CP-violation parameters from decay rates of $B^\pm \to D K^\pm$, $D\to$ multibody final states

We describe a method for measuring CP-violation parameters from which the Cabibbo-Kobayashi-Maskawa angle $\gamma$ may be extracted. The method makes use of the total decay rates in $B^\pm \to DK^\pm$ decays, where the neutral $D$ meson decays to multibody final states. We analyze the error of the method using experimental CP-violation analysis variables that enable straightforward sensitivity comparison with other methods for extracting $\gamma$, and discuss the use of $B$-factory and charm-factory data to obtain the relevant charm decay information needed for this measurement. Measurement sensitivities are estimated for the currently available $B$-factory data sample, and $D$ decay modes for which use of this method can make a significant contribution toward reducing the total error on $\gamma$ are identified.