Selection of Fully Reconstructed Hadronic $B_s^0$ Decays for the Observation of $B^0_s$-$\bar B_s^0$ Oscillations

We present the neural network based selection of hadronic $B_s^0$ decay modes used for the time-dependent measurement of $B^0_s$-$\bar B_s^0$ oscillation frequency $\Delta m_s$. Using a data sample of 1~fb$^{-1}$ of $p\bar p$ collisions at $\sqrt s=1.96$~TeV collected with the CDF\,II detector at the Fermilab Tevatron Collider, we find signals of 5600 fully reconstructed hadronic $B_s^0$ decays. We measure the probability as a function of proper decay time that the hadronic $B^0_s$ candidate decays with the same or opposite flavor as the flavor at production. We find a signal for $B_s$-$\bar B_s$ oscillations and measure $\Delta m_s$ = 17.77 $\pm$ 0.10 (stat) $\pm$ 0.07 (syst) ps$^{-1}$. From this we extract $|V_{td}/V_{ts}|$ = 0.2060 $\pm$ 0.0007 (exp) + 0.0081 - 0.0060 (theor).