G. Kramer et Wf. Palmer, ELECTROWEAK AND STRONG PENGUIN DIAGRAMS IN B-+ -,B-0-]PI-PI, PI-K, AND K(K)OVER-BAR DECAYS/, Physical review. D. Particles and fields, 52(11), 1995, pp. 6411-6421
We calculate CP-violating rates and asymmetry parameters in charged an
d neutral B --> pi pi, pi K, and (K) over bar K decays arising from th
e interference of tree and penguin (strong and electroweak) amplitudes
with different strong and CKM phases. The perturbative strong (electr
oweak) phases develop at order alpha(s) (alpha(em)) from absorptive pa
rts of one-loop matrix elements of the next-to-leading (leading) logar
ithm corrected effective Hamiltonian. The BSW model is used to estimat
e the hadronic matrix elements. Based on this model, we find that the
effect of strong phases and penguin diagrams is substantial in most ch
annels, drastic in many. However, a measurement of the time dependence
parameter alpha(epsilon+epsilon') in the pi(+)pi(-) channel is only i
nfluenced at the 20% level by the complication of the penguin diagrams
. Recent flavor sum rules developed for B-0'+/- --> pi pi, pi K, K (K)
over bar amplitudes are tested in this model. Some are well satisfied
, others badly violated, when electroweak penguin diagrams are include
d.