Measurement of the branching fraction and time-dependent $CP$ asymmetry in the decay $B^0\to D^{*+}{D}^{*-}{K}_s^0$

We study the decay $B^0\to D^{*+}{D}^{*-}{K}_S^0$ using $(230\pm 2)\times {10}^{6}B\overline{B}$ pairs collected by the BABAR detector at the PEP-II $B$ factory. We measure a branching fraction $\mathcal{B}(B^0\to D^{*+}{D}^{*-}{K}_S^0)=(4.4\pm 0.4\pm 0.7)\times {10}^{-3}$ and find evidence for the decay $B^0\to D^{*-}{D}_{s1}^{+}(2536)$ with a significance of $4.6\sigma$. A time-dependent $CP$ asymmetry analysis is also performed to study the possible resonant contributions to $B^0\to D^{*+}{D}^{*-}{K}_S^0$ and the sign of $\cos 2\beta$. Our measurement indicates that there is a sizable resonant contribution to the decay $B^0\to D^{*+}{D}^{*-}{K}_S^0$ from an unknown $D_{s1}^{+}$ state with large width, and that $\cos 2\beta$ is positive at the 94% confidence level under certain theoretical assumptions.

Figure 1

(a) Measured distribution of $m_{\mathrm{ES}}$. The solid line is the projection of the fit result. The dashed line represents the background components. (b) The efficiency-corrected yield of $B^0\to D^{*+}{D}^{*-}{K}_S^0$ signal events as a function of $m(D^{*\pm }{K}_S^0)$ in data (points) and in three-body phase-space signal MC (histogram) with an arbitrary normalization. Errors shown are statistical only. Note that the vertical axis shows events per unit $m(D^{*\pm }{K}_S^0)$, not the events in each bin. (c) Measured distribution of $m(D^{*\pm }{K}_S^0)-m(D^{*\pm })-m(K_S^0)$ in the region ${\mathrm{m}}_{\mathrm{ES}}>5.27\mathrm{GeV}/c^2$. The solid line is the projection of the fit result.

Figure 2

(a) The distribution of $\Delta t$ in the region ${\mathrm{m}}_{\mathrm{ES}}>5.27\mathrm{GeV}/c^2$ for $B^0$ $({\overline{B}}^0)$ tag candidates in the half Dalitz space $s^{+}<s^{-}$ (${\eta }_y=-1$). The solid (dashed) curve represents the fit projections in $\Delta t$ for $B^0$ $({\overline{B}}^0)$ tags. (b) The raw asymmetry $(N_{B^0}-N_{{\overline{B}}^0})/(N_{B^0}+N_{{\overline{B}}^0})$, as functions of $\Delta t$, where $N_{B^0}$ $(N_{{\overline{B}}^0})$ is the number of candidate with $B^0$ $({\overline{B}}^0)$ tag. (c) and (d) contain the corresponding information for the $B^0$ candidates in the other half Dalitz space $s^{+}>s^{-}$ (${\eta }_y=+1$).