Measurement of the CKM angle $\gamma$ and development of a novel, combined GGSZ analysis of $B \rightarrow D^{(*)} h^{(*)}$ decays at LHCb

The angle $\gamma$ is a fundamental parameter of the Standard Model, within which it quantifies the degree to which CP violation is permitted. It is presently one of the least well-constrained parameters of the CKM sector, which embodies the description of quark interactions. This thesis details work undertaken by the author at the LHCb experiment with the aim of reducing the uncertainty in $\gamma$. It describes a measurement performed using a Dalitz analysis of $B^0 \rightarrow D K^{*0}$ decays, and a study which extends this work to a simultaneous Dalitz analysis of several $B$-meson decay modes of the form $B \rightarrow D^{(*)} K^{(*)}$. In each analysis, $\gamma$ is extracted by studying the interference between CP eigenstates $D^0$ and $\overline{D^0}$ in the common final state $D \rightarrow K_S^0 \pi^+ \pi^-$, where $D$ represents either a $D^0$ or $\overline{D^0}$ meson. The measurement of $\gamma$ in $B^0 \rightarrow D K^{*0}$ decays includes the full $3\mathrm{fb}^{-1}$ Run 1 dataset gathered at LHCb, and uses a model-dependent approach to yield the 'Cartesian parameters' $\begin{eqnarray*} x_- &=& -0.15 \pm 0.14 \pm 0.03 \pm 0.01,\\ y_- &=& \phantom{-}0.25 \pm 0.15 \pm 0.06 \pm 0.01,\\ x_+ &=& \phantom{-}0.05 \pm 0.24 \pm 0.04 \pm 0.01, \quad \text{and}\\ y_+ &=& -0.65~^{+0.24~~}_{-0.23~~} \pm 0.08 \pm 0.01, \end{eqnarray*}$ where the first uncertainties are statistical, the second systematic and the third arise from the uncertainty on the $D \rightarrow K_S^0 \pi^+ \pi^-$ amplitude model used. These results imply (the relation between $\{x_\pm,y_\pm\}$, and angle $\gamma$, is described within) a value for $\gamma$ of $\begin{equation*} \gamma = (80^{+21}_{-22} )^\circ. \end{equation*}$ In the simultaneous analysis, both model-dependent and model-independent approaches to the determination of $\gamma$ are studied. Using the full Run 1 LHCb dataset, the model-dependent approach yields preliminary uncertainties of $\begin{eqnarray*} \sigma_{x_-} &=& \pm 0.019 \pm 0.010 \pm 0.001,\\ \sigma_{y_-} &=& \pm 0.013 \pm 0.010 \pm 0.005,\\ \sigma_{x_+} &=& \pm 0.018 \pm 0.010 \pm 0.005, \quad \text{and} \\ \sigma_{y_+} &=& \pm 0.018 \pm 0.010 \pm 0.010, \end{eqnarray*}$ where the first numbers are statistical, the second are estimated systematics arising from the experimental method used, and the third are estimated systematics arising from the uncertainty on the $D \rightarrow K_S^0 \pi^+ \pi^-$ amplitude model. The statistical covariances obtained for the Cartesian parameters propagate to give an estimated statistical uncertainty of $12^\circ$ on the value of $\gamma$. The model-independent approach yields preliminary uncertainties of $\begin{eqnarray*} \sigma_{x_-} &=& \pm 0.021 \pm 0.010 \pm 0.005,\\ \sigma_{y_-} &=& \pm 0.022 \pm 0.005 \pm 0.010,\\ \sigma_{x_+} &=& \pm 0.023 \pm 0.010 \pm 0.005, \quad \text{and} \\ \sigma_{y_+} &=& \pm 0.029 \pm 0.005 \pm 0.010, \end{eqnarray*}$ where in this case the final numbers are estimated systematics arising from the uncertainty on the binned $D \rightarrow K_S^0 \pi^+ \pi^-$ strong phase parameters. The statistical covariances obtained for the Cartesian parameters propagate to give an estimated statistical uncertainty of $13.5^\circ$ on the value of $\gamma$. In addition, work undertaken to ensure the continued performance of the RICH subdetectors of LHCb is described. These subdetectors form a crucial part of the particle-identification system of LHCb, whose accuracy allows the precise study of processes with hadronic final states, such as the decays mentioned above