Rare decays Λ b → Λγ and Λ b → Λl + l − (l= e, µ) are examined. We use QCD sum rules to calculate the hadronic matrix elements governing the decays. The Λ polarization in the decays is analyzed and it is shown that the polarization parameter in Λ b → Λγ does not depends on the values of hadronic form factors. And the energy spectrum of Λ in Λ b → Λl + l − is given.

The Λ b → p semileptonic decay is analyzed by using QCD sum rules within the framework of heavy quark effective theory. The Isgur-Wise function of Λ b → plν has been calculated. The decay width is given.

The rare decays ⌳ b →⌳␥ and ⌳ b →⌳l ϩ l Ϫ (lϭe,) are examined. We use QCD sum rules to calculate the hadronic matrix elements governing the decays. The ⌳ polarization in the decays is analyzed and it is shown that the polarization parameter in ⌳ b →⌳␥ does not depend on the values of hadronic form factors. The energy spectrum of ⌳ in ⌳ b →⌳l ϩ l Ϫ is given. ͓S0556-2821͑99͒02511-4͔

The inclusive rate and τ spectrum for a polarized Λ b -baryon to decay to charm hadronic final states and leptons τ ν in the SM and a two-Higgs doublet model are computed.The O(αs) QCD corrections to τ spectrum in the two-Higgs model are also given.

Recently the exotic event observed at the Yunnan Cosmic Ray Station (YCRS) is reinterpreted as a neutral supersymmetric (SUSY) particle bombarding on proton to produce a charged SUSY particle which decays afterwards. The kinematics analysis determines the lower bounds of its mass and lifetime. Taking this bounds as inputs and following recent literatures to assume the scalar neutrino (sneutrino) as the main constituent of the cold SUSY dark matter, we calculate the flux of sneutrino at the earth detector in terms of the standard rate equation of cosmic matter.