Testing the Standard Model Lepton Symmetries in Collider and Fixed-Target Experiments

There has been much excitement in the high energy physics community in recent years. The discovery of the Higgs boson at CERN confirmed all the predictions of the Standard Model, the theory that describes elementary particles and their interactions. Despite this tremendous success, other experimental results have been observed that cannot be described by the Standard Model. This inspires physicists around the world to search for evidence of physics beyond the Standard Model. One potential manifestation of this would be discrepancies between experimental results and theoretical predictions. This requires not only increasing the precision of existing measurements by increasing the luminosity of existing experiments, but also designing new experiments that allow the exploration of new physical phenomena that have not yet been detected. The results of this work contribute to the various areas of the search for physics beyond the Standard Model. The presented $R$ ($\Lambda$$_{c}$) = $\Lambda$0 $b$→$\Lambda$+ $c$ $\tau$ −$ν$$\tau$ $\Lambda$0 $b$→$\Lambda$ + $c$$\mu$−$ν$$\mu$ analysis is devoted to the study of lepton flavour universality in $\Lambda$$_{b}$ decays using data collected in 2016 from the LHCb experiment. Anomalous deviations in semileptonic decays have been observed recently in several measurements, and are known as flavour anomalies. The measurement of the $R$ ($\Lambda$$_{c}$) ratio will help to solve this puzzle. The LHCb experiment is currently undergoing a major upgrade to improve the sensitivity of all measurements that contributed to the anomalies. The system for validation tests of readout chips for one of the detectors has been developed and the results of these tests are presented. Feasibility studies for a newly proposed SHiP experiment are also presented in this work, which would allow to open new regions for the search of new physics. The most dangerous background for the experiment comes from neutrino interactions. Its estimation and the possibilities of the experiment to suppress it are demonstrated. The second most dangerous background is from muons. The optimization of the magnetic system to eliminate this background is presented. Overall the work in this thesis has contributed to a broad spectrum of how experimental particle physics is performed. The hope is that one of these avenues will lead to a potential discovery.