Direct Limits on the B s 0 Oscillation Frequency

We report the first direct two-sided bound on the $B^0_s$ oscillation frequency using a large sample of $B^0_s$ semileptonic decays corresponding to approximately 1 fb$^{-1}$ of integrated luminosity collected by the \dzer\ experiment in 2002--2006 during Run II of the Fermilab Tevatron Collider. The flavor (i.e., $B^0_s$ or $\bar{B}^0_s$) of the \bs meson at the time of production was found using an opposite-side tagging technique, and the flavor at the time of decay was determined from the charge of the muon in the partially reconstructed decay $\bs\to \mu^{+}D_{s}^{-}X$, $D_{s}^{-}\to \phi \pi^{-}$, $\phi\to K^{+}K^{-}$. A likelihood scan over the oscillation frequency, $\Delta m_s$, gives a most probable value of 19 ps$^{-1}$ and a range of $17 < \Delta m_s < 21$ ps$^{-1}$ at the 90% C.L. At $\Delta m_s=19$ ps$^{-1}$, the amplitude method yields a result that deviates from the hypothesis of an oscillation amplitude of zero by 2.5 standard deviations, corresponding to a two-sided C.L. of 1%.