Implications ofB¯0→D0π0decays onB¯→DK¯,D¯K¯decays

The recently observed color-suppressed ${\overline{B}}^0\to D^0{\pi }^0$, $D^0{\eta }^{(\prime )}$, $D_s^{+}{K}^{-}$ and $D^0{\overline{K}}^0$ decay modes all have rates larger than expected, hinting at the presence of final state interactions. We study rescattering effects in $\overline{B}\to DP$, $D\overline{K}$ and $\overline{D}\overline{K}$ modes in the quasielastic approach, which is extended to accommodate $D^0{\eta }^{\prime }$ without using U(3) symmetry. The ${\overline{D}}^0\overline{K}$ modes are of interest in the determination of the unitarity angle ${\varphi }_3/\gamma$. The updated $DP$ data are used to extract the effective Wilson coefficients $a_1^{\mathrm{eff}}\simeq 0.92$, $a_2^{\mathrm{eff}}\simeq 0.22$, three strong phases $\delta \simeq 62°$, $\theta \simeq 24°$, $\sigma \simeq 127°$, and the mixing angle $\tau \simeq 2°$. The values of $\delta$ and $\theta$ are close to our previous results. The smallness of $\tau$ implies small mixing of $D^0{\eta }_1$ with other modes. Predictions for $D^0{K}^{-}$, $D^{+}{K}^{-}$ and $D^0{\overline{K}}^0$ agree with data. Since strong interaction respects charge conjugation symmetry, the framework applies to $\overline{B}\to \overline{D}\overline{K}$, and rates for ${\overline{D}}^0{K}^{-}$, $D^{-}{K}^0$, $D_s^{-}{\pi }^0$, $D_s^{-}\eta$ and $D_s^{-}{\eta }^{\prime }$ modes are predicted. From $B^{-}\to {\overline{D}}^0{K}^{-}$ and $D^0{K}^{-}$ rates, we find $r_B=0.09\pm 0.02$, where the error is propagated from the experimental $DP$ rate uncertainties. The error on $r_B$ is doubled when the universality on $a_2^{\mathrm{eff}}$ is relaxed.