The final-state interaction phases of the two-body B decay: The bounds from the updated data

Abstract

The updated experimental data are used to analyze the final-state interaction phases of the two-body decay amplitudes of the B mesons. Combining the upper bounds on the branching fractions of the color-suppressed modes with those of the charged modes, we have set constraints on the relative phases between the amplitudes $A(B^0 \to X^- Y^+)$ and $A(B^+ \to X^0 Y^+)$ where $X=\overlien{D}$ or $\overine{D}^*$ and $Y=\pi$ and $\rho$. The numbers that we have obtained point to small final-state interactions. When these relative phases are expressed in those of the isospin amplitudes, the bounds become less tight since experimental errors accumulate. In the decay where many multibody channels are open, however, there is little advantage in breaking up the observed amplitudes into the isospin eigenchannels for analysis of the final-state interactions.