Final state rescattering and color-suppressedB0→D(*)0h0decays

The color-suppressed $B^0\to D^{\left(*\right)0\mathrm{}}{\pi }^0,D^{\left(*\right)0\mathrm{}}\eta ,D^0\omega$ decay modes have just been observed for the first time. The rates are all larger than expected, hinting at the presence of final state interactions. Considering the $B^0\to D^{\left(*\right)0\mathrm{}}{\pi }^0$ mode alone, an elastic $D^{\left(*\right)}\overrightarrow{\pi }{D}^{\left(*\right)}\pi$ rescattering phase difference $\delta \equiv {\delta }_{1/2}-{\delta }_{3/2}\sim 30°$ would suffice, but the $B^0\to D^{\left(*\right)0\mathrm{}}\eta ,D^0\omega$ modes compel one to extend the elastic formalism to SU(3) symmetry. We find that a universal $a_2{/a}_1=0.25\mathrm{}$ and two strong phase differences $20°\sim \theta <\delta <{\delta }^{\prime }\sim 50°$ can describe both $\mathrm{DP}$ and $D^{*}P$ modes rather well; the large phase of order $50°$ is needed to account for the strength of both the $D^{\left(*\right)0\mathrm{}}{\pi }^0$ and $D^{\left(*\right)0\mathrm{}}\eta$ modes. For $\mathrm{DV}$ modes, the nonet symmetry reduces the number of physical phases to just one, giving better predictive power. Two solutions are found. We predict the rates of the $B^0\to D_s^{+}{K}^{-},$ $D_s^{*+}{K}^{-},$ $D^0{\rho }^0,$ $D_s^{+}{K}^{*-},$ and $D^0\phi$ modes, as well as the $B^0\to D^0{K}^0,$ $D^{*0}{K}^0,$