Measurement of the $B\to {\overline{D}}^{(*)}{D}^{(*)}K$ branching fractions

We present a measurement of the branching fractions of the 22 decay channels of the $B^0$ and $B^{+}$ mesons to ${\overline{D}}^{(*)}{D}^{(*)}K$, where the $D^{(*)}$ and ${\overline{D}}^{(*)}$ mesons are fully reconstructed. Summing the 10 neutral modes and the 12 charged modes, the branching fractions are found to be $\mathcal{B}(B^0\to {\overline{D}}^{(*)}{D}^{(*)}K)=(3.68\pm 0.10\pm 0.24)\%$ and $\mathcal{B}(B^{+}\to {\overline{D}}^{(*)}{D}^{(*)}K)=(4.05\pm 0.11\pm 0.28)\%$, where the first uncertainties are statistical and the second systematic. The results are based on $429{\mathrm{fb}}^{-1}$ of data containing $471\times {10}^{6}B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the BABAR detector at the SLAC National Accelerator Laboratory.

Figure 1

Top left: external W-emission amplitude for the decays $B^{+}\to {\overline{D}}^{(*)0}{D}^{(*)+}{K}^0$. Top center: internal W-emission amplitude for the decays $B^{+}\to D^{(*)-}{D}^{(*)+}{K}^{+}$. Top right: $\mathrm{\text{external}}+\mathrm{\text{internal}}$ W-emission amplitudes for the decays $B^{+}\to {\overline{D}}^{(*)0}{D}^{(*)0}{K}^{+}$. Bottom row: same as top row, respectively, for $B^0\to D^{(*)-}{D}^{(*)0}{K}^{+}$, $B^0\to {\overline{D}}^{(*)0}{D}^{(*)0}{K}^0$, and $B^0\to D^{(*)-}{D}^{(*)+}{K}^0$.

Figure 2

Distributions of the $\Delta E$ variable (top plots) and of the $m_{\mathrm{ES}}$ variable (bottom plots) for the sum of all the $B^0\to {\overline{D}}^{(*)}{D}^{(*)}K$ modes (left-hand plots) and for the sum of all the $B^{+}\to {\overline{D}}^{(*)}{D}^{(*)}K$ modes (right-hand plots). The $\Delta E$ distributions are shown after the complete selection but before the choice of the best candidate and for $5.27<m_{\mathrm{ES}}<5.29\mathrm{GeV}/c^2$, and the $m_{\mathrm{ES}}$ distributions are shown after the complete selection, including the selection on the $\Delta E$ variable.

Figure 3

Fits of the $m_{\mathrm{ES}}$ data distributions for the neutral modes, $B^0\to {\overline{D}}^{(*)}{D}^{(*)}K$. The decay mode is indicated in the plots. Points with statistical errors are data events, the red dashed line represents the signal PDF, the blue long-dashed line represents the cross-feed event PDF, the blue dashed-dotted line represents the combinatorial background PDF, and the blue dotted line represents the peaking background PDF. The black solid line shows the total PDF.

Figure 4

Fits of the $m_{\mathrm{ES}}$ data distributions for the charged modes, $B^{+}\to {\overline{D}}^{(*)}{D}^{(*)}K$. The decay mode is indicated in the plots. Points with statistical errors are data events, the red dashed line represents the signal PDF, the blue long-dashed line represents the cross-feed event PDF, the blue dashed-dotted line represents the combinatorial background PDF, and the blue dotted line represents the peaking background PDF. The black solid line shows the total PDF.