Measurement of the branching fraction and $CP$ asymmetry for $B\to {\overline{D}}^0\pi$ decays

We measure the branching fractions and $CP$ asymmetries for the decays $B^0\to {\overline{D}}^0{\pi }^0$ and $B^{+}\to {\overline{D}}^0{\pi }^{+}$, using a data sample of $772\times {10}^{6}B\overline{B}$ pairs collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. The branching fractions obtained and direct $CP$ asymmetries are $\mathcal{B}(B^0\to {\overline{D}}^0{\pi }^0)=[2.70\pm 0.06(\mathrm{stat})\pm 0.10(\mathrm{syst})]\times {10}^{-4}$, $\mathcal{B}(B^{+}\to {\overline{D}}^0{\pi }^{+})=[4.53\pm 0.02(\mathrm{stat})\pm 0.15(\mathrm{syst})]\times {10}^{-3}$, ${\mathcal{A}}_{CP}(B^0\to {\overline{D}}^0{\pi }^0)=[+0.42\pm 2.05(\mathrm{stat})\pm 1.22(\mathrm{syst})]\%$, and ${\mathcal{A}}_{CP}(B^{+}\to {\overline{D}}^0{\pi }^{+})=[+0.19\pm 0.36(\mathrm{stat})\pm 0.57(\mathrm{syst})]\%$. The measurements of $\mathcal{B}$ are the most precise to date and are in good agreement with previous results, as is the measurement of ${\mathcal{A}}_{CP}(B^{+}\to {\overline{D}}^0{\pi }^{+})$. The measurement of ${\mathcal{A}}_{CP}$ for $B^0\to {\overline{D}}^0{\pi }^0$ is the first for this mode, and the value is consistent with Standard Model expectations.

Figure 1

Tree-level Feynman diagrams for (a) color-suppressed $B^0\to {\overline{D}}^0{\pi }^0$ decay, (b) W exchange diagram, and (c) color-suppressed and doubly Cabibbo-suppressed ${\overline{B}}^0\to {\overline{D}}^0{\pi }^0$ decay.

Figure 2

Projections of the $B^{+}\to {\overline{D}}^0{\pi }^{+}$ fit results into the signal region ($5.275<M_{\mathrm{bc}}<5.285\mathrm{GeV}$, $-0.05<\mathrm{\Delta }E<0.05\mathrm{GeV}$, $-1<C_{\mathrm{NN}}^{\prime }<6$) for $M_{\mathrm{bc}}$ (left), $\mathrm{\Delta }E$ (middle), and $C_{\mathrm{NN}}^{\prime }$ (right) split into the $B_{2b}$ mode (top) and $B_{3b}$ (bottom). The blue short-dashed curve shows the signal PDF, red dotted curve shows the $B\overline{B}$ background PDF, green dash-dotted curve shows the continuum background PDF, pink long-dashed curve shows the (almost negligible) rare background PDF, black line is the fit result, points are data. Also shown underneath each graph are the residual pulls between the data points and fitted PDF.

Figure 3

Projections of the $B^0\to {\overline{D}}^0{\pi }^0$ fit results into the signal region ($5.275<M_{\mathrm{bc}}<5.285\mathrm{GeV}$, $-0.12<\mathrm{\Delta }E<0.07\mathrm{GeV}$, $-1<C_{\mathrm{NN}}^{\prime }<6$) for $M_{\mathrm{bc}}$ (left), $\mathrm{\Delta }E$ (middle), and $C_{\mathrm{NN}}^{\prime }$ (right) split into the $B_{2b}$ mode (top) and $B_{3b}$ (bottom). The blue short-dashed curve shows the signal PDF, red dotted curve shows the $B\overline{B}$ background PDF, green dash-dotted curve shows the continuum background PDF, pink long-dashed curve shows the (almost negligible) rare background PDF, black line is the fit result. Also shown underneath each graph are the residual pulls between the data points and fitted PDF.

Figure 4

Projections of the $B^0\to {\overline{D}}^0{\pi }^0$ fit results for $M_{\mathrm{bc}}$ into the signal region ($-0.12<\mathrm{\Delta }E<0.07\mathrm{GeV}$, $-1<C_{\mathrm{NN}}^{\prime }<6$) for $B^0\to {\overline{D}}^0(K^{+}{\pi }^{-}){\pi }^0$ (top left), ${\overline{B}}^0\to D^0(K^{-}{\pi }^{+}){\pi }^0$ (top right), $B^0\to {\overline{D}}^0(K^{+}{\pi }^{-}{\pi }^0){\pi }^0$ (bottom left), ${\overline{B}}^0\to D^0(K^{-}{\pi }^{+}{\pi }^0){\pi }^0$ (bottom right). The blue short-dashed curve shows the signal PDF, red dotted curve shows the $B\overline{B}$ background PDF, green dash-dotted curve shows the continuum background PDF, pink long-dashed curve shows the (almost negligible) rare background PDF, black line is the fit result. Also shown underneath each graph are the residual pulls between the data points and fitted PDF.