Measurement of the partial width of theZ0 intob\(\bar b\) final states using their semi-leptonic decays

The spectra of prompt electrons and muons from the semi-leptonic decays of heavy hadrons produced inZ0 decays have been used to measure the coupling of theZ0 tob quarks weighted by theB hadrons mean semi-leptonic branching fraction, giving a value:\(BR_{sl}^b *{{\Gamma _{b\bar b} } \mathord{\left/ {\vphantom {{\Gamma _{b\bar b} } {\Gamma _H }}} \right. \kern-\nulldelimiterspace} {\Gamma _H }} = 0.0221 \pm 0.0015\). The data has also been used to measure the value of the fragmentation parameter, defined in the context of the LUND PS Model, version 7.2, giving:\(\varepsilon (b) = \left( {8\begin{array}{*{20}c} { + 5} \\ { - 3} \\ \end{array} \pm 2} \right)10^{ - 3} \). The corresponding value of the mean fraction of the beam energy taken by aB hadron in the fragmentation of ab quark is:\(\overline {X_E^b } = 0.69\begin{array}{*{20}c} { + 0.02} \\ { - 0.03} \\ \end{array} \pm 0.01\). If the values of\(\Gamma _{b\bar b} \) andΓ H are taken from the Standard Model, the following value is obtained for the mean semi-leptonic braching fraction ofB hadrons: BR sl b =(10.1±0.7)%. Taking the value of\({{\Gamma _{b\bar b} } \mathord{\left/ {\vphantom {{\Gamma _{b\bar b} } {\Gamma _{\rm H} }}} \right. \kern-\nulldelimiterspace} {\Gamma _{\rm H} }}\) from an independent analysis of DELPHI data based on the use of the boosted sphericity product, a value: BR sl b =(10.1±1.3)% is obtained.