Measurement of the $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ Oscillation Frequency

We present the first precise measurement of the $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillation frequency $\Delta m_s$. We use $1{\mathrm{fb}}^{-1}$ of data from $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected with the CDF II detector at the Fermilab Tevatron. The sample contains signals of 3600 fully reconstructed hadronic $B_s$ decays and 37 000 partially reconstructed semileptonic $B_s$ decays. We measure the probability as a function of proper decay time that the $B_s$ decays with the same, or opposite, flavor as the flavor at production, and we find a signal consistent with $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillations. The probability that random fluctuations could produce a comparable signal is 0.2%. Under the hypothesis that the signal is due to $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillations, we measure $\Delta m_s={17.31}_{-0.18}^{+0.33}(\mathrm{stat})\pm 0.07(\mathrm{syst}){\mathrm{ps}}^{-1}$ and determine $|V_{td}/V_{ts}|={0.208}_{-0.002}^{+0.001}(\mathrm{expt}{)}_{-0.006}^{+0.008}(\mathrm{theor})$.

Figure 1

The invariant mass distributions for ${\overline{B}}_s^0\to D_s^{+}{\pi }^{-}$ (left panel) and $D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ (right panel).

Figure 2

(Upper panel) The measured amplitude values and uncertainties versus the $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillation frequency $\Delta m_s$. Shown in light gray and dark gray are the 95% one-sided confidence level bands for statistical uncertainties only and including systematic uncertainties, respectively. (Lower panel) The logarithm of the ratio of likelihoods for amplitude equal to zero and amplitude equal to one, $\Lambda =\log [{\mathcal{L}}^{\mathcal{A}=0}/{\mathcal{L}}^{\mathcal{A}=1}(\Delta m_s)]$, versus the oscillation frequency. The dashed horizontal line indicates the value of $\Lambda$ that corresponds to a probability of 1% in the case of randomly tagged data.