due to hadronization and fragmentation properties b quarks that largely dilute and obscure b polarization effects in the observed final states. We suggest a strategy for detecting b polarization effects in the $e^+e^-$ collision on Z resonance. We select dilepton events in the $Z → b\bar{b}$ events, in which both b hadrons decay semileptonically. Then we catalog these events into the ``like-sign`` events in which leptons have same charge and the ``unlike-sign`` events in which leptons have different charge. Clearly the existence of the ``like-sign`` events is a signal of b-$\bar{B}$ mixing. In the ``like-sign`` events, one of the b hadrons must be a $B_s$ or $B_d$ meson. However this is not the case in the ``unlike-sign`` events. So the fractions of $∧_b$ would be different for each types of events. Then we have two types of inclusive leptonic samples with different $∧_b$ fractions. With these dileptonic events, the several polarization-dependent variables are calculated. Using this method, the b polarization effects may be detected without large uncertainties of b fragmentation and $∧_b$ decay model. The inclusive semi-leptonic decays of b mesons are attracting a lot of attention as testing ground for hadronic models and as a source for the weak parameters $V_ub$ and $V_cb$. In general there are two kinds of models which predict the lepton energy spectrum of inclusive decays of b meson. In the ACCMM model, the free quark decay picture is improved by taking into account the Fermi motion of the spectator in the b-meson. The second approach uses the parton model at an infinite momentum frame(IMF). It pictures the mesonic decay as the decay of the partons. The probabil...