Analysis of the three-bodyB→D+D−π0decay

The decay process $\overrightarrow{B}{D}^{+}{D}^{-}{\pi }^0$ is an interesting channel for the investigation of CP violating effects in the b sector. We write down a decay amplitude constrained by a low-energy theorem, which also includes the contribution of resonant S- and P-wave b-flavored and charmed mesons, and we determine the relevant matrix elements in the infinite heavy quark mass limit, assuming the factorization ansatz and a suitable heavy meson effective chiral Lagrangian. We estimate the rate of the decay: $\mathcal{B}\left(\overrightarrow{B}{D}^{+}{D}^{-}{\pi }^0\right)\simeq 1\times {10}^{-3}.$ We also analyze the time-independent and time-dependent differential decay distributions, concluding that a signal for this process should be observed at the B factories. Finally, we give an estimate of the decay rate of the Cabibbo-favored process $\overrightarrow{B}{D}^{+}{D}^{-}{K}_S$ for which we find a branching ratio $\simeq 9\times {10}^{-3}.$