Measuring CP asymmetry in B--> rho pi decays without ambiguities.

We reexamine the question of isospin analysis applied to the [rho][pi] decay modes of the [ital B] as a tool to extract the CKM angle between [ital V][sub [ital u][ital b]][sup *][ital V][sub [ital u][ital d]] and [ital V][sub [ital t][ital b]][sup *][ital V][sub [ital t][ital d]], without ambiguities or uncertainties due to penguin amplitude contributions. We find that a maximum-likelihood fit of the parameters to the full Dalitz plot distribution can successfully extract the parameters---perhaps with as few as 1000 events. This result is from a study of Monte Carlo--generated events without inclusion of detector efficiency or background effects. The interference between channels is a large effect and provides additional constraints on the parameters compared to channel-by-channel studies. These can usually lift the degeneracy between the multiple solutions that plague such studies. The inclusion of charged [ital B] decays in the analysis would provide a direct check of the standard model prediction that the penguin amplitude weak phase for this channel is canceled by the weak mixing phase.