Production of four heavy quarks and $B_c$-mesons at the $Z^0$-boson pole

Abstract

The cross-section for the production of $b{\bar b} c{\bar c}$ quarks in $e^+e^-$ annihilation, that proves to be at a level of $\sigma (e^+e^- \rightarrow b{\bar b} c{\bar c})/ \sigma (e^+e^- \rightarrow b{\bar b}) \sim 10^{-2}$ for ${\sqrt s}=M_Z$ is calculated within the frames of the QCD perturbation theory. The cross sections for the associated production of $1S$- and $2S$-wave states of $B_c$-meson in the reaction $e^+e^- \rightarrow B_c b{\bar c}$ were calculated in the nonrelativistic model of a heavy quarkonium. The fragmentation function of $b\to B_c^{(*)}$ is analysed in the scaling limit. The number of $\Lambda_{bc}$-hyperons to be expected at LEP is estimated on the basis of the assumption on quark-hadron duality.