Study of GigaTracker performance and a search for Axion-Like Particles at the NA62 experiment

This thesis discusses the results of two projects carried out within the NA62 collaboration operating a fixed-target kaon experiment located in the North area of the CERN SPS. The NA62 experiment aims to measure the ultra-rare kaon decay $K^+ \rightarrow \pi^+ \nu \bar\nu$ with 10% precision. This task is impossible without using the beam spectrometer, an hybrid silicon detector called GigaTracKer (GTK). The development of the dedicated time calibration procedure, crucial for achieving the best timing performance of the GTK, is discussed. The timing performance of the GTK and the effects of radiation damage on the detectors installed during the 2016-2018 data taking periods are also investigated. The results of this work can be directly used in any NA62 physics analysis, which relies on the GTK performance. The second project focuses on the searches for New Physics processes. A sensitivity study to the production of a light scalar or pseudoscalar particle coupling to fermions produced in the rare decays of B-mesons is performed. A model-independent approach, the analysis strategy, the signal Monte Carlo, and the analysis of the 2017-2018 data are discussed. Dedicated trigger conditions are set up to be used in future data taking at improved sensitivity.