Analyse du canal $\Lambda_b \to \Lambda + J/\Psi$ et mesure de la polarisation du baryon $\Delta$ produit dans les collisions $p-p$ à 7 TeV avec le détecteur LHCb

The topics discussed and developed in this dissertation aim to propose a new way to test, in a direct manner, the symmetry of time reversal (T): an opportunity is offered by the LHC through the copious production of beauty baryons, especially the $\Lambda_b$ whose decay channels in $\Lambda V (1^{-})$ would reveal the existence of new odd observables under T. The Emphasis is put on the importance of the $\Lambda_b$ initial polarization produced in p-p collisions, and especially those of intermediate resonances coming from $\Lambda_b$. We first present the theoretical framework of this work and secondly the different procedures concerning the direct search of T violation. A phenomenological model considering the decay $\Lambda_b \to \Lambda J/\Psi$ has been developed, from which angular distributions are computed. A detailed study of the reconstruction and selection of the channel $\Lambda_b \to \Lambda J/\Psi$ is exposed as well as that of the channel $B_d^0 \to J/\Psi K_S^0$; channel used to validate the extraction of the $\Lambda_b$ lifetime. On another side and due to the start of the LHC, a preliminary analysis of data recorded by the LHCb has been made. A promising first measure of the hyperon $\Lambda$ polarization was also performed.