Role of a charm factory in extracting CKM-phase information viaB→DK

In this paper we study the impact of data that can be obtained from a charm factory on the determination of the Cabibbo-Kobayashi-Maskawa parameter $\gamma$ from decays of the form $\overrightarrow{B}{D}^{0}K$ where the $D^0$ decays to specific inclusive and exclusive final states. In particular, for each exclusive final state f, the charm factory can determine the strong phase difference between $D^0\to f$ and $D^0\to f$ by exploiting correlations in $\psi \mathrm{}\left(3770\right)\mathrm{}\to D^0{D}^0.$ This provides crucial input to the determination of $\gamma$ via the interference of $B^{\pm }\to K^{\pm }{D}^0\to f$ with $B^{\pm }\to K^{\pm }{D}^0\to f.\mathrm{}$ We discuss how the method may be generalized to inclusive final states and illustrate with a toy model how such methods may offer one of the best means to determine $\gamma$ with ${O(10\mathrm{}}^8–{10}^9)$ B mesons.