Branching fraction measurements of the color-suppressed decays ${\overline{B}}^0$ to $D^{(*)0}{\pi }^0$, $D^{(*)0}\eta$, $D^{(*)0}\omega$, and $D^{(*)0}{\eta }^{\prime }$ and measurement of the polarization in the decay ${\overline{B}}^0\to D^{*0}\omega$

We report updated branching fraction measurements of the color-suppressed decays ${\overline{B}}^0\to D^0{\pi }^0$, $D^{*0}{\pi }^0$, $D^0\eta$, $D^{*0}\eta$, $D^0\omega$, $D^{*0}\omega$, $D^0{\eta }^{\prime }$, and $D^{*0}{\eta }^{\prime }$. We measure the branching fractions ($\times {10}^{-4}$): $\mathcal{B}({\overline{B}}^0\to D^0{\pi }^0)=2.69\pm 0.09\pm 0.13$, $\mathcal{B}({\overline{B}}^0\to D^{*0}{\pi }^0)=3.05\pm 0.14\pm 0.28$, $\mathcal{B}({\overline{B}}^0\to D^0\eta )=2.53\pm 0.09\pm 0.11$, $\mathcal{B}({\overline{B}}^0\to D^{*0}\eta )=2.69\pm 0.14\pm 0.23$, $\mathcal{B}({\overline{B}}^0\to D^0\omega )=2.57\pm 0.11\pm 0.14$, $\mathcal{B}({\overline{B}}^0\to D^{*0}\omega )=4.55\pm 0.24\pm 0.39$, $\mathcal{B}({\overline{B}}^0\to D^0{\eta }^{\prime })=1.48\pm 0.13\pm 0.07$, and $\mathcal{B}({\overline{B}}^0\to D^{*0}{\eta }^{\prime })=1.49\pm 0.22\pm 0.15$. We also present the first measurement of the longitudinal polarization fraction of the decay channel $D^{*0}\omega$, $f_L=(66.5\pm 4.7\pm 1.5)\%$. In the above, the first uncertainty is statistical and the second is systematic. The results are based on a sample of $(454\pm 5)\times {10}^6$ $B\overline{B}$ pairs collected at the $\mathit{{\rm Y}}(4S)$ resonance, with the BABAR detector at the PEP-II storage rings at SLAC. The measurements are the most precise determinations of these quantities from a single experiment. They are compared to theoretical predictions obtained by factorization, Soft Collinear Effective Theory (SCET) and perturbative QCD (pQCD). We find that the presence of final state interactions is favored and the measurements are in better agreement with SCET than with pQCD.

Figure 1

External (a) and internal (b) tree diagrams for ${\overline{B}}^0\to D^{(*)}h$ decays.

Figure 2

Fits of $\Delta E$ distributions in data for modes ${\overline{B}}^0\to D^0{\pi }^0$ (a), ${\overline{B}}^0\to D^0\omega$ (b), ${\overline{B}}^0\to D^0\eta (\gamma \gamma )$ (c), ${\overline{B}}^0\to D^0\eta (\pi \pi {\pi }^0)$ (d), ${\overline{B}}^0\to D^0{\eta }^{\prime }(\pi \pi \eta )$ (e), and ${\overline{B}}^0\to D^0{\eta }^{\prime }({\rho }^0\gamma )$ (f). The data points with error bars are measurements in data, the curves are the various PDF components: the solid (blue) fitted total PDF, the dotted (red) signal PDF, the dotted-dashed (black) cross-feed PDF, the double dotted-dashed (brown) $B^{-}\to D^{(*)0}{\rho }^{-}$ PDF, and the long dashed (blue) combinatorial background PDF.

Figure 3

Fits of $\Delta E$ distributions in data for modes ${\overline{B}}^0\to D^{*0}{\pi }^0$ (a), ${\overline{B}}^0\to D^{*0}\omega$ (b), ${\overline{B}}^0\to D^{*0}\eta (\gamma \gamma )$ (c), ${\overline{B}}^0\to D^{*0}\eta (\pi \pi {\pi }^0)$ (d), ${\overline{B}}^0\to D^{*0}{\eta }^{\prime }(\pi \pi \eta )$ (e), and ${\overline{B}}^0\to D^{*0}{\eta }^{\prime }({\rho }^0\gamma )$ (f), where the $D^{*0}$ mesons decay into the signal mode $D^0{\pi }^0$. A detailed legend is provided in the caption of Fig. 2.

