Exploring CP violation through correlations in B→πK, Bd→π+π-, Bs→K+K- observable space -: art. no. 054009

We investigate the allowed regions in the observable space of B-->piK, B-d-->pi(+)pi(-), and B-s-->K+K- decays, characterizing these modes in the standard model. After a discussion of a new kind of contour plot for the B-->piK system, we focus on the mixing-induced and direct CP asymmetries of the decays B-d-->pi(+)pi(-) and B-s-->K+K-. Using experimental information on the CP-averaged B-d-->pi(-/+)K(+/-) and B-d-->pi(+)pi(-) branching ratios, the relevant hadronic penguin parameters can be constrained, implying certain allowed regions in observable space. In the case of B-d-->pi(+)pi(-), an interesting situation arises now in view of the recent B-factory measurements of CP violation in this channel, allowing us to obtain new constraints on the CKM angle gamma as a function of the B-d(0)-<(B-d(0))over bar> mixing phase phi(d)=2beta, which is fixed through A(CP)(mix)(B-d-->J/psiK(S)) up to a twofold ambiguity. If we assume that A(CP)(mix)(B-d-->pi(+)pi(-)) is positive, as indicated by recent Belle data, and that phi(d) is in agreement with the "indirect" fits of the unitarity triangle, also the corresponding values for gamma around 60degrees can be accommodated. On the other hand, for the second solution of phi(d), we obtain a gap around gammasimilar to60degrees. The allowed region in the space of A(CP)(mix)(B-s-->K+K-) and A(CP)(dir)(B-s-->K+K-) is very constrained in the standard model, thereby providing a narrow target range for run II of the Fermilab Tevatron and the experiments of the CERN LHC era.