Mixing-Induced CP Violation in the Decay $B_d\to K^0 \bar K^0$ within the Standard Model

Abstract

Recently, flavour $SU(3)$ symmetry of strong interactions has been combined with certain dynamical assumptions to derive triangle relations among $B$-meson decay-amplitudes. We show that these relations allow a prediction of the mixing-induced CP asymmetry $\acpmi(B_d\to K^0\bar K^0)$. Contrary to statements made in several previous papers, this asymmetry should be non-vanishing in the Standard Model due to QCD-penguins with internal up- and charm-quark exchanges and could be as large as $\order(30\%)$. The branching ratio BR$(B_d\to K^0\bar K^0)$ is expected to be of $\order(10^{-6})$. In the future, the results presented in this letter should allow interesting tests of the $SU(3)$ triangle relations and of the Standard Model description of CP violation.