Supersymmetric CP Violation in $B \to X_s l^+ l^-$ in Minimal Supergravity Model

Direct CP asymmetries and the CP violating normal polarization of lepton in inclusive decay B \to X_s l^+ l^- are investigated in minimal supergravity model with CP violating phases. The contributions coming from exchanging neutral Higgs bosons are included. It is shown that the direct CP violation in branching ratio, A_{CP}^1, is of {\cal{O}}(10^{-3}) for l=e, \mu, \tau. The CP violating normal polarization for l=\mu can reach 0.5 percent when tan\beta is large (say, 36). For l=\tau and in the case of large \tan\beta, the direct CP violation in backward-forward asymmetry, A_{CP}^2, can reach one percent, the normal polarization of \tau can be as large as a few percent, and both are sensitive to the two CP violating phases, \phi_\mu and \phi_{A_0}, and consequently it could be possible to observe them (in particular, the normal polarization of \tau) in the future B factories.