Figure 4

Fits of $\Delta E$ distributions in data for modes ${\overline{B}}^0\to D^{*0}{\pi }^0$ (a), ${\overline{B}}^0\to D^{*0}\omega$ (b), ${\overline{B}}^0\to D^{*0}\eta (\gamma \gamma )$ (c), ${\overline{B}}^0\to D^{*0}\eta (\pi \pi {\pi }^0)$ (d), and ${\overline{B}}^0\to D^{*0}{\eta }^{\prime }(\pi \pi \eta )$ (e), where the $D^{*0}$ mesons decay into the signal mode $D^0\gamma$. The unfitted $\Delta E$ distribution of ${\overline{B}}^0\to D^{*0}(D^0\gamma ){\eta }^{\prime }({\rho }^0\gamma )$ candidates is also displayed (f). A detailed legend is provided in the caption of Fig. 2.

Figure 5

$\mathcal{B}({\overline{B}}^0\to D^0{h}^0)$ ($\times {10}^{-4}$) for the individual reconstructed $D^0$ and $h^0$ decay channels (blue points) together with the BLUE combination of this paper measurements (vertical yellow bands and the red points). The previous experimental results from BABAR [7, 14], Belle [11, 12], and CLEO [10] are also shown (black points). The horizontal bars represent the statistical contribution alone and the quadratic sum of the statistical and systematic uncertainty contributions. The width of the vertical yellow band corresponds to $\pm 1\sigma$ of the combined measurement, where the statistical and systematic uncertainties are summed in quadrature.

Figure 6

$\mathcal{B}({\overline{B}}^0\to D^{*0}{h}^0)$ ($\times {10}^{-4}$) for the individual reconstructed $D^0$, $D^{*0}$, and $h^0$ decay channels together with the BLUE combination of this paper measurements (vertical yellow bands and the red points). The blue squares (triangles) are for measurements with the subdecay $D^{*0}\to D^0{\pi }^0$ ($D^0\gamma$). The previous experimental results from BABAR [7, 14], Belle [11, 12], and CLEO [10] are also shown (black points). The horizontal bars represent the statistical contribution alone and the quadratic sum of the statistical and systematic uncertainty contributions. The width of the vertical yellow band corresponds to $\pm 1\sigma$ of the combined measurement, where the statistical and systematic uncertainties are summed in quadrature.

Figure 7

Fitted distributions of the helicity $\cos {\theta }_{D^{*}}$ and $\cos {\theta }_{\omega }$ in the decay channel ${\overline{B}}^0\to D^{*0}\omega$ for the $D^0$ decay modes $K^{-}{\pi }^{+}$ (a) and (b), $K^{-}{\pi }^{+}{\pi }^0$ (c) and (d), $K^{-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ (e) and (f),and $K_S^0{\pi }^{+}{\pi }^{-}$ (g) and (f). The dots with error bars are data, the curves are the various PDF contributions: the solid blue (blue) is the total PDF, the dash-dot (grey) is the background contribution, the long dash (blue) is the $f_L=1$ signal part and the dots (red) is the $f_L=0$ signal.

Figure 8

Measurements of $f_L$ with the four $D^0$ modes in data. The yellow band represents the BLUE combination.

Figure 9

Combined ratios $\mathcal{B}({\overline{B}}^0\to D^{*0}{h}^0)/\mathcal{B}({\overline{B}}^0\to D^0{h}^0)$ measured in this paper compared to theoretical prediction by SCET [22] (vertical solid line). The vertical band represent the estimated theoretical uncertainty from SCET (for the case where $h^0$ is the $\omega$ meson see text).

Figure 10

Combined ratios $\mathcal{B}({\overline{B}}^0\to D^{*0}{\eta }^{\prime })/\mathcal{B}({\overline{B}}^0\to D^{*0}\eta )$ and $\mathcal{B}({\overline{B}}^0\to D^0{\eta }^{\prime })/\mathcal{B}({\overline{B}}^0\to D^0\eta )$ measured in this paper compared to theoretical prediction by SCET [22] (vertical line) and from factorization [49] (vertical bands).