On Puzzles and Non-Puzzles in B -> pi pi, pi K Decays

Abstract

Recently, we have seen interesting progress in the exploration of CP violation in B^0_d -> pi^+ pi^-: the measurements of mixing-induced CP violation by the BaBar and Belle collaborations are now in good agreement with each other, whereas the picture of direct CP violation is still unclear. Using the branching ratio and direct CP asymmetry of B^0_d -> pi^- K^+, this situation can be clarified. We predict A_CP^dir(B_d -> pi^+ pi^-) = -0.24+-0.04, which favours the BaBar result, and extract gamma=(70.0^{+3.8}_{-4.3})deg, which agrees with the unitarity triangle fits. Extending our analysis to other B -> pi K modes and B^0_s -> K^+ K^- with the help of the SU(3) flavour symmetry and plausible dynamical assumptions, we find that all observables with colour-suppressed electroweak penguin contributions are measured in excellent agreement with the Standard Model. As far as the ratios R_{c,n} of the charged and neutral B -> pi K branching ratios are concerned, which are sizeably affected by electroweak penguin contributions, our Standard-Model predictions have almost unchanged central values, but significantly reduced errors. Since the new data have moved quite a bit towards these results, the "B -> pi K puzzle" for the CP-conserving quantities has been significantly reduced. However, the mixing-induced CP violation of B^0_d -> pi^0 K_S does look puzzling; if confirmed by future measurements, this effect could be accommodated through a modified electroweak penguin sector with a large CP-violating new-physics phase. Finally, we point out that the established difference between the direct CP asymmetries of B^+- -> pi^0 K^+- and B_d -> pi^-+ K^+- appears to be generated by hadronic and not by new physics.

12 pages, 4 figures. References added, to appear in EPJC

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