Measurement of the $e^+ e^- \to Z \to b\overline{b}$ forward-backward asymmetry and the $B^{0}\overline{B}^0$ mixing parameter using prompt leptons

The time-integrated $\mathrm{B}^{0}\bar{\mathrm{B}}^{0}$ mixing parameter and the forward-backward charge asymmetry in the process $\mathrm{e}^{+}\mathrm{e}^{-} \rightarrow \mathrm{b}\bar{\mathrm{b}}$ are measured in hadronic \Z events containing prompt muons or electrons, collected by the L3 experiment in the years 1990 to 1995. The total sample of 3.3 million hadronic $\mathrm{Z}$ events with a mean centre-of-mass energy of 91.26 GeV yields: \begin{eqnarray*} \mbox{$A_{\mathrm{FB}}^{\mathrm{b} }$} & = & 0.0960 \pm 0.0066(stat.) \pm 0.0033(sys.) \,, \\ %corel-6 \mbox{$\chi_{\mathrm{b}}$} & = & 0.1192 \pm 0.0068(stat.) \pm 0.0051(sys.) \,. % \end{eqnarray*} %%% %%% %%% %%% This asymmetry measurement together with measurements at energies away from the $\mathrm{Z}$ pole energy yield a pole asymmetry and corresponding effective electroweak mixing angle of: \begin{eqnarray*} \mbox{$A_{\mathrm{FB}}^{0,\mathrm{b}}$} & = & 0.1015 \pm 0.0064(stat.) \pm 0.0035(sys.) \,, \\ %corel-6.nb \mbox{$\sin^{2}\bar{\theta}_{\mathrm{W}}$} & = & 0.2318 \pm 0.0013 \, .\\ %sin2tw-3.nb \end{eqnarray*}