Abstract
We discuss the correlations induced by the charming penguin contributions to B → ππ, πK and KK modes in the flavor SU(3) diagrammatic approach. Strong constraints are found from the measurements of the direct CP asymmetries, especially that of πK modes. We make global fits to the latest data, and show that only a relatively small charming penguin is allowed. In the presence of the charming penguin, the size of color-suppressed tree amplitude (C) relative to that of tree amplitude (T) still remains large C/T ≃ 0.6, which disfavors the possibility of a large charming penguin alone as an explanation for the ππ puzzle. We find that this conclusion remains unchanged for various SU(3) breaking schemes. Nevertheless, together with an enhanced annihilation-type W-exchange diagram (E) which is allowed by the current data, the ratio C/T can be reduced to ∼0.4. We show that a small charming penguin amplitude can still have significant contribution to the time-dependent CP asymmetry in the KSKS mode.
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