Measurement of the Time-Dependent $CP$ Asymmetry in the $B^0\to \varphi K^0$ Decay

We present a measurement of the time-dependent $CP$ asymmetry for the neutral $B$-meson decay $B^0\to \varphi K^0$. We use a sample of approximately $114\times {10}^6$ $B$-meson pairs taken at the ${\rm Y}(4S)$ resonance with the BABAR detector at the PEP-II $B$-meson factory at SLAC. We reconstruct the $CP$ eigenstates $\varphi K_S^0$ and $\varphi K_L^0$, where $\varphi \to K^{+}{K}^{-}$, $K_S^0\to {\pi }^{+}{\pi }^{-}$, and $K_L^0$ is observed via its hadronic interactions. The other $B$ meson in the event is tagged as either a $B^0$ or ${\overline{B}}^0$ from its decay products. The values of the $CP$-violation parameters are $S_{\varphi K}=0.47\pm 0.34{\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}}_{-0.06}^{+0.08}\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}$ and $C_{\varphi K}=0.01\pm 0.33\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\pm 0.10\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}$.

Figure 1

Distribution of the event variable (a) $m_{ES}$ for the $\varphi K_S^0$ final state and (b) $\Delta E$ for the $\varphi K_L^0$ final state after reconstruction and a requirement for the likelihood with total signal efficiency of 32% and 5%, respectively. The solid line represents the fit result for the total event yield and the dotted line for the background.

Figure 2

Plots (a) and b) show the $\Delta t$ distributions of $B^0$- and ${\overline{B}}^0$-tagged $\varphi K_S^0$ events. The solid lines refer to the fit for all events; the dashed lines correspond to the background. Plot (c) shows the asymmetry. A requirement for the event likelihood is applied. Plots (d)–(f) are the corresponding plots for $\varphi K_L^0$ events.