Study of time-dependent CP-violating asymmetries and flavor oscillations in neutral B decays at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$

We present a measurement of time-dependent CP-violating asymmetries in neutral B meson decays collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at the Stanford Linear Accelerator Center. The data sample consists of 29.7 ${\mathrm{fb}}^{\mathrm{-}1}$ recorded at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance and 3.9 ${\mathrm{fb}}^{\mathrm{-}1}$ off resonance. One of the neutral B mesons, which are produced in pairs at the ${\rm Y}\mathrm{}\left(4S\right),$ is fully reconstructed in the CP decay modes $J/\psi K_S^0,$ $\psi {\mathrm{}\left(2S\right)K}_S^0,$ ${\chi }_{c1\mathrm{}}{K}_S^0,$ $J/\psi K^{*0}$ ${(K}^{*0}\to K_S^0{\pi }^0)$ and $J/\psi K_L^0,$ or in flavor-eigenstate modes involving $D^{\left(*\right)}\pi /\rho {/a}_1$ and $J/\psi K^{*0}$ ${(K}^{*0}\to K^{+}{\pi }^{-}).\mathrm{}$ The flavor of the other neutral B meson is tagged at the time of its decay, mainly with the charge of identified leptons and kaons. A neural network tagging algorithm is used to recover events without a clear lepton or kaon tag. The proper time elapsed between the decays is determined by measuring the distance between the decay vertices. Wrong-tag probabilities, the time-difference resolution function, and the $B^0-B^0$ oscillation frequency $\Delta m_d$ are measured with a sample of about 6350 fully-reconstructed $B^0$ decays in hadronic flavor-eigenstate modes. A maximum-likelihood fit to this flavor eigenstate sample finds $\Delta m_d=0.516\mathrm{}\pm 0.016\left(\mathrm{stat}\right)\pm 0.010\left(\mathrm{syst}\right){\mathrm{ps}}^{-1}.$ The value of the asymmetry amplitude $\sin 2\beta$ is determined from a simultaneous maximum-likelihood fit to the time-difference distribution of the flavor-eigenstate sample and about 642 tagged $B^0$ decays in the CP-eigenstate modes. We find $\sin 2\beta =0.59\mathrm{}\pm 0.14\left(\mathrm{stat}\right)\pm 0.05\left(\mathrm{syst}\right),$ demonstrating that CP violation exists in the neutral B meson system. We also determine the value of the CP violation parameter $|\lambda |=0.93\mathrm{}\pm 0.09\left(\mathrm{stat}\right)\pm 0.03\left(\mathrm{syst}\right),$ which is consistent with the expectation of $|\lambda |=1\mathrm{}$ for no direct CP violation.