Exploring CP violation through correlations in B→πK, B <inf>d</inf>→π⁺π^-, B<inf>s</inf>→K ⁺K^- observable space

We investigate the allowed regions in the observable space of B→πK, Bd→π+π-, and Bs→ K+K- decays, characterizing these modes in the standard model. After a discussion of a new kind of contour plot for the B→πK system, we focus on the mixing-induced and direct CP asymmetries of the decays Bd→π+π- and Bs→ K+K-. Using experimental information on the CP-averaged Bd→π∓K± and B d→π+π- branching ratios, the relevant hadronic penguin parameters can be constrained, implying certain allowed regions in observable space. In the case of Bd→π +π-, 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 γ as a function of the B d0-Bd0̄ mixing phase φd=2β, which is fixed through ACPmix(Bd→J/ψKs) up to a twofold ambiguity. If we assume that ACPmix(Bd→ π+π-) is positive, as indicated by recent Belle data, and that φd is in agreement with the "indirect" fits of the unitarity triangle, also the corresponding values for γ around 60° can be accommodated. On the other hand, for the second solution of φd, we obtain a gap around γ∼60°. The allowed region in the space of Acpmix(Bs→K +K-) and ACPdir;(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. © 2002 The American Physical Society.