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Flavour-Conserving CP Phases in Supersymmetry and Implications for Exclusive B Decays

We study rare exclusive B decays based on the quark-level transition b->s(d)l^+l^-, where l=e or mu, in the context of supersymmetric theories with minimal flavour violation. We present analytic expressions for various mixing matrices in the presence of new CP-violating phases, and examine their impact on observables involving B and \bar{B} decays. An estimate is obtained for CP-violating asymmetries in B->K^(*)l^+l^- and B->rho(pi)l^+l^- decays for the dilepton invariant mass region 1.2 GeV < M_{l^+l^-}< M_{J/psi}. As a typical result, we find a CP-violating partial width asymmetry of about -6% (-5%) in the case of B->pi (B->rho) in effective supersymmetry with phases of O(1), taking into account the measurement of the inclusive b->s gamma branching fraction. On the other hand, CP asymmetries of less than 1% are predicted in the case of B->K^(*). We argue that it is not sufficient to have additional CP phases of O(1) to observe large CP-violating effects in exclusive b->s(d)l^+l^- decays.