MeasuringCPasymmetry inB→ρπdecays without ambiguities

We reexamine the question of isospin analysis applied to the $\rho \pi$ decay modes of the $B$ as a tool to extract the CKM angle between $V_{\mathrm{ub}}^{*}{V}_{\mathrm{ud}}$ and $V_{\mathrm{tb}}^{*}{V}_{\mathrm{td}}$, 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 $B$ 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.