A study of charged $B \rightarrow D K$ and $B \rightarrow D \pi$ decays with the LHCb experiment

The LHCb experiment at the Large Hadron Collider is dedicated to making precision measurements of CP-violation and rare decays, thereby searching indirectly for new phenomena beyond the Standard Model (SM) of particle physics. The Ring Imaging CHerenkov (RICH) subdetectors provide essential particle identification information for many LHCb physics analyses, including the analysis detailed in this thesis. Selection criteria have been developed which allow the monitoring of the refractive indices of the RICH radiators using isolated Cherenkov light rings, both with and without information from other subdetectors. This, in turn, ensures that the information provided by the RICH subdetectors is of the highest quality. The decay $B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) K^{\pm}$ allows a measurement of the CKM angle $\gamma$ to be made using the GGSZ (Dalitz) method. This provides a SM benchmark against which new phenomena can be compared. Accurate RICH particle identification is vital in separating signal $B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) K^{\pm}$ decays from those of the control channel $B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) \pi^{\pm}$. The selection of signal decays has been optimised using simulated events. In the first proton-proton collision data collected at a centre-of-mass energy of $7$ TeV during $2010$ and corresponding to an integrated luminosity of ~$36.5 pb^{-1}$, the ratio of branching fractions $\cfrac{\textrm{Br(} B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) K^{\pm} \textrm{)} }{\textrm{Br(} B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) \pi^{\pm} \textrm{)} } = 0.12^{+0.06}_{-0.05} \pm 0.03$ has been measured, where the first error is statistical and the second systematic. A further data set, recorded in $2011$ and corresponding to an integrated luminosity of ~$342 pb^{-1}$ at $\sqrt{s}=7$ TeV, has been used to measure the ratio of branching fractions to higher precision. The results were extracted using two independent samples of $B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) K^{\pm}$ and $B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) \pi^{\pm}$ decays where the $K_S^{0}$ decay occurs either near to the proton-proton interaction point or further into the LHCb detector. The results are $\cfrac{\textrm{Br(} B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) K^{\pm} \textrm{)} }{\textrm{Br(} B^{\pm} \rightarrow \overline{D}^{0} / D^{0} (K_S^{0} \pi^{+} \pi^{-}) \pi^{\pm} \textrm{)} } = 0.089^{+0.015}_{-0.014} \pm0.006$ and $0.07\pm0.02 \pm 0.01$ respectively, where the first errors are statistical and the second systematic.