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Direct CP asymmetries and the CP violating normal polarization of lepton ininclusive decay B \to X_s l^+ l^- are investigated in minimal supergravitymodel with CP violating phases. The contributions coming from exchangingneutral Higgs bosons are included. It is shown that the direct CP violation inbranching ratio, A_{CP}^1, is of {\cal{O}}(10^{-3}) for l=e, \mu, \tau. The CPviolating normal polarization for l=\mu can reach 0.5 percent when tan\beta islarge (say, 36). For l=\tau and in the case of large \tan\beta, the direct CPviolation in backward-forward asymmetry, A_{CP}^2, can reach one percent, thenormal polarization of \tau can be as large as a few percent, and both aresensitive to the two CP violating phases, \phi_\mu and \phi_{A_0}, andconsequently it could be possible to observe them (in particular, the normalpolarization of \tau) in the future B factories.Comment: 14 pages, latex, 5 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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