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Within the Standard Model, we investigate the weak decays of $\Lambda_b \to\Lambda + \gamma$ and $\Lambda_b \to \Lambda + l^{+} l^{-}$ with the light-conesum rules approach. The higher twist distribution amplitudes of $\Lambda$baryon to the leading conformal spin are included in the sum rules fortransition form factors. Our results indicate that the higher twistdistribution amplitudes almost have no influences on the transition formfactors retaining the heavy quark spin symmetry, while such corrections canresult in significant impacts on the form factors breaking the heavy quark spinsymmetry. Two phenomenological models (COZ and FZOZ) for the wave function of$\Lambda$ baryon are also employed in the sum rules for a comparison, which cangive rise to the form factors approximately 5 times larger than that in termsof conformal expansion. Utilizing the form factors calculated in LCSR, we thenperform a careful study on the decay rate, polarization asymmetry andforward-backward asymmetry, with respect to the decays of $\Lambda_b \to\Lambda \gamma$, $\Lambda l^{+}l^{-}$.

Rare Decays of \Lambda_b->\Lambda + \gamma and \Lambda_b ->\Lambda + l^{+} l^{-} in the Light-cone Sum Rules