Alignment of the Ring Imaging Cherenkov Detectors and Sensitivity to the Isospin Asymmetry in the Rare Decay $B_{d} \to K^{*} \mu^{+}\mu^{-}$ at LHCb

LHCb is a dedicated B physics experiment based at the LHC accelerator at CERN. The detector will use the large number of b hadrons produced at the LHC to study CP violation in the B meson system and search for New Physics beyond the Standard Model in rare decays. This thesis documents two pieces of research undertaken as part of the LHCb Collaboration. First a method of determining and monitoring the alignment of the LHCb Ring Imaging Cherenkov (RICH) detectors using the output RICH data is introduced. This method was validated as part of the 2006 RICH testbeam experiment, where it was used to align the recorded data runs. Application of this method to the full RICH detector system is discussed. Secondly a study to determine the sensitivity of LHCb to the isospin asymmetry in the rare B meson decay $B_d \to K^{*} \mu^{+}\mu^{-}$ is presented. A selection study of the decay $B_{u}^{\pm} \to K^{*\pm}\mu^{+}\mu^{-}$ is performed and optimised using a Fisher discriminant. The expected annual yield for this channel in a nominal $2fb^{-1}$ year of data taking at LHCb is found to be $150\pm 38$ events. The precision of an isospin asymmetry measurement of zero in the decay $B \to K^{*} \mu^{+}\mu^{-}$ is found to be $\pm 0.180$ in the low dimuon invariant mass region. This is equivalent to the precision that has been achieved by the B Factories BABAR and Belle using their full datasets.