Observation of $B_s^0-{\overline{B}}_s^0$ Oscillations

We report the observation of $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillations from a time-dependent measurement of the $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillation frequency $\Delta m_s$. Using a data sample of $1{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected with the CDF II detector at the Fermilab Tevatron, we find signals of 5600 fully reconstructed hadronic $B_s$ decays, 3100 partially reconstructed hadronic $B_s$ decays, and 61 500 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 for $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillations. The probability that random fluctuations could produce a comparable signal is $8\times {10}^{-8}$, which exceeds $5\sigma$ significance. We measure $\Delta m_s=17.77\pm 0.10(\mathrm{stat})\pm 0.07(\mathrm{syst}){\mathrm{ps}}^{-1}$ and extract $|V_{\mathrm{td}}/V_{\mathrm{ts}}|=0.2060\pm 0.0007(\Delta m_s{)}_{-0.0060}^{+0.0081}(\Delta m_d+\mathrm{theor})$.

Figure 1

Left panel: the invariant mass distributions for the $D_s^{+}(\varphi {\pi }^{+})$ candidates [inset] and the ${\ell }^{-}{D}_s^{+}(\varphi {\pi }^{+})$ pairs. The contribution labeled “false lepton & physics” (dashed line) refers to backgrounds from hadrons mimicking the lepton signature combined with real $D_s$ mesons and physics backgrounds such as $B^0\to D_s^{+}{D}^{-}$, $D_s^{+}\to \varphi {\pi }^{+}$, $D^{-}\to {\ell }^{-}X$. Right panel: the invariant mass distribution for ${\overline{B}}_s^0\to D_s^{+}(\varphi {\pi }^{+}){\pi }^{-}$ decays including the contributions from ${\overline{B}}_s^0\to D_s^{*+}{\pi }^{-}$ and ${\overline{B}}_s^0\to D_s^{+}{\rho }^{-}$. In this panel, signal contributions are drawn added on top of the combinatorial background.

Figure 2

The invariant mass distributions for ${\overline{B}}_s^0\to D_s^{+}{\pi }^{-}$ (top panels) and $D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ (bottom panels). Signal contributions are added on top of the combinatorial background. Contributions from partially reconstructed $B_s$ decays are taken into account in the fit and are not shown.

Figure 3

Left panel: the distribution of the correction factor $\kappa$ in semileptonic and partially reconstructed hadronic decays from Monte Carlo simulation. Right panel: the average proper decay-time resolution for $B_s$ decays as a function of proper decay time.

Figure 4

The measured amplitude values and uncertainties versus the $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillation frequency $\Delta m_s$. Upper left: semileptonic decays only. (Lower Left) hadronic decays only. Upper right: all decay modes combined. Lower right: the logarithm of the ratio of likelihoods for amplitude equal to one and amplitude equal to zero, $\Lambda =\log [{\mathcal{L}}^{\mathcal{A}=0}/{\mathcal{L}}^{\mathcal{A}=1}(\Delta m_s)]$, versus the oscillation frequency. The horizontal line indicates the value $\Lambda =-15$ that corresponds to a probability of $5.7\times {10}^{-7}$ ($5\sigma$) in the case of randomly tagged data.

Figure 5

The $B_s^0\mathrm{\text{−}}{\overline{B}}_s^0$ oscillation signal measured in five bins of proper decay-time modulo the measured oscillation period $2\pi /\Delta m_s$. The figure is described in the text.