  We present a systematic analysis for the rare baryonic exclusive decays of
$\Lambda_b\to\Lambda l^+ l^- (l=e,\mu,\tau)$. We study the differential decay
rates and the di-lepton forward-backward, lepton polarization and various CP
asymmetries with a new simple set of form factors inspired by the heavy quark
effective theory. We show that most of the observables are insensitive to the
non-perturbative QCD effects. To illustrate the effect of new physics, we
discuss our results in an explicit supersymmetric extension of the standard
model, which contains new CP violating phases and therefore induces sizable CP
violating asymmetries.
