Charge asymmetry in decays $ B\rightarrow D\bar DK$

Abstract

We discusses the charge asymmetry in $ B\rightarrow D\bar DK$ decays with an invariant mass of the $D\bar D$ pair near the $\Psi(3770)$ resonance. Unlike $ \Psi (3770) $ decays in $ e^+e^- $ annihilation, in $B^+$ decays the probability of $D^0\bar D^0$ production is almost three times higher than $D^+ D^-$. In $B^0$ decays, the ratio of these probabilities will be opposite. The effect is explained by the fact that, in $B$ -meson decays, the $D\bar D$ pair is produced in a superposition of isoscalar and isovector states, and only in combination with $K$ -mesons the total state has $ 1/2 $ isospin. We present a simple model in which the interference of the nonresonant isovector amplitude with the resonant isoscalar amplitude explains the experimental data.