Study of ${\overline{B}}^0\to D^{+}{h}^{-}(h=K/\pi )$ decays at Belle

We present a measurement of the branching fractions of the Cabibbo favored ${\overline{B}}^0\to D^{+}{\pi }^{-}$ and the Cabibbo suppressed ${\overline{B}}^0\to D^{+}{K}^{-}$ decays. We find $\mathcal{B}({\overline{B}}^0\to D^{+}{\pi }^{-})=(2.48\pm 0.01\pm 0.09\pm 0.04)\times {10}^{-3}$ and $\mathcal{B}({\overline{B}}^0\to D^{+}{K}^{-})=(2.03\pm 0.05\pm 0.07\pm 0.03)\times {10}^{-4}$ decays, where the first uncertainty is statistical, the second is systematic, and the third uncertainty is due to the $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ branching fraction. The ratio of branching fractions of ${\overline{B}}^0\to D^{+}{K}^{-}$ and ${\overline{B}}^0\to D^{+}{\pi }^{-}$ is measured to be $R^D=[8.19\pm 0.20(\mathrm{stat})\pm 0.23(\mathrm{syst})]\times {10}^{-2}$. These measurements are performed using the full Belle dataset, which corresponds to $772\times {10}^{6}B\overline{B}$ pairs and use the Belle II software framework for data analysis.

Figure 1

Fit to the invariant mass distribution for $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ in data. The black vertical dotted lines show the $D$ mass window. The dashed curve shows the signal component and dotted black line shows the background component. The distribution of pulls between the fit and the data points is also shown.

Figure 2

$\mathrm{\Delta }E$ distributions for ${\overline{B}}^0\to D^{+}{h}^{-}$ candidates obtained from the (left) pion-enriched ${\overline{B}}^0\to D^{+}{\pi }^{-}$ and (right) kaon-enriched ${\overline{B}}^0\to D^{+}{K}^{-}$ data samples. The projections of the combined fit and individual components of a simultaneous unbinned maximum-likelihood fit are overlaid. The long-dashed red curve shows the ${\overline{B}}^0\to D^{+}{\pi }^{-}$ component. The large-dotted magenta curve shows the ${\overline{B}}^0\to D^{+}{K}^{-}$ component. The small-dotted gray curve shows the combinatorial background component and the dash-dotted green curve show the peaking background component in ${\overline{B}}^0\to D^{+}{\pi }^{-}$ decay. The distribution of pulls between the fit and the data points is also shown.