Branching Fractions and $CP$ Asymmetries in $B^0\to K^{+}{K}^{-}{K}_S^0$ and $B^{+}\to K^{+}{K}_S^0{K}_S^0$

We measure the branching fractions and $CP$ asymmetries in the decays $B^0\to K^{+}{K}^{-}{K}_S^0$ and $B^{+}\to K^{+}{K}_S^0{K}_S^0$ using a sample of approximately $122\times {10}^6$ $B\overline{B}$ pairs collected by the BABAR detector. From a time-dependent analysis of the $K^{+}{K}^{-}{K}_S^0$ sample that excludes $\varphi K_S^0$, the values of the $CP$-violation parameters are $S=-0.56\pm 0.25\pm 0.04$ and $C=-0.10\pm 0.19\pm 0.10$, where the first uncertainty is statistical and the second is systematic. We confirm that the final state is nearly purely $CP$ even and extract the standard model parameter $\sin 2\beta =0.57\pm 0.26\pm {0.04}_{-0}^{+0.17}$ where the last error is due to uncertainty on the $CP$ content. We present the first measurement of the $CP$-violating charge asymmetry ${\mathcal{A}}_{CP}(B^{+}\to K^{+}{K}_S^0{K}_S^0)=-0.04\pm 0.11\pm 0.02$. The branching fractions are $\mathcal{B}(B^0\to K^{+}{K}^{-}{K}^0)=(23.8\pm 2.0\pm 1.6)\times {10}^{-6}$ and $\mathcal{B}(B^{+}\to K^{+}{K}_S^0{K}_S^0)=(10.7\pm 1.2\pm 1.0)\times {10}^{-6}$.

Figure 1

Projection plots of the $m_{\mathrm{E}\mathrm{S}}$ variable in the fits for (a) $B^0\to K^{+}{K}^{-}{K}_S^0$ and (b) $B^{+}\to K^{+}{K}_S^0{K}_S^0$ decays. The points are data and the curves are projections from the likelihood fit. The signal-to-background ratio is enhanced with a cut on the event probability.

Figure 2

(a),(b) The $\Delta t$ distributions of $B^0$- and ${\overline{B}}^0$-tagged $K^{+}{K}^{-}{K}_S^0$ events. The solid lines refer to the fit for all events; the dashed lines correspond to the background. (c) The raw asymmetry, where the solid line is obtained from the fit and the dotted line is the SM expectation for the measured $CP$ content. The signal-to-background ratio is enhanced with a cut on the event probability.