The weak decays of Λ b → Λ + γ and Λ b → Λ + l + l − are investigated in the Standard Model using light-cone sum rules approach. The higher twist distribution amplitudes of Λ baryon to the leading conformal spin are included in the sum rules for transition form factors. Our results indicate that the higher twist distribution amplitudes almost have no influences on the transition form factors retaining the heavy quark spin symmetry, while such corrections can result in significant impacts on the form factors breaking the heavy quark spin symmetry. Two phenomenological models (COZ and FZOZ) for the wave function of Λ baryon are also employed in the sum rules for a comparison, which can give rise to the form factors approximately five times larger than that in terms of conformal expansion. Utilizing the form factors calculated in LCSR, the physical observables like decay rate, polarization asymmetry and forward-backward asymmetry are analyzed for the decays of Λ b → Λγ, Λl + l − . I. INTRODUCTION Generally, new physics can be accessible through rare decays, where the contributions from the Standard Model (SM) are suppressed enough. Hence, such decays can provide an ideal platform to test the SM precisely as well as to bound new physics parameters stringently. Rare decays involving b → s flavor changing neutral current (FCNC), which are forbidden at the tree level in the standard model, can only be induced by Glashow-Iliopoulos-Maiani mechanism [1] via loop diagrams. The Cabibbo-Kobayashi-Maskawa (CKM) matrix [2, 3] elements can be determined quantitatively from b → s rare decays, B 0 s −B 0 s mixing [4] etc., which will test its unitarity under the requirement of the SM.It is well known that the inclusive decays are relatively robust theoretically, since the decay rate can be systematically and reasonably approximated by the decay of a free b quark into light quarks, gluons and photons; but the counterpart of experimental measurements are quite difficult. On the