Interplay of the Cabibbo-Kobayashi-MaskawaCP-violating phase and penguin diagram effects inB¯→ππ

We use the perturbative QCD methods of Lepage and Brodsky to calculate the rate for B¯→ππ, with an eye toward the CP-violating unitarity triangle angle α. We show that, in the ${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$ mode, penguin diagrams are small and α is generally measurable but that, in the ${\mathrm{\pi }}^0$ ${\mathrm{\pi }}^0$ mode, the relative importance of penguin diagrams is a strong function of the CP-violating phase ${\mathrm{\delta }}_{13}$ in the Cabibbo-Kobayashi-Maskawa mixing matrix.