Electroweak and Strong Penguins in B^{\pm, 0}\to \pi\pi, \pi K and KK Decays

Abstract

We calculate CP-violating rates and asymmetry parameters in charged and neutral $B\to \pi\pi, \pi K$ and $\bar K K$ decays arising from the interference of tree and penguin (strong and electroweak) amplitudes with different strong and CKM phases. The perturbative strong (electroweak) phases develop at order $\alpha_s$ ($\alpha_{em}$) from absorptive parts of one-loop matrix elements of the next-to-leading (leading) logarithm corrected effective Hamiltonian. The BSW model is used to estimate the hadronic matrix elements. Based on this model, we find that the effect of strong phases and penguins is substantial in most channels, drastic in many. However, a measurement of the time dependence parameter $a_{\epsilon+\epsilon'}$ in the $\pi^+\pi^-$ channel is only influenced at the 20\% level by the complication of the penguins. Recent flavor sum rules developed for $B^{0,\pm} \rightarrow \pi\pi, \pi K, K \bar K$ amplitudes are tested in this model. Some are well satisfied, others badly violated, when electroweak penguins are included.