Study of the Bose--Einstein correlations in proton-proton and proton-lead collisions at LHCb

This thesis describes a study of the Bose--Einstein correlations for same-sign charged pions originating from proton-proton and proton-lead collisions recorded in the LHCb experiment at $\sqrt{s} = 7 \, \mathrm{TeV}$ centre-of-mass energy and $\sqrt{s_{\mathrm{NN}}} = 5.02 \, \mathrm{TeV}$ centre-of-mass energy per nucleon. Both measurements are the first of this type performed in the forward region at LHC energies. The proton-proton (proton-lead) dataset used in the analysis was recorded in 2011 (2013) and corresponds to an integrated luminosity of $1.0 \, \mathrm{fb}^{-1}$ ($1.6 \, \mathrm{nb}^{-1}$). Correlation parameters are determined for different regions of charged-particle multiplicity. It is observed that the correlation radius (the intercept parameter) increases (decreases) with the charged-particle multiplicity, which is consistent with observations from other experiments at the LHC in the central rapidity region. The measured correlation radii scale linearly with the cube root of the charged-particle multiplicity. Such a behaviour is compatible with predictions based on the hydrodynamic models. Moreover, hints for a dependence of the correlation radius on pseudorapidity are observed. The thesis also reports the developments in the simulation of the RICH detectors for the upgrade of the LHCb experiment. The main focus of this work is the preparation for the Run3 data-taking period. The developed tools are used to assess the performance of the RICH system in the Run3 conditions with different detector configurations. Conducted studies indicate that the upgraded RICH detectors well meet their nominal performance expectations.