Precise measurements of charmed baryon properties with the LHCb detector at the LHC

Charmed baryon polarization is not predicted by theory and it is a necessary input for the measurement of the charmed baryons magnetic dipole moment (MDM) which is foreseen at the LHC. Baryon's polarization has been measured for strange ($\Lambda$) and beauty ($\Lambda^0_b$) baryons in different colliding systems, however, no measurement exists for charmed baryons as of today. In this thesis, the $\Lambda_c^+$ polarization is measured by means of a five-dimensional amplitude analysis of the three-body weak decay $\Lambda_c^+\rightarrow pK^-\pi^+$ of $\Lambda_c^+$ produced in $pp$ collisions at a center of mass energy of 13 TeV. The $\Lambda_c^+\rightarrow pK^-\pi^+$ decay passes through intermediate resonant states which interfere with each other, and which need to be included in the amplitude. First, the equations describing the amplitude of this three-body decay have been derived within the helicity formalism. The polarization is accounted for by means of the spin density matrix and the intermediate resonant states are described using the isobar model factorization. This work allowed to better understand the helicity amplitudes and can be easily extended to other three-body baryonic decays featuring particles with spin in the final state. The helicity amplitudes obtained are used to describe the data collected by the LHCb detector at CERN during the 2016 data taking period (Run 2), corresponding to an integrated luminosity of $1.7fb^{-1}$. The analysis is performed on $\Lambda_c^+$ produced directly after the $pp$ collisions via strong interactions (prompt production). The next data acquisition phase, foreseen in 2022, will see an increase of the collision rate by a factor of 5 at LHCb. A new detector, PLUME, has been designed to perform a luminosity measurement in the new running conditions. In this thesis, the front-end electronics of the LHCb calorimeter has been tested to prove that it is adapted for the PLUME detector needs and it is now the baseline electronics for PLUME. Finally, a preliminary measurement of the LHCb clock shift using the PLUME detector is proposed.