Characterisation of Hybrid Photon Detectors for the LHCb and an analysis of the rare decay $B_{s}^{o} \rightarrow \phi \phi$

The LHCb experiment at CERN is nearing completion and is expected to begin operation in 2008. It will make precision measurements of Charge-Parity in the $B$ meson system. Two Ring Imaging Cherenkov detectors provide excellent charged particle recognition, particularly in their separation of kaons and pions. This thesis outlines the production and testing of Hybrid Photon Detectors, used to measure Cherenkov light in the Ring Imaging Cherenkov detectors. We also report an analysis of the rare decay $B_s^o \rightarrow \phi (K^+K^-) \phi (K^+K^-)$ using data produced in a Monte Carlo simulation. The ability to distinguish kaons and pions is vital to reduce the combinatorial background. In this decay a $b \rightarrow s$ transition occurs which is heavily suppressed in the Standard Model, and thus provides an excellent opportunity to search for New Physics. We find an expected yield of 1834$\pm$1136 $B_s^o \rightarrow \phi \phi$ events in a $2\rm fb^{-1}$ data sample. A background to signal ratio of $0.25 \pm 0.18$ was obtained.