Upgrades of the SND@LHC detector during LHC Run~3 and search for muon neutrinos from proton--proton collisions at $\sqrt{s}=13.6\,\mathrm{TeV}$

This thesis presents the SND@LHC experiment, a forward detector at the CERN LHC. SND@LHC studies neutrinos produced in proton–proton collisions at the LHC, bridging the gap between low-energy reactor experiments and astrophysical neutrino observations. All neutrino flavours are studied; in particular, a small but significant sample of tau neutrino interactions is expected. The experimental setup required to detect such elusive particles also opens sensitivity to feebly interacting particles, offering a window into physics beyond the Standard Model. Moreover, SND@LHC will enable the study of charmed hadrons production in proton–proton interactions and provide precision tests of the Standard Model through the lepton flavour universality of the weak interaction. Since its commissioning in 2022, SND@LHC has undergone an extensive process of detector characterisation and optimisation, in which this work plays a role spanning both hardware developments and data analysis. I contributed to the upgrade of the Veto System, crucial for rejecting charged-particle backgrounds in neutrino searches. An additional module was constructed, tested, and installed before the restart of 2024 LHC operation, reducing the system inefficiency by an order of magnitude and achieving uniform performance across the full target acceptance. I took part in a test-beam campaign in 2023, which was used to calibrate the detector response to hadronic showers. The resulting calibration constants are a crucial step toward neutrino energy reconstruction. At the same time, I began studying charged-current $\nu_\mu$ interactions using the 2024 data, which benefited from improved background suppression. Selection strategy, control samples, and preliminary results are presented. Finally, I contributed to a second upgrade in March 2025: the installation of drift-tube modules to enhance muon identification and tracking. Early performance studies indicate a performance consistent with expectations. Collectively, these results enhance the SND@LHC detector's capability for precision neutrino measurements at the LHC and broaden its discovery reach.