Measurement of mixing and CP violation in D0→KS0π+π- decays with 2024 Data and Performance studies of the RICH detectors in the Upgrade I and Upgrade II of LHCb

This thesis presents studies of charm mixing and CP violation, together with investigations of the performance of the Ring Imaging Cherenkov (RICH) detectors of the LHCb experiment in Run 3 and in the context of the Upgrade II programme. The first part of this thesis focuses on a measurement of charm mixing and CP-violation observables in the decay channel D0→KS0π+π- using Run 3 data collected in 2024 by the LHCb experiment. The analysis employs the bin-flip method, a model-independent approach that avoids reliance on amplitude modelling and reduces systematic effects related to efficiency variations across the Dalitz plane. Although based on a subset of the full Run 3 dataset, the integrated luminosity already exceeds that of Run 2, resulting in sensitivities that are slightly improved. The stability of the results is investigated as a function of the data-taking blocks, and good overall consistency and robustness of the measurement are observed. The second part of the thesis evaluates the performance of the upgraded RICH detectors using Run 3 data from 2024. Studies of photon timing and hit distributions validate the detector performance under real data-taking conditions and provide insight into background contributions and their impact on the single photon resolution. The final part addresses the prospects for particle identification at the high luminosities foreseen for the LHCb Upgrade II. Simulation-based studies of several RICH detector configurations highlight the importance of timing and spatial resolution in maintaining excellent particle identification performance, and provide input to the design choices for the future upgrade of the experiment.