This PhD thesis presents a search for Heavy Neutral Leptons (HNLs) using data collected by the CMS experiment at the CERN Large Hadron Collider (LHC). HNLs are hypothetical new particles proposed in several theoretical extensions of the Standard Model (SM) to account for the origin of neutrino masses. Additionally, their existence could explain other open questions in particle physics, such as the origin of dark matter and the baryon asymmetry of the Universe. This analysis considers final states with three muons, one of which is produced close to the interaction point while the other two originate from a common displaced vertex. The analysis strategy is optimised for high HNL decay lengths by selecting two muon objects that are exclusively reconstructed outside the CMS inner tracker. Looking at such displaced signatures gives access to a high lifetime region for the HNLs, where tracker-based analyses have limited acceptance, and at the same time effectively suppresses SM backgrounds. This search uses proton-proton collision data collected by CMS during the full LHC Run 2 and the first year of Run 3, corresponding to integrated luminosities of 138/fb at $\sqrt{s}$=13 TeV and 34.6/fb at $\sqrt{s}$=13.6 TeV. The results are presented as upper limits on the mixing parameter $|V_{N\mu}|^2$ between the HNL and the muon neutrino as a function of the HNL mass. The observed upper limits exceed the constraints set by CMS tracker searches for masses below 3.5 GeV and provide the current most stringent limits in the mass range between 2.5 and 3.5 GeV.

The second part of this PhD work is dedicated to the characterisation of the scintillating fibre (SciFi) tracker of SND@LHC, a neutrino experiment in operation at the LHC since 2022. The SND@LHC target region is instrumented with five SciFi modules, each following a wall of emulsion cloud chambers, with the function of assigning a timestamp to the reconstructed neutrino events and measuring the energy of electromagnetic showers. The SciFi tracker technology is based on closely packed layers of scintillating fibres and multichannel arrays of silicon photomultipliers originally developed for the LHCb experiment. A new DAQ system was built for SND@LHC to meet stringent time resolution requirements and allow the measurement of signal amplitudes from the photodetectors. In this thesis, three aspects of the SciFi tracker performance are analysed using both test-beam data and laboratory studies: the detector's time resolution, the measurement of the signal amplitude in the front-end ASIC, and the system's response to particle showers. The obtained results provide the first characterisation of the SciFi tracker paired with the new DAQ system, allow the definition of the best operation parameters for the SND@LHC detector, and improve the software for data acquisition.