Amplitude analysis and polarisation measurement of the $\Lambda^+_c$ baryon in $pK^-\pi^+$ final state for electromagnetic dipole moment experiment

The first part of the thesis presents an experiment proposal for short-lived heavy baryon electromagnetic dipole moments measurement, exploiting spin precession of particles channeled in bent crystals, produced from fixed-target collisions of multi-TeV energy protons extracted from the main beam of the Large Hadron Collider accelerator. The LHCb detector is considered to measure the baryon polarisation from its decay distribution. The same methodology is further extended to the measurement of $\tau$ lepton electromagnetic dipole moments, which is complicated by the presence of undetectable neutrinos. The second part of the thesis presents the amplitude analysis of $\Lambda^+_c\to pK^-\pi^+$ decays from $\Lambda^0_b \to \Lambda^+_c \mu X$ production recorded by the LHCb experiment, including the extraction of the $\Lambda^+_c$ polarisation vector. This analysis is an essential tool in light of the $\Lambda^+_c$ baryon dipole moments measurement, providing an unprecedented knowledge of the main $\Lambda^+_c$ decay mode and the $\Lambda^+_c$ polarisation. Order one million events are selected from LHCb data with negligible background contributions. The $\Lambda^+_c\to pK^-\pi^+$ decay model for generic polarisation is written in the helicity formalism and fitted to data. An amplitude model describing $\Lambda^+_c\to pK^-\pi^+$ decays has been obtained from two-dimensional Dalitz plot fits, giving valuable information on the main intermediate resonances, including the observation of new $\Lambda^*$ resonant contributions. The third part of the thesis deals with the $\Lambda^+_c$ polarisation measurement in proton-neon collisions at 68.6 GeV centre-of-mass energy recorded by LHCb, which provides information on the $\Lambda^+_c$ baryon structure. A significant $\Lambda^+_c$ polarisation is also crucial for the proposed dipole moments experiment. The feasibility of the measurement has been proved achieving two essential results: a few hundreds $\Lambda^+_c\to pK^-\pi^+$ decays are selected from proton-neon LHCb data, separated from background contributions; the $\Lambda^+_c$ polarisation measurement from the selected sample has been proved feasible on simulated pseudo-experiments, showing that the main associated systematic uncertainty is negligible compared to statistical fluctuations.