Flavour physics with (semi)leptonic decays at forward spectrometers

Particle physics is going through a very unusual and intriguing period. All particles predicted by the Standard Model (SM) have been found; nevertheless, strong experimental evidence suggests that some pieces of the puzzle are still missing. The key issue addressed in this thesis is the use of flavour physics to shed light on the yet unknown components of matter. Three different projects are reported on. The first is a detailed simulation of the behaviour of hidden particles predicted by some of the most acknowledged New Physics theories, aimed at estimating the discovery potential of a newly proposed beam dump experiment, Search for HIdden Particles (SHiP). SHiP is aimed at looking for weakly interacting hidden particles, and has the unique capability of providing the combination of energy and intensity required to probe the validity of several theories designed to explain most of the currently not understood phenomena. The work presented here assesses SHiP's sensitivity to Heavy Neutral Leptons (HNL) and Dark Photons, and explores its possible synergy with a Future Circular Collider (FCC) experiment in the search for HNLs. Another possible way to look for new physics exists. One can challenge the Standard Model by testing the properties of known particles up to very high precision. LHCb is a forward spectrometer dedicated to the study of flavour-changing processes at the Large Hadron Collider (LHC), and it is the experiment the second and third projects reported here focus on. The second project addresses the challenges of operating a high-precision silicon microstrip tracker, such as the one used by LHCb, in the remarkably radioactive environment of the LHC. This thesis describes two methods to monitor the evolution of silicon properties due to radiation damage, reporting in particular on the outcome of dedicated Charge Collection Efficiency (CCE) scans performed at regular intervals during the LHCb operation. The results are compared to the predicted evolution of the detector properties based on phenomenological models, proving that the ageing of the LHCb Silicon Tracker is under control. The universality of lepton flavour is arguably one of the most interesting consequences of the Standard Model. Contrary to this prediction, recently published results suggest that the three generations of fermions may behave slightly differently. These anomalies detected in the flavour sector sparked interest for the analysis of semileptonic $b\to c\ell\bar{\nu}_\ell$ transitions. The last project described in this thesis undertakes the first study of Lepton Flavour Universality (LFU) in a baryonic occurrence of this transition, analysing the $\Lambda_b\to\Lambda_c^*\ell\bar{\nu}_\ell$ decay. The ratio $R\left(\Lambda_c^*\right)$ between the rate of semitauonic and that of semimuonic transitions is a powerful probe for LFU. In this thesis, preparatory studies defining the strategy for such an analysis are described, and the level of background due to faulty identification of particles and to their incorrect combination is evaluated. A SM calculation predicting the value of the $R\left(\Lambda_c^*\right)$ ratio is not available yet, due to lack of information on the hadronic component of the underlying processes. Therefore, another study is presented, aimed at providing all the necessary experimental and theoretical ingredients to calculate $R\left(\Lambda_c^*\right)$ in the SM. The measurement of the form factor parameters governing the $\Lambda_b\to\Lambda_c^*$ transition would enable a precise estimation of $R\left(\Lambda_c^*\right)$. The sensitivity of such a measurement is reported here, together with an estimate of the resulting uncertainty on the theoretical value of $R\left(\Lambda_c^*\right)$.