Measurement of the forward-backward asymmetry in $Z \to b\overline{b}$ and $Z \to c\overline{c}$ decays with leptons

The sample of hadronic Z decays collected by the ALEPH detector at LEP in the years 1991-1995 is analysed in order to measure the forward-backward asymmetry in $Z \to b\bar{b}$ and $Z \to c\bar{c}$ events and the $B^0-\bar{B^0}$ average mixing parameter $\bar{\chi}$. Quark charges are tagged by the charges of electrons and muons produced in b and c semileptonic decays. Multivariate analyses are used to separate the event flavours and $b \to \ell$/$b \to c \to ell$ processes. The b and c quark asymmetries are measured simultaneously; the average mixing parameter and the pole asymmetries are determined to be \begin{eqnarray*} \bar{\chi} &=& 0.1196 \pm 0.0049 (stat) {}^{+0.0043}_{-0.0050} (syst) \\ \A^{0,b}_{FB} &=& 0.0998 \pm 0.0040 (stat) \pm 0.0017 (syst),\\ \A^{0.c}_{FB} &=& 0.0732 \pm 0.0053 (stat) \pm 0.0037 (syst).\\ \end{eqnarray*} These asymmetries, combined with the ALEPH measurements of the b asymmetry using inclusive b hadron decays and of the c asymmetry using reconstructed D mesons, correspond to a value of the effective electroweak mixing angle of $\sin^2\theta^{eff}_{W} = 0.23188 \pm 0.00046$