A Study of the LHCb Experiment's Sensitivity to CP Violation in Mixing and to Production Asymmetry in $B_s$ Mesons, Using Semi-Leptonic Decays

LHCb is a detector that will operate at the LHC at CERN. It is designed to make specialised studies of $B$ physics, in particular studies of $CP$ violation and rare decays. In this thesis, three studies pertaining to LHCb are presented. The optical properties of the mirrors used in the RICH 1 subdetector were measured, and the aging effects of the LHCb environmental investigated. All mirrors were within design specifications. No degradation of mirrors has been observed after 11 months exposure to $C_{4}F_{10}$ gas, nor after a 10kGy radiation dose. The Monte Carlo generator Pythia is used by LHCb for event simulation. A retuning of Pythia was undertaken to improve the modelling of LEP data. A substantial improvement was achieved. A retuning of the $p_{\perp min}$ parameter, which controls Pythia's multiple-interaction model, was also required. The retuned value is $p_{\perp min}$ = 3.45 GeV. A study was made of LHCb experiment's ability to measure $CP$ violation in mixing and production asymmetry using semi-leptonic $B_s$ decays. The method uses kinematic constraints to calculate the momentum of the neutrino. $CP$ violation is characterised by the parameter $a_{fs}$. The resolution for $a_{fs}$ was found to be $\sigma_{a_{fs}}$ = 1.34 x 10$^3$, and for the production asymmetry, $\sigma_{A_{p}}$ = 16.5 x 10$^{-3}$ for 2.2 x 10$^6$ events, one year's data.