Lepton polarization in the decays B->X(s)mu(+)mu(-) and B->X(s)tau(+)tau(-)

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 P-L, two orthogonal components P-T and P-N, lying in and perpendicular to the decay plane which are proportional to m(l)/m(b), and therefore significant for the tau(+)tau(-) channel. The normal polarization component P-N is a T-odd effect connected with the nonhermiticity of the effective Hamiltonian, arising mainly from <c(c)over bar> intermediate states. We calculate all three polarization components for the decay B --> X(s) tau(+)tau(-) as a function of the lepton pair mass, and find average values [P-L](tau) = -0.37, [P-T](tau) = -0.63, [P-N](tau) = 0.03. By comparison, the mu(-) polarization is [P-L](mu) = -0.77, [P-T](mu) = [P-N](mu) approximate to 0.