Lepton Polarization in the Decays B→ Xₛμ+μ- and B→ Xₛτ+τ-

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The effective Hamiltonian for the decay b→ s l+ 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 mₗ/mb, 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> = -0.37, <Pₜ> = -0.63, <Pₙ> = 0.03. By comparison, the μ- polarization is <Pₗ> = -0.77, <Pₜ> = <Pₙ>≈ 0.