Extraction of a Weak Phase from $B\to D^{(\ast )}\pi$

Abstract

To observe CP-violating asymmetries through the interference of a weaker amplitude with a stronger one in $\text{bo}\to D^{(\ast )}\pi$ and $\text{ob}\to D^{(\ast )}\pi$ decays, one must collect enough events that the intensity associated with the weaker amplitude would be statistically significant. We show that provided the weaker amplitude is measured separately in $B^{\pm }\to D^{(\ast )\pm }{\pi }^0$ decays, the time-integrated approach requires around $2.5\cdot 10^{8}B\bar{B}$ pairs for measurements of the weak phase $\sin (2\beta +\gamma )$ with an uncertainty of $0.05$ or better. We also determine the optimal conditions for precise $2\beta +\gamma$ measurements and discuss the possibilities for resolving a discrete ambiguity.

Comments: 18 pages, LaTeX, 4 figures, to be submitted to Phys. Rev. D