The B → πK puzzle revisited

For a number of years, there has been a certain inconsistency among the measurements of the branching ratios and CP asymmetries of the four B → πK decays (B+ → π+K0, B+ → π0K+, Bd0 → π−K+, Bd0 → π0K0). In this paper, we re-examine this B → πK puzzle. We find that the key unknown parameter is |C′/T′|, the ratio of color-suppressed and color-allowed tree amplitudes. If this ratio is large, |C′/T′| = 0.5, the SM can explain the data. But if it is small, |C′/T′| = 0.2, the SM cannot explain the B → πK puzzle —new physics (NP) is needed. The two types of NP that can contribute to B → πK at tree level are Z′ bosons and diquarks. Z′ models can explain the puzzle if the Z′ couples to right-handed uū and/or dd¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ d\overline{d} $$\end{document}, with gRdd ≠ gRuu. Interestingly, half of the many Z′ models proposed to explain the present anomalies in b → sμ+μ− decays have the required Z′ couplings to uū and/or dd¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ d\overline{d} $$\end{document}. Such models could potentially explain both the b → sμ+μ− anomalies and the B → πK puzzle. The addition of a color sextet diquark that couples to ud can also explain the puzzle.