Mesure de la polarisation du baryon lourd $\Lambda_b$ avec le détecteur LHCb. Recherche de la violation directe de la symétrie de renversement du temps T

This thesis subject focuses on the study of the weak decay of the beauty baryon $\Lambda_{b} \to \Lambda J/\Psi$ with the LHCb detector. Firstly, it offers the opportunity to test the validity of the CP symmetry in the baryon sector and, secondly, the one of time-reversal symmetry $T$ whose experimental evidence is tiny. Emphasis is put on the measurement of the components of the polarization-vectors of the $\Lambda_{b}$ and the ones of the intermediate resonances $\Lambda$ and $J/\Psi$, whose some components exhibit a clear sign of direct $T$ violation. The development of a phenomenological model of the $\Lambda_{b} \to \Lambda J/\Psi$ decay in the framework of the helicity formalism of Jacob-Wick and Jackson leads to the calculations of the angular distributions which allow to deduce the values of the polarization vector components. A thorough study of the reconstruction and the selection of the data recorded by LHCb in 2011 and 2012 is exposed, as well as a full Monte Carlo simulation. The compatibility between the measured values of the polarization-vector of $\Lambda_{b}$ and $\bar{\Lambda}_{b}$ implies the absence of CP violation. The direct violation of the T symmetry has not been observed in the hadronic decays of $\Lambda_{b}$ ( $\bar{\Lambda}_{b}$). On another side, first measurements of the longitudinal polarization of $\Lambda_{b}$ and of $\bar{\Lambda}_{b}$ as well as the longitudinal polarization of the vector-meson $J/\Psi$ have been performed in the context of this work.