The Trigger Tracker and a Monte Carlo Study of the $B_{s}^{0} \to J/\psi \eta'$ decay in the LHCb experiment

The LHCb experiment, which is currently under construction at the Large Hadron Collider (CERN, Geneva), is designed to study CP violation and find rare decays in the B meson system. An important element of the LHCb tracking system is the Trigger Tracker, which covers a sensitive surface of about 7.7 m$^2$ with silicon microstrip detectors. This dissertation is dedicated to this part of the LHCb spectrometer. In particular, the detector design, its main characteristics, the main results from the R&D programme and the quality assurance programme for detector modules are discussed. In addition, the XML-based detector description of the Trigger Tracker for the Monte Carlo simulation of the LHCb experiment is presented. Also, this dissertation presents the analysis of the $B_{s}^{0} \to J/\psi \eta'$ decay based on the full Monte Carlo simulation. By measuring the time-dependent \CP asymmetry arising in this channel, the $B^0_s$ weak mixing phase $\phi_{s}$, which refers to the CKM angle $\chi$, can directly be extracted without theoretical uncertainties. Since $\phi_{s}$ is expected to be very small in the Standard Model, the measurements of this phase will provide a sensitive probe for contributions from New Physics beyond the Standard Model. In this dissertation, the reconstruction and selection of $B_{s}^{0} \to J/\psi \eta'$ events at LHCb using the decay channels $J/\psi \to \mu^{+}\mu^{-}$ and $\eta' \to \rho^{0}(\pi^{+}\pi^{-})\gamma$ is described. Finally, the sensitivity of the LHCb detector to measure $\phi_{s}$ with this decay mode is presented.