An Angular Analysis and Search for CP Violation in the Decay $B^0 \to J/\psi K^{*0}$

LHCb is a precision heavy-flavour experiment at the Large Hadron Collider and in 2011 collected just over 1 fb$^{-1}$ of data at a centre-of-mass energy of $\sqrt{s}$ = 7 Tev. The Ring Imaging Cherenkov (RICH) detectors allow LHCb to identify charged hadrons by measuring their velocity. The system uses Hybrid Photon Detectors to detect rings of single photons emitted by particles travelling through the RICH radiators. The performance-monitoring of these photon detectors whilst data-taking is presented and discussed. LHCb aims to perform precise measurements of Charge-Parity violation in B and D mesons. The final state of $B^0 \to J/\psi(\to \mu^+ \mu^-) K^{*}(\to K^+\psi^-)$ is an admixture of parity-odd and parity-even final states, which are either longitudinally or transversely polarized. These contributions can be separated by performing an angular analysis. The polarization amplitudes and phases of the final state are measured. No difference is observed between the $B^0$ and $\bar{B^0}$ flavour eigenstates which indicates that Charge-Parity symmetry has been conserved. The ambiguity in the measurement of the strong phase has been resolved by studying the P-wave and S-wave interference in the $K/\pi$ mass system. The deviation from zero or $\pi$ in the measurement of the strong phases indicates that the final state interactions have occurred. In addition, the prediction that the polarization amplitudes should be similar to those of $B^0_s \to J/\psi\phi$ is confirmed.