Large Strong Phases and CP Violation in the Annihilation Processes   $\bar{B}^0\to K^+K^-$, $K^{*\pm}K^\mp$, $K^{*+}K^{*-}$
  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. 
Fang Su, Yue-Liang Wu, Ya-Dong Yang, and Ci Zhuang