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We calculate CP-violating rates and asymmetry parameters in charged andneutral $B\to \pi\pi, \pi K$ and $\bar K K$ decays arising from theinterference of tree and penguin (strong and electroweak) amplitudes withdifferent strong and CKM phases. The perturbative strong (electroweak) phasesdevelop at order $\alpha_s$ ($\alpha_{em}$) from absorptive parts of one-loopmatrix elements of the next-to-leading (leading) logarithm corrected effectiveHamiltonian. 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 issubstantial in most channels, drastic in many. However, a measurement of thetime dependence parameter $a_{\epsilon+\epsilon'}$ in the $\pi^+\pi^-$ channelis 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, othersbadly violated, when electroweak penguins are included.Comment: 29 pages, latex/revtex, no figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Electroweak and strong penguin diagrams in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">B</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mn /></mml:mrow></mml:msup></mml:mrow></mml:math>→ππ, π<i>K</i>, and<i>KK¯</i>decays

Electroweak and strong penguin diagrams inB±,0→ππ, πK, andKK¯decays