Determining the CP Violation Angle $\gamma$ in $B_s$ Decays without Hadronic Uncertainty

Abstract

We study the rare decays $B_s^0\to D^{\pm }{\pi }^{\mp }$ and ${\bar{B}}_s^0\to D^{\mp }{\pi }^{\pm }$, which can occur only via annihilation type $W$ exchange diagrams in the standard model. The time-dependent decay rates of the four channels can provide four CP parameters, which are experimentally measurable. We show that the CKM angle ${\varphi }_3=\gamma$ can be determined from these parameters without any theoretical model dependence. These channels can be measured in future LHCb experiments to provide a clean way for $\gamma$ measurement.

Comments: 4 pages, including 2 figures, Revtex