Measuring the CKM Angle $\gamma$ with $B^{\pm} \to DK^{\pm}$ Decays at LHCb and a Determination of the $D \to K\pi\pi\pi$ Coherence Factor at CLEO-c

With an uncertainty of $\sim 30^{\circ}$ from current direct measurements, the CKM angle $\gamma$ is the least experimentally constrained CP-violating parameter of the Standard Model. Consequently, a precision determination of this phase is one of the most crucial goals of flavour physics in the coming decade. A series of highly promising strategies have been proposed that exploit the interference effects present within $B^{\pm} \to DK^{\pm}$ decays. Since the LHCb experiment at CERN is set to become the most copious source of $B$ hadrons in the world, it is in a unique position to utilise such strategies. This thesis investigates LHCb's capabilities to make a precision measurement of $\gamma$ with the exclusive decays $B^{\pm} \to D(KK\pi\pi)K^{\pm}$ and $B^{\pm} \to D(K\pi\pi\pi)K^{\pm}$.\\ LHCb simulation studies have been performed in order to develop efficient reconstruction algorithms for the above two modes. Signal and background yields are estimated for a nominal year of LHCb data (equivalent to an integrated luminosity of $\rm 2~fb^{-1}$). Sensitivities to $\gamma$ are determined using the appropriate analysis techniques for the two final states. In the case of the self-conjugate mode $D \to KK\pi\pi$, a four-body amplitude analysis must be used. With this technique it is demonstrated that a sensitivity of $\sim 18^{\circ}$ is achievable from a $\rm 2~fb^{-1}$ dataset.\\ Due to the multiple charge combinations possible with the $B^{\pm} \to D(K\pi\pi\pi)K^{\pm}$ mode, a `counting' technique can be utilised to extract $\gamma$. For this to be possible, an additional parameter associated with the $D \to K\pi\pi\pi$ decay must be know: the coherence factor, $R_{K3\pi}$. A determination of this parameter, and the associated strong-phase difference $\delta_{D}^{K3\pi}$, are presented following analysis of $818~{\rm pb^{-1}}$ of $e^{+}e^{-} \to \psi(3770)$ data collected at the CLEO-c experiment. The result $R_{K3\pi} = 0.24^{+0.21}_{-0.17}$ and $\delta_{D}^{K3\pi} = (161^{+85}_{-48})^{\circ}$ is found. Studies demonstrate that introducing these constraints from CLEO-c into a combined $B^{\pm} \to D(K\pi, \pi\pi, KK)K^{\pm}$ and $B^{\pm} \to D(K\pi\pi\pi)K^{\pm}$ analysis at LHCb, a sensitivity of $(7 - 10)^{\circ}$ is achievable from a $\rm 2~fb^{-1}$ dataset.\\ Critical to these analyses is the particle identification provided by the LHCb Ring Imaging Cherenkov (RICH) sub-detector. To ensure high performance a Level-0 readout system is developed, in addition to a laser-light tool for calibration of the detector's trigger-timing prior to installation into the LHCb experiment.