Measurement of the $B_{d}^{0} -\overline{B_{d}^{0}}$ oscillation freque

The time dependence of $B^0_d$ oscillations is measured using three techniques by the ALEPH experiment at LEP. In the first, inclusive lepton-jet events are used. When one of the $b$ hadrons in the event undergoes semileptonic decay, the charge of its parent $b$ quark at decay time is reflected by that of the lepton, its flight length is reconstructed by a topological vertexing technique, and the $b$ hadron momentum is measured using an energy flow method. The charge at production time is opposite to that of the other $b$ hadron in the event, which is inferred from the momentum-weighted sum of the charges of decay products emitted in the hemisphere opposite to the lepton. The frequency of the $B^0_d$ oscillation is fitted to the time dependence of the product of the lepton and jet charges. Updates of two other published analyses are also presented, using $D^*$--lepton (or jet charge) correlations, and dilepton events. The combined result is $\Delta m_d = (0.448\pm 0.038)\,$ps$^{-1}$. The dilepton analysis also gives a limit on the $B^0_s$ oscillation frequency, $\Delta m_s > 5.6$\,ps$^{-1}$ (at 95\% CL).