Measurement of the forward-backward asymmetries of $e^+e^- \rightarrow Z \rightarrow b \overline{b}$ and $e^+e^- \rightarrow Z \rightarrow c \overline{c}$ using prompt leptons

The forward-backward asymmetries of the processes $e^+e^- \rightarrow Z \rightarrow b \overline{b}$ and $e^+e^- \rightarrow Z \rightarrow c \overline{c}$ were measured from a sample of hadronic Zdecays collected by the DELPHI experiment between 1993 and 1995. Enriched samples of $b\bar{b}$ and $c\bar{c}$ events were obtained using lifetime information. The tagging of b and c quarks in these samples was based on the semileptonic decay channels $b/c \rightarrow X + \mu $ and $ b/c \rightarrow X + e $ combined with charge flow information from the hemisphere opposite to the lepton. Combining the $A_{\mathrm{FB}}^{\mathrm{b\overline{\mathrm{b}}}}$ and $A_{\mathrm{FB}}^{\mathrm{c\overline{\mathrm{c}}}}$ measurements presented in this paper with published results based on 1991 and 1992 DELPHI data samples, the following pole asymmetries were obtained: \begin{displaymath}\mbox{$A_{\mathrm{FB}}^{\mathrm{0, b}}$}= 0.1021 \pm 0.0052 \mathrm{~(stat)} \pm 0.0024 \mathrm{~(syst)} \end{displaymath} \begin{displaymath}\mbox{$A_{\mathrm{FB}}^{\mathrm{0, c}}$}= 0.0728 \pm 0.0086 \mathrm{~(stat)} \pm 0.0063 \mathrm{~(syst)}\end{displaymath} The effective value of the weak mixing angle derived from these measurements is \begin{displaymath}\mbox{$\sin ^2 \theta_{\mathrm{W,eff}}^{\mathrm{lept}}$}= 0.23170 \pm 0.00097 .\end{displaymath