Triple-GEM detectors for the innermost region of the muon apparatus at the LHCb experiment

The LHCb experiment will take place at the future LHC accelerator at CERN and will start in 2007. It is a single arm spectrometer to precision measurements of CP violation and rare decays in the b quark sector. Recent experimental results have shown that CP violation is large in this sector. LHCb is designed with a robust and flexible trigger in order to extensively gain access to a wide spread of different physical processes involving the beauty particles. This will allow to over-constrain the Standard Model predictions about $\mathcal{CP}$ violation, and to discover any possible inconsistency, which would reveal the presence of ''New Physics''. The work presented in this thesis has two main parts: the development of a charged particle detector based on Gas Electron Multiplication (GEM) and the study of luminosity measurements with the physical channels $Z^{0} \rightarrow \mu^{+} \mu^{-}$ and $W^{\pm} \rightarrow \mu^{\pm} \nu$. At the ''Laboratori Nazionali di Frascati'', in collaboration with a group of the ''Universit\`a degli Studi di Cagliari'', we developed a triple-GEM detector in order to equip the inner region (R1) of the first muon station (M1) of the LHCb experiment. The use of a triple-GEM detector as a triggering device is certainly a novelty in the field of high energy physics. The first application of GEM detectors in high energy physics is the COMPASS experiment, where they are currently used as a tracking device. A little interest has been devoted so far to the optimization of the time response of GEM detectors, while at LHC a critical issue is the high efficiency in the bunch-crossing identification, which requires a high detector time resolution. Since the time resolution of a triple-GEM detector operated with an Ar/CO$_{2}$ (70/30) gas mixture is about 10 ns (r.m.s.), an intense R\&D activity on GEM detectors for the Level 0 LHCb muon trigger has been performed by our group. The use of fast $CF_{4}$ and isobutane based gas mixtures, together with an optimization of the geometry and the electric fields of the detector, has allowed to improve the time resolution of the single detector down to 5 ns (r.m.s.), largely fulfilling the requirements of the experiment ($\sigma_{t}$ $\leq$ 3 ns is achieved by two OR-ed detectors, as foreseen in the muon station of LHCb). In addition we have demonstrated that the detector is robust from the point of view of both discharges and ageing processes, and can tolerate the radiation dose foreseen in 10 years of operation in the region M1R1 of the LHCb experiment. In the second part of the thesis is reported a complete study of the processes $pp \rightarrow Z^{0} \rightarrow \mu^{+} \mu^{-}$ and $pp \rightarrow W^{\pm} \rightarrow \mu^{\pm} \nu$ in order to perform an on-line luminosity measurement during the data taking of LHCb. These physical channels, marginal respect to the main LHCb physics program, have recently gained interest due to the increased theoretical accuracy in the calculation of their production cross-sections. A particular focus has been put on the detection performances of LHCb, on off-line and on-line event selections, as well as on the time needed to perform an absolute luminosity measurement with a high accuracy.