Rare Λb→Λι+ι- decays with polarized Λ

We investigate the rare baryonic exclusive decays of Λ_b→Λι⁺ι^- (ι=e, μ, τ) with polarized Λ. Under the approximation of the heavy quark effective theory, in the standard model we derive the differential decay rates and various polarization asymmetries by including lepton mass effects. We find that with the long-distance effects the decay branching ratios are 5.3×10^-5 for Λ_b→Λι⁺ι^- (ι=e, μ) and 1.1×10^-5 for Λ_b→Λτ⁺τ^- The effects of new physics in the decay rates are also. discussed. The integrated longitudinal Λ polarizations are -0.31 and -0.12, while that of the normal ones 0.02 and 0.01, for di-muon and tau modes, respectively. The CP-odd transverse polarization of Λ is zero in the standard model but it is expected to be sizable in some theories with new physics.