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

Abstract. Oscillations of $\mbox{B}^0_{\mathrm{s}}$ mesons have been studied in samples selected from about 3.5 million hadronic $\mathrm{Z}$ decays detected by DELPHI between 1992 and 1995. One analysis uses events in the exclusive decay channels: $\mathrm{B^0_s}\rightarrow \rm{D}_{s}^{-} \pi^{+}$ or $\rm{D}_{s}^{-}\mathrm{a_1^+}$ and $\mathrm{B^0_s} \rightarrow \overline{\mathrm{D}}^0\mathrm{K}^-\pi^+ $ or $\overline{\mathrm{D}}^0\mathrm{K}^-\mathrm{a_1^+}$, where the ${\mathrm{D}}$ decays are completely reconstructed. In addition, $\mbox{B}^0_{\mathrm{s}}-\overline{\mbox{B}^0_{\mathrm{s}}}$ oscillations have been studied in events with an exclusively reconstructed ${\mathrm{D_s}}$ accompanied in the same hemisphere by a high momentum hadron of opposite charge. Combining the two analyses, a limit on the mass difference between the physical $\mbox{B}^0_{\mathrm{s}}$ states has been obtained: \[ \Delta m_{\mathrm{B^0_s}} > 4.0 \mbox{ps}^{-1} \mbox{at the 95% C.L.}\]\[ \mbox{with a sensitivity of} \Delta m_{\mathrm{B^0_s}} = 3.2 \mbox{ps}^{-1}.\] Using the latter sample of events, the $\mathrm{B^0_s}$ lifetime has been measured and an upper limit on the decay width difference between the two physical $\mathrm{B^0_s}$ states has been obtained: \[\tau_{\mathrm{B^0_s}} = 1.53^{+0.16}_{-0.15}(\rm{stat}.)\pm{0.07}(\rm{syst}.) \mathrm{ps}\]\[\Delta \Gamma_{\mathrm{B^0_s}}/\Gamma_{\mathrm{B^0_s}} < 0.69 \mbox{at the 95% C.L.}\] The combination of these results with those obtained using ${\rm{D}_{s}^{\pm}} \ell^{\mp}$ sample gives: \[ \Delta m_{\mathrm{B^0_s}} > 4.9 \mbox{ps}^{-1} \mbox{at the 95% C.L.}\]\[ \mbox{with a sensitivity of} \Delta m_{\mathrm{B^0_s}} = 8.7 \mbox{ps}^{-1}.\]\[ \tau_{\mathrm{B^0_s}} = 1.46\pm{0.11} \mathrm{ps}\quad \mbox{and}\quad \Delta \Gamma_{\mathrm{B^0_s}}/\Gamma_{\mathrm{B^0_s}} < 0.45 \mbox{at the 95% C.L.} \]