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 $\phi_3=\gamma$ 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.