Constraining Charming Penguins in Charmless B Decays

We discuss the correlations of charming penguin contributions to $B\toππ$, $πK$ and KK using approximate flavor SU(3) symmetry. Strong constraints are found from the direct CP asymmetries especially in $πK$ modes. We make a global fit to the latest data and find that only a small charming penguin is allowed, and the size of color-suppressed tree amplitude (C) relative to tree amplitudes (T) remains large $C/T\simeq0.6$, which disfavors the possibility of a large charming penguin as an explanation for the $ππ$ puzzle. We show that a small charming penguin can still have sizable effect in the time-dependence CP asymmetries in KK mode.

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