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We investigate allowed regions in observable space of B --> pi K, B_d -->pi^+pi^- and B_s --> K^+K^- decays, characterizing these modes in the StandardModel. After a discussion of a new kind of contour plots for the $B\to\pi K$system, we focus on the mixing- induced and direct CP asymmetries of the decaysB_d --> pi^+pi^- and B_s--> K^+K^-. Using experimental information on theCP-averaged B_d --> pi^{+/-}K^{+/-} and B_d --> pi^+pi^- branching ratios, therelevant hadronic penguin parameters can be constrained,implying certainallowed regions in observable space. In the case of B_d --> pi^+pi^-, aninteresting situation arises now in view of the recent B-factory measurementsof CP violation in this channel, allowing us to obtain new constraints on theCKM angle gamma as a function of the B^0_d--\bar{B^0_d} mixing phasephi_d=2beta, which is fixed through A_{CP}^{mix}(B_d --> J/psi K_S) up to atwofold ambiguity. If we assume that A_{CP}^{mix}(B_d --> pi^+pi^-) ispositive, as indicated by recent Belle data, and that phi_d is in agreementwith the ``indirect'' fits of the unitarity triangle, also the correspondingvalues for gamma around 60 degrees can be accommodated. On the other hand, forthe second solution of phi_d, we obtain a gap around gamma ~ 60 degrees. Theallowed region in the space of A_{CP}^{mix}(B_s --> K^+K^-) andA_{CP}^{dir}(B_s --> K^+K^-) is very constrained in the Standard Model, therebyproviding a narrow target range for run II of the Tevatron and the experimentsof the LHC era.Comment: 34 pages, LaTeX, 12 figures. More detailed introduction and a few  Comments added, conclusions unchanged. To appear in Phys. Rev.

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

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ExploringCPviolation through correlations inB→πK,