Measurement of Branching Fractions and Resonance Contributions for $B^0\to {\overline{D}}^0{K}^{+}{\pi }^{-}$ and Search for $B^0\to D^0{K}^{+}{\pi }^{-}$ Decays

Using $226\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ events collected with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ storage ring at the Stanford Linear Accelerator Center, we measure the branching fraction for $B^0\to {\overline{D}}^0{K}^{+}{\pi }^{-}$, excluding $B^0\to D^{*-}{K}^{+}$, to be $\mathcal{B}(B^0\to {\overline{D}}^0{K}^{+}{\pi }^{-})=(88\pm 15\pm 9)\times {10}^{-6}$. We observe $B^0\to {\overline{D}}^0{K}^{*}(892{)}^0$ and $B^0\to D_2^{*}(2460{)}^{-}{K}^{+}$ contributions. The ratio of branching fractions $\mathcal{B}(B^0\to D^{*-}{K}^{+})/\mathcal{B}(B^0\to D^{*-}{\pi }^{+})=(7.76\pm 0.34\pm 0.29)\%$ is measured separately. The branching fraction for the suppressed mode $B^0\to D^0{K}^{+}{\pi }^{-}$ is $\mathcal{B}(B^0\to D^0{K}^{+}{\pi }^{-})<19\times {10}^{-6}$ at the 90% confidence level.

Figure 1

$\Delta E$ distributions and PDF projections with $m_{\mathrm{ES}}>5.27\mathrm{GeV}/c^2$ for (a) $B^0\to {\overline{D}}^0{K}^{+}{\pi }^{-}$ excluding $D^{*-}{K}^{+}$ candidates, (b) $B^0\to D^0{K}^{+}{\pi }^{-}$, (c) $B^0\to {\overline{D}}^0{K}^{*}(892{)}^0$, and (d) $B^0\to D_2^{*}(2460{)}^{-}{K}^{+}$, for the three $D^0$ modes combined. Circles with error bars are data points. Four curves from top to bottom represent the total PDF (solid line), total background (dashed line), combinatorial background plus peaking background $B$ described in the text (dot-dashed line), and combinatorial background only (dotted line). In (a)–(c), the middle two curves overlap because the peaking background $A$ is negligible.

Figure 2

The signal weight distribution as a function of $m_{K^{+}{\pi }^{-}}$ and $m_{{\overline{D}}^0{\pi }^{-}}$. The shaded histograms include only events with (a) $|m_{{\overline{D}}^0{\pi }^{-}}-2460\mathrm{MeV}/c^2|<75\mathrm{MeV}/c^2$, and (b) $|m_{K^{+}{\pi }^{-}}-896\mathrm{MeV}/c^2|<150\mathrm{MeV}/c^2$.

Figure 3

(a) $\Delta E$ and (b) Cherenkov angle $({\theta }_C-{\theta }_C^{\pi })/{\sigma }_C$ distributions for $D^{*-}{h}^{+}$ candidates and PDF projections. Circles with error bars are data points. Shaded distribution is the combinatorial background, the dotted curve adds the $D^{*}\pi$ contribution, and the solid curve is the full PDF. The dashed curve represents the $D^{*}K$ contribution only. $\Delta E$ for $D^{*}\pi$ is centered near zero, while for $D^{*}K$ it is shifted to lower values because the prompt track is assumed to be a pion.