Measurement of $CP$ asymmetries in $B^0\to \varphi K^0$ and $B^0\to K^{+}{K}^{-}{K}_s^0$ decays

We measure the time-dependent $CP$ asymmetry parameters in $B^0\to K^{+}{K}^{-}{K}^0$ based on a data sample of approximately $227\times {10}^6$ $B$-meson pairs recorded at the ${\rm Y}(4S)$ resonance with the BABAR detector at the PEP-II $B$-meson Factory at SLAC. We reconstruct two-body $B^0$ decays to $\varphi (1020)K_S^0$ and $\varphi (1020)K_L^0$, and the three-body decay $K^{+}{K}^{-}{K}_S^0$ with $\varphi (1020)K_S^0$ excluded. For the $B^0\to \varphi K^0$ decays, we measure $\sin 2{\beta }_{\mathrm{eff}}(\varphi K^0)=+0.50\pm 0.25(\mathrm{stat}{)}_{-0.04}^{+0.07}(\mathrm{syst})$. The $B^0\to K^{+}{K}^{-}{K}_S^0$ decays are dominated by $K^{+}{K}^{-}$ $S$ wave, as determined from an angular analysis; we measure $\sin 2{\beta }_{\mathrm{eff}}(K^{+}{K}^{-}{K}_S^0)=+0.55\pm 0.22(\mathrm{stat})\pm 0.04(\mathrm{syst})\pm 0.11(CP)$, where the last error is due to the uncertainty in the fraction of $CP$-even contributions to the decay amplitude. We find no evidence for direct $CP$ violation.

Figure 1

Distributions of (a) $m_{\mathrm{ES}}$ for $\varphi K_S^0$ candidates, (b) $\Delta E$ for $\varphi K_L^0$ candidates, and (c) $m_{\mathrm{ES}}$ for $K^{+}{K}^{-}{K}_S^0$ candidates excluding $\varphi K_S^0$, together with the results from the final extended maximum-likelihood fits after applying a requirement on the ratio of signal likelihood to signal-plus-background likelihood (computed without the displayed variable) to reduce the background. The requirement is chosen to roughly maximize $N_S^2/(N_S+N_C)$ where $N_C$ is the total number of continuum events, and is applied only for the purpose of making these plots. The curves are projections from the likelihood fits for total yield (solid lines), continuum background (short dashed lines), and total background [long dashes in (b) only]. The efficiency of the likelihood-ratio cut is (a) 79% for signal and 5% for background, (b) 35% for signal, 16% for $B$-background, and 3% for continuum background, and (c) 77% for signal and 5% for background.

Figure 2

The time-dependent asymmetry distributions for (a) $\varphi K_S^0$, (b) $\varphi K_L^0$, and (c) $K^{+}{K}^{-}{K}_S^0$ with no $\varphi K_S^0$ decays. The asymmetry is defined as $A_{B^0/{\overline{B}}^0}=(N_{B^0}-N_{{\overline{B}}^0})/(N_{B^0}+N_{{\overline{B}}^0})$, where $N_{B^0}$ ($N_{{\overline{B}}^0}$) is the number of $B_{\mathrm{tag}}$ mesons identified as a $B^0$ (${\overline{B}}^0$) for a given measured value of $\Delta t$. The signal-to-background ratio is enhanced with a cut on the likelihood ratio as in Fig. 1.

Figure 3

Distributions of $S$- and $P$-wave intensities and $CP$ even fraction as a function of $K^{+}{K}^{-}$ invariant mass. Notice that the first bin integrates a wider mass range than the $\varphi$ resonance occupies. Insets show $S$- and $P$-wave intensities in the $\varphi$ mass region.