Mixing among the neutral Higgs bosons and rare B decays in the CP violating MSSM

Considering corrections from two-loop Feynman diagrams which involve gluino at large $\tan\beta$, we analyze the effects of possible CP phases on the rare B decays: $\bar{B}_{_{s}} \to l^+l^-$ and $\bar{B}\to Kl^+l^-$ in the CP violating minimal supersymmetric extension of the standard model. It is shown that the results of exact two loop calculations obviously differ from that including one-loop contributions plus threshold radiative corrections. The numerical analysis indicates that the possibly large CP phases strongly affect the theoretical estimation of the branching ratios, and this results coincide with the conclusion of some other works appearing in recent literature.