The Rare Decays $B^0_{(s)}\to\mu^+\mu^-$ and $Z$ Boson Production at LHCb and Radiation Damage in its Silicon Tracker

The LHCb experiment at the Large Hadron Collider is dedicated to the study of physics involving beauty and charm quarks. Its detector $-$ designed as a single-arm forward spectrometer $-$ uses tracking stations upstream and downstream of a dipole magnet to measure the trajectories and the momenta of charged particles. Parts of this tracking system are built from silicon micro-strip detectors. This thesis describes the monitoring of the radiation damage in these detectors using leakage current measurements and so-called Charge Collection Efficiency scans performed in regular intervals during data taking. The results of this monitoring during the first LHC data taking period from 2010 to 2013 are presented and predictions for the future evolution of the detector ageing are discussed. A main goal of LHCb is the measurement of rare decays. As these decays are heavily suppressed in the Standard Model, their properties, for example the branching fraction, angular distributions or $CP$ asymmetries, can be significantly modified by contributions from physics beyond the Standard Model. ``Golden'' channels among such indirect searches are the decays $B_s^0\to\mu^+\mu^-$ and $B^0\to\mu^+\mu^-$. This thesis describes for these two decays the determination of the expected signal response in terms of the invariant dimuon mass and a multivariate classifier based on topological and kinematical decay properties. This calibration is based on known dimuon resonances such as $J/\psi\to\mu^+\mu^-$, $\varUpsilon(1S)\to\mu^+\mu^-$ or $Z\to\mu^+\mu^-$ and charmless two-body decays of $B^0_s$ and $B^0$ mesons into pairs of charged kaons and pions. The developed techniques were also applied to the determination of the signal yield of normalisation channels, the estimation of background contamination and the comparison of selection variables between data and simulation. These investigations were a part of the analysis that led to the first evidence of the decay $B_s^0\to\mu^+\mu^-$ and the measurement of its branching fraction. Besides measurements involving beauty and charm quarks, LHCb is well suited to measure particles produced in hadron collisions at small angles with respect to the beam axis. An interesting measurement to investigate the dynamics of partons inside nuclei is the study of electroweak gauge boson production in proton-lead collisions. A first measurement of $Z$ boson production based on proton-lead data collected by LHCb in 2013 is also presented in this thesis. It led to the first observation ever of $Z$ boson production in proton-nuclei collisions.