Studies of RICH detectors and the $B_d \rightarrow K^{*}\mu^{+}\mu^{-}$ decay at the LHCb experiment

LHCb is an experiment designed for precise studies of the large number of b-hadrons expected at the Large Hadron Collider. This thesis first introduces the Standard Model of Particle Physics and motivates the LHCb experiment. The design of the LHCb forward spectrometer is then described, including performance of the detector with recent LHC collisions. The ring imaging Cherenkov (RICH) sub-detector is described in particular detail. This uses three radiators to identify particles over the momentum range 1-100 GeV/c. Tests performed of an LHCb RICH prototype with a charged pion beam are described in detail. Excellent performance is found in agreement with that expected from studies of simulated data. The decay $B_d \rightarrow K^{*}\mu^{+}\mu^{-}$ is a powerful indirect probe of new physics. In particular, the forward-backward asymmetry of the muon pair is precisely predicted in the Standard Model and many new physics models, and measurements of this asymmetry will discriminate between the widely varying expectations of different models. Two methods of selecting $B_d \rightarrow K^{*}\mu^{+}\mu^{-}$ events at LHCb are investigated. An automated tool is developed to choose a set of selection cuts automatically, and this improves on the performance of the previous selection. A further selection is then developed, based on a Fisher discriminant and vetoes to remove two peaking backgrounds. This selection yields 6200$^{+1700}_{-150 0}$ signal and 1550$\pm$310 background events per 2fb$^{-1}$ at the nominal LHC energy of $\sqrt{s}$=14TeV. Finally, a toy Monte Carlo is used to estimate the precision with which LHCb can make a single-bin measurement of the forward-backward asymmetry during the first LHC physics run. This initial run is expected to accumulate approximately 1fb$^{-1}$ over 2010-11 at $\sqrt{s}$ = 7TeV. With approximately 0.3 fb$^{-1}$, an LHCb measurement will be competitive with published results from other experiments.