Direct Limits on theBs0Oscillation Frequency

We report results of a study of the $B_s^0$ oscillation frequency using a large sample of $B_s^0$ semileptonic decays corresponding to approximately $1{\mathrm{fb}}^{-1}$ of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron Collider in 2002–2006. The amplitude method gives a lower limit on the $B_s^0$ oscillation frequency at $14.8{\mathrm{ps}}^{-1}$ at the 95% C.L. At $\Delta m_s=19{\mathrm{ps}}^{-1}$, the amplitude deviates from the hypothesis $\mathcal{A}=0$ (1) by 2.5 (1.6) standard deviations, corresponding to a two-sided C.L. of 1% (10%). A likelihood scan over the oscillation frequency, $\Delta m_s$, gives a most probable value of $19{\mathrm{ps}}^{-1}$ and a range of $17<\Delta m_s<21{\mathrm{ps}}^{-1}$ at the 90% C.L., assuming Gaussian uncertainties. This is the first direct two-sided bound measured by a single experiment. If $\Delta m_s$ lies above $22{\mathrm{ps}}^{-1}$, then the probability that it would produce a likelihood minimum similar to the one observed in the interval $16–22{\mathrm{ps}}^{-1}$ is $(5.0\pm 0.3)\%$.