The LHCb RICH: its application to the study of the $\rm B_s \rightarrow J/\Psi \Phi$ decay channel and magnetic distortions corrections

The LHCb experiment has been designed to study CP violation and rare B meson decays with very high precision. Particle identification over the wide momentum range 1--100\,GeV/c is provided by two Ring Imaging Cherenkov (RICH1 and RICH2) detectors. The Cherenkov photons are detected by 484 Hybrid Photon Detectors (HPD) which cover a $\rm 2.6\,m^2$ surface with a granularity of $\rm 2.5\times2.5\,mm^2$. A HPD consists of a vacuum tube operating at a high--voltage of -20\,kV. Cherenkov photons converted to photoelectrons in a photocathode are accelerated towards a pixelised Silicon anode bump--bonded to the encapsulated front--end electronics. Two additional electrodes determine the shape of the accelerating electric field. The work presented in this thesis was carried out at CERN (European Organization for Nuclear Research) during the commissioning phase of the LHCb experiment. The main part of my work was the development of a software for the magnetic distortion compensation. A magnetic field of less than 10 Gauss can be present inside the HPD in spite of all the magnetic shields. Given that 484 HPDs are installed in RICH1 and RICH2, an automated procedure to determine the magnetic distortion in each tube, and the resulting correction factors, is required. A general pattern recognition tool was developed to analyse data both with and without magnetic field and for alignment purpose. The ultimate goal was to achieve such an accuracy in the correction procedure that the residual uncertainty due to magnetic distortions is negligible in comparison to the pixel size, i.e. $\rm2.5\times2.5\,mm^2$. A centre--of--gravity procedure is combined with a maximum local search and an advanced clusterization algorithms obtaining an uncertainty of $\rm 0.9\times0.6\,mm^2$ (at the photocathode) in the pattern reconstruction. The second main project was the study of a a selection procedure for the decay channel $\rm B^0_s \rightarrow J/\psi(\mu^+ \mu^-) \phi(K^+ K^-)$. A Monte Carlo simulation is used for the $\rm B^0_s \rightarrow J/\psi(\mu^+ \mu^-) \phi(K^+ K^-);$ events and for the background channels $\rm B_d^0 \rightarrow J/\Psi(\mu^+ \mu^-)K^*$ and $\rm B^{\pm} \rightarrow J/\Psi(\mu^+ \mu^-) K^{\pm}$ to search for the adequate selection cuts to be applied in order to extract the signal. An annual event yield, using the nominal integrated luminosity of 2f$\rm b^{-1}$ and a $b-\overline{b}$ production cross section of 500$\rm \mu b$} of 93000 is then expected for the decay channel $\rm B^0_s \rightarrow J/\psi(\mu^+ \mu^-) \phi(K^+ K^-)$ using the proposed selection.