An Isospin Analysis of $CP$ Violation in $B_d\to D\pi$, $D^{\ast }\pi$ and $D\rho$

Abstract

By use of current experimental data, we carry out an isospin analysis of the weak decays $B\to D\pi ,D^{\ast }\pi$ and $D\rho$. It is found that only in $B\to D\rho$ the strong phase shift of two different isospin amplitudes can be approximately neglected. We derive some useful relations between the $CP$-violating measurables and the weak and strong transition phases, and illustrate the different effects of final-state interactions on $CP$ violation in $B_d\to D\pi ,D^{\ast }\pi$ and $D\rho$.

Comments: LaTex 9 pages (3 figs). A misleading assumption is removed and a little more material is added. (Accepted for publication in Phys. Lett. B)