  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.
