Measurement of theBs0−B¯s0Oscillation 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 $|V_{td}/V_{ts}|={0.208}_{-0.002}^{+0.001}(\mathrm{expt}{)}_{-0.006}^{+0.008}(\mathrm{theor})$.