  We work out the semileptonic $\Lambda_b\rightarrow \Lambda \ell^+ \ell^-$
transition in standard as well as different supersymmetric models. In
particular, considering the parametrization of the matrix elements entered the
low energy effective Hamiltonian in terms of form factors in full QCD, we
calculate the amplitude and differential decay rate responsible for this decay
channel in supersymmetric models. We then use the form factors calculated via
light cone QCD sum rules in full theory to analyze the differential branching
ratio and lepton forward-backward asymmetry of this decay channel in different
supersymmetric models and compare the obtained results with those of the
standard model. We also discuss how the results of different supersymmetric
models deviate from the standard model predictions and which SUSY scenarios are
favored.
