CP-violating asymmetry in $B^- \to \pi^+ \pi^- K^-$ and $B^- \rarr K^+ K^- K^-$ decays

Abstract

The recent Belle and Babar measurements of the branching ratios $B^- \to \pi^+ \pi^- K^-$ and $B^- \to K^+ K^- K^-$ and $B^\pm \to \chi_{c0} K^\pm$ have renewed interests in these decays as another mean to look for direct CP violation in B decays. In this talk, I would like to discuss a recent analysis of the CP violating asymmetry in the partial widths for the decays $B^- \to \pi^+ \pi^- K^-$ and $B^- \to K^+ K^- K^-$, which results from the interference of the non resonant amplitude with the resonant amplitude $B^\pm \to \chi_{c0} K^\pm $ $ \rarr\pi^+ \pi^- K^\pm $ and $B^\pm \to \chi_{c0} K^\pm$ $ \to K^+ K^- K^\pm$. For $\gamma \simeq 58^o$ we predict that the partial width asymmetry could reach 10% for the $B^- \to \pi^+ \pi^- K^-$ decay and 16% for the $B^- \to K^+ K^- K^-$decay.