  The strong phases and CP violation in the rare $\bar{B}^0\to K^+K^-$,
$K^{*\pm}K^\mp$, $K^{*+}K^{*-}$ decays are investigated. As these decays
proceed only via annihilation type diagrams in the standard model (SM), a
dynamical gluon mass is introduced to avoid the infrared divergence in the soft
endpoint regions. The Cutkosky rule is adopted to deal with a physical-region
singularity of the on mass-shell quark propagators, which leads to a big
imaginary part and hence a large strong phase. As a consequence, large CP
asymmetries are predicted in those decay modes due to a big interference
between the annihilation amplitudes from penguin and tree operators, which may
be tested in future more precise experiments.
