Analysis of the Three-Body $B\to D^{+}{D}^{-}{\pi }^0$ Decay

Abstract

The decay process $B\to D^{+}{D}^{-}{\pi }^0$ 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 beauty and charmed mesons, and we determine the relevant matrix elements in the infinite heavy quark mass limit, assuming the factorization ansatz. We estimate the rate of the decay: $\mathcal{B}(B\to D^{+}{D}^{-}{\pi }^0)\simeq 1\times 10^{-3}$. 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-favoured process $B\to D^{+}{D}^{-}{K}_S$.

Comments: LaTex, 20 pages, 4 figures