Testing Fundamental Symmetries with \Lambda_b \to \Lambda -Vector Decay

Putting together kinematical and dynamical analysis, a complete study of the decay channels $\Lambda_b \to {\Lambda} V(1^-)$, with $\Lambda \to p {\pi}^-$ and $V (J/\psi) \to {\ell}^+ {\ell}^-$ or $V ({\rho}^0) \to {\pi}^+ {\pi}^-,$ is performed. An intensive use of the helicity formalism is involved on the kinematical side, while on the dynamical side, Heavy Quark Effective Theory (HQET) is applied for an accurate determination of the hadronic matrix elements between the baryons $\Lambda_b$ and $\Lambda$. Emphasis is put on the major role of the $\Lambda_b$ polarization for constructing T-odd observables and the standard ${\rho}^0-{\omega}$ mixing has the benefit effect of amplifying the process of direct CP violation between $\Lambda_b \mathrm{and} {\bar \Lambda}_b$ decays.