Observation of Time-Dependent $CP$ Violation in $B^0\to {\eta }^{\prime }{K}^0$ Decays and Improved Measurements of $CP$ Asymmetries in $B^0\to \phi K^0$, $K_S^0{K}_S^0{K}_S^0$ and $B^0\to J/\psi K^0$ Decays

We present improved measurements of $CP$-violation parameters in $B^0\to \varphi K^0$, ${\eta }^{\prime }{K}^0$, $K_S^0{K}_S^0{K}_S^0$ decays based on a sample of $535\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB energy-asymmetric $e^{+}{e}^{-}$ collider. We obtain $\sin 2{\varphi }_1^{\mathrm{eff}}=+0.64\pm 0.10(\mathrm{stat})\pm 0.04(\mathrm{syst})$ for $B^0\to {\eta }^{\prime }{K}^0$, $+0.50\pm 0.21(\mathrm{stat})\pm 0.06(\mathrm{syst})$ for $B^0\to \varphi K^0$, and $+0.30\pm 0.32(\mathrm{stat})\pm 0.08(\mathrm{syst})$ for $B^0\to K_S^0{K}_S^0{K}_S^0$ decays. We have observed $CP$ violation in the $B^0\to {\eta }^{\prime }{K}^0$ decay with a significance of 5.6 standard deviations. We also perform an improved measurement of $CP$ asymmetries in $B^0\to J/\psi K^0$ decays and obtain $\sin 2{\varphi }_1=+0.642\pm 0.031(\mathrm{stat})\pm 0.017(\mathrm{syst})$.

Figure 1

${\mathcal{R}}_{s/b}$, $M_{\mathrm{bc}}$, and $p_B^{*}$ distributions for reconstructed candidates: ${\mathcal{R}}_{s/b}$, $M_{\mathrm{bc}}$ with ${\mathcal{R}}_{s/b}\le 0.5$ and $M_{\mathrm{bc}}$ with ${\mathcal{R}}_{s/b}>0.5$ distributions for (a)–(c) $B^0\to {\eta }^{\prime }{K}_S^0$, (d)–(f) $B^0\to \varphi K_S^0$, and (g)–(i) $B^0\to K_S^0{K}_S^0{K}_S^0$; ${\mathcal{R}}_{s/b}$ and $p_B^{*}$ for (j),(k) $B^0\to {\eta }^{\prime }{K}_L^0$ and (l),(m) $B^0\to \varphi K_L^0$. The solid curves and histograms show the fits to signal plus background distributions, and hatched areas show the background contributions. Background contributions are subtracted in (k),(m).

Figure 2

(a) $M_{\mathrm{bc}}$ distribution in the $\Delta E$ signal region for selected $B^0\to J/\psi K_S^0$ candidates and (b) $p_B^{*}$ distribution for selected $B^0\to J/\psi K_L^0$ candidates.

Figure 3

Background-subtracted $\Delta t$ distributions and asymmetries for events with good tags ($r>0.5$) for (a) $B^0\to {\eta }^{\prime }{K}^0$, (b) $B^0\to \varphi K^0$, (c) $B^0\to K_S^0{K}_S^0{K}_S^0$, and (d) $B^0\to J/\psi K^0$. In the asymmetry plots, solid curves show the fit results; dashed curves show the SM expectation from our $B^0\to J/\psi K^0$ measurement.