The B-CP Puzzles in QCD Factorization

Within the framework of QCD factorization (QCDF), power corrections due to penguin annihilation can account for theobserved rates of penguin-dominated two-body decays of $B$ mesons and direct CP asymmetries $A_{CP}(K^{-}{\pi }^{+})$, $A_{CP}((K^{\ast -}{\pi }^{+})$, $A_{CP}((K^{-}{\rho }^0)$ and $A_{CP}(({\pi }^{+}{\pi }^{-})$. However, the predicted direct CP-violating effects in QCDF for $B^-\to K^-\pi^0,K^-\eta,\pi^-\eta$and$\bar B^0\to\pi^0\pi^0$ are wrong in signs when confronted with experiment. We consider two different types of power correction effects in order to resolve the CP puzzles and rate deficit problems with penguin-dominated two-body decays of $B$ mesons and color-suppressed tree-dominated ${\pi }^0{\pi }^0$ and ${\rho }^0{\pi }^0$ modes: penguin annihilation and soft corrections to the color-suppressed tree amplitude.