Study of $B^0_s - \overline{B^0_s}$ oscillations and $B^0_s$ lifetimes using hadronic decays of $B^0_s$ mesons

Oscillations of $\mbox{B}^0_{\mathrm{s}}$ mesons have been studied in samples selected from about 3.5 million hadronic $\Zz$ decays detected by DELPHI betwee. One analysis uses events in the exclusive decay channels: $\Bs \rightarrow \rm{D}_{s}^{-} \pi^{+}$ or $\rm{D}_{s}^{-}\mathrm{a_1^+}$ and $\Bs \rightarrow \ overline{\mathrm{D}}^0\mathrm{K}^- \pi^+ $ or $\ overline{ where the ${\mathrm{D}}$ decays are completely reconstructed. In addition, $\mbox{B}^0_{\mathrm{s}}-\ overline{\mbox{B}^0_{\mathrm{s}}}$ osciln exclusively reconstructed $\Ds$ accompanied in the same hemisphere by a high m Combining the two analyses, a limit on the mass difference between the physical: \bes \ba{c} \dms 4.0~\mbox{ps}^{-1}~\mbox{at the 95\% C.L.} \\ \mbox{$\mathrm{with~ a~ sensitivity~ of}$}~\dms = 3.2~\mbox{ps}^{-1}. \ea \ees Using the latter sample of events, the $\Bs$ lifetime has been measured and an decay width difference between the two physical $\Bs$ states has been obtained: \tau_{\Bs} = 1.53^{+0.16}_{-0.15}(\rm{stat}.)\pm{0.07}(\rm{syst}.)~ \mathrm{ps} $\dgbs 0.69~\mbox{at the 95\% C.L.} The combination of these results with those obtained using $\mathrm{\rm{D}_{s}^{\pm}} \ell^{\mp}$ sample gives: %\cite{ref:dsl} \bes \ba{c} \dms 4.9~\mbox{ps}^{-1}~\mbox{at the 95\% C.L.} \\ \mbox{$\mathrm{with~ a~ sensitivity~ of}$}~\dms = 8.7~\mbox{ps}^{-1}. \ea \ees \begin{center} $\tau_{\Bs} = 1.46\pm{0.11}~\mathrm{ps}~$ and $~\dgbs 0.45~\mbox{at the 95\% C.L.}$