Direct Limits on the $B_s^0$ Oscillation 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 $(5.0\pm 0.3)\%$.

Figure 1

$(K^{+}{K}^{-}){\pi }^{-}$ invariant mass distribution (a) for the untagged $B_s^0$ sample, and (b) for candidates that have been flavor tagged. The left and right peaks correspond to ${\mu }^{+}{D}^{-}$ and ${\mu }^{+}{D}_s^{-}$ candidates, respectively. The curve is a result of fitting a signal plus background model to the data.

Figure 2

Value of $-\Delta \log \mathcal{L}$ as a function of $\Delta m_s$. Star symbols do not include systematic uncertainties, and the shaded band represents the envelope of all $\log \mathcal{L}$ scan curves due to different systematic uncertainties.

Figure 3

$B_s^0$ oscillation amplitude as a function of oscillation frequency, $\Delta m_s$. The solid line shows the $\mathcal{A}=1$ axis for reference. The dashed line shows the expected limit including both statistical and systematic uncertainties.