Final-State Phases in $B\to D\pi ,D^{\ast }\pi$, and $D\rho$ Decays

Abstract

The final-state phases in $\bar{B}\to D\pi ,D^{\ast }\pi$, and $D\rho$ decays appear to follow a pattern similar to those in $D\to \bar{K}\pi$, ${\bar{K}}^{\ast }\pi$, and $\bar{K}\rho$ decays. Each set of processes is characterized by three charge states but only two independent amplitudes, so the amplitudes form triangles in the complex plane. For the first two sets the triangles appear to have non-zero area, while for the $D\rho$ or $\bar{K}\rho$ decays the areas of the triangles are consistent with zero. Following an earlier discussion of this behavior for $D$ decays, a similar analysis is performed for B decays, and the relative phases and magnitudes of contributing amplitudes are determined. The significance of recent results on $\text{ob}\to D^{(\ast )0}{\bar{K}}^{(\ast )0}$ is noted. Open theoretical and experimental questions are indicated.

Comments: 16 pages, LaTeX, 3 figures, to be submitted to Phys. Rev. D. References added; comments on new experimental results and analysis