Lepton polarization in the decays B → Xsμ+μ− and B → Xsτ+τ−

The effective Hamiltonian for the decay b → sl+l− predicts a characteristic polarization for the final-state lepton, which can serve as an important test of the underlying theory. The lepton polarization has, in addition to a longitudinal component PL, two orthogonal components PT and PN, lying in and perpendicular to the decay plane which are proportional to mlmb, and therefore significant for the τ+τ− channel. The normal polarization component PN is a T-odd effect connected with the nonhermiticity of the effective Hamiltonian, arising mainly from cc intermediate states. We calculate all three polarization components for the decay B → Xsτ+τ− as a function of the lepton pair mass, and find average values 〈PL〉τ = −0.37, 〈PT〉τ = −0.63, 〈PN〉τ = 0.03. By comparison, the μ− polarization is 〈PL〉μ = −0.77, 〈PT〉μ = 〈PN〉μ ≈ 0.