Model-independent electroweak penguins in B decays to two pseudoscalars

Abstract

We study the effects of electroweak penguin (EWP) amplitudes in $B$ meson decays into two charmless pseudoscalars in the approximation of retaining only the dominant EWP operators $Q_9$ and $Q_{10}$. Using flavor SU(3) symmetry, we derive a set of model-independent relations between EWP contributions and tree-level decay amplitudes one of which was noted recently by Neubert and Rosner. Two new applications of these relations are demonstrated in which uncertainties due to EWP corrections are eliminated in order to determine a weak phase. Whereas the weak angle $\alpha$ can be obtained from $B\to\pi\pi$ free of hadronic uncertainties, a determination of $\gamma$ from $B^{0,\pm}\to K\pi^{\pm}$ requires the knowledge of a ratio of certain tree-level hadronic matrix elements. The smallness of this ratio implies a useful constraint on $\gamma$ if rescattering can be neglected.