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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 $A_{CP}(K^-π^+)$, $A_{CP}((K^{*-}π^+)$, $A_{CP}((K^-ρ^0)$ and $A_{CP}((π^+π^-)$. However, the predicted direct CP-violating effects in QCDF for $B^-\to K^-π^0,K^-η,π^-η$ and $\bar B^0\toπ^0π^0$ 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 $π^0π^0$ and $ρ^0π^0$ modes: penguin annihilation and soft corrections to the color-suppressed tree amplitude.