Measurement of branching fraction and time-dependent $CP$ asymmetry parameters in $B^0\to D^{*+}{D}^{*-}{K}_S^0$ decays

We present a measurement of the branching fraction and time-dependent $CP$ violation parameters for $B^0\to D^{*+}{D}^{*-}{K}_S^0$ decays. These results are obtained from a $414{\mathrm{fb}}^{-1}$ data sample that contains $449\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We obtain the branching fraction, $\mathcal{B}(B^0\to D^{*+}{D}^{*-}{K}_S^0)=[3.4\pm 0.4(\mathrm{stat})\pm 0.7(\mathrm{syst})]\times {10}^{-3}$, which is in agreement with the current world average. We also obtain an upper limit on the product branching fraction for a possible two-body decay, $\mathcal{B}(B^0\to D_{\mathrm{s}1}^{+}(2536)D^{*-})\mathcal{B}(D_{\mathrm{s}1}^{+}(2536)\to D^{*+}{K}_S^0)<7.1\times {10}^{-4}$ (90% CL). In the traditional 2-parameter time-dependent $CP$ analysis, we measure the $CP$ violation parameters, ${\mathcal{A}}_{CP}=-{0.01}_{-0.28}^{+0.28}(\mathrm{stat})\pm 0.09(\mathrm{syst})$, $D\sin 2{\varphi }_1={0.06}_{-0.44}^{+0.45}(\mathrm{stat})\pm 0.06(\mathrm{syst})$. No evidence for either mixing-induced or direct $CP$ violation is found. In a 3-parameter fit sensitive to $\cos 2{\varphi }_1$ performed in the half-Dalitz spaces, $s^{-}\le s^{+}$ and $s^{-}>s^{+}$, where $s^{\pm }\equiv m^2(D^{*\pm }{K}_S^0)$, we extract the $CP$ violation parameters, $J_{\mathrm{c}}/J_0={0.60}_{-0.28}^{+0.25}(\mathrm{stat})\pm 0.08(\mathrm{syst})$, $2J_{\mathrm{s}1}/J_0\sin 2{\varphi }_1=-{0.17}_{-0.42}^{+0.42}(\mathrm{stat})\pm 0.09(\mathrm{syst})$, $2J_{\mathrm{s}2}/J_0\cos 2{\varphi }_1=-{0.23}_{-0.41}^{+0.43}(\mathrm{stat})\pm 0.13(\mathrm{syst})$. A large value of $J_{\mathrm{c}}/J_0$ would indicate a significant resonant contribution from a broad unknown $D_{\mathrm{s}}^{**+}$ state. Although the sign of the factor, $2J_{\mathrm{s}2}/J_0$, can be deduced from theory, no conclusion can be drawn regarding the sign of $\cos 2{\varphi }_1$ given the errors.

Figure 1

$M_{\mathrm{bc}}-\Delta E$ fit projections. The solid curve shows the fit result.

Figure 2

(a) Background subtracted $D^{*+}{K}_S^0$ raw yield vs invariant mass with a superimposed reconstructed phase space histogram from signal MC. (b) Measured distribution of $m(D^{*+}{K}_S^0)-m(D^{*+})-m(K_S^0)$ in the signal box. The solid line shows the fit results.

Figure 3

2-parameter fit results of $B^0\to D^{*+}{D}^{*-}{K}_S^0$. (a) and (b) show the background subtracted $\Delta t$ distribution for poor tags ($0.0<r\le 0.5$) and good tags ($0.5<r\le 1.0$). Background subtraction is performed by subtracting the background PDF from the raw $\Delta t$ distribution. The solid curve represents $B^0$ tagged candidates and the dashed curve represents ${\overline{B}}^0$ tagged candidates. (c) and (d) show the $B^0-{\overline{B}}^0$ raw asymmetry, $(N_{B^0}-N_{{\overline{B}}^0})/(N_{B^0}+N_{{\overline{B}}^0})$, where $N_{B^0}$ ($N_{{\overline{B}}^0}$) is the number of $B^0$ (${\overline{B}}^0$) tags in $\Delta t$ for poor tags and good tags, respectively.

Figure 4

3-parameter fit results of $B^0\to D^{*+}{D}^{*-}{K}_S^0$. (a) and (b) show the background subtracted $\Delta t$ distribution for good tags ($0.5<r\le 1.0$) in the region, $s^{-}\le s^{+}$ and $s^{-}>s^{+}$. The solid curve represents $B^0$ tags and the dashed curve represents ${\overline{B}}^0$ tags. (c) and (d) show the $B^0-{\overline{B}}^0$ raw asymmetry in $\Delta t$ for each half-Dalitz space and for good tags only.