CP-violating asymmetry in $B^{-}\to {\pi }^{+}{\pi }^{-}{K}^{-}$ and $B^{-}\to K^{+}{K}^{-}{K}^{-}$ 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 $B^{\pm }\to {\chi }_{c0}{K}^{\pm }$ $\to {\pi }^{+}{\pi }^{-}{K}^{\pm }$ 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.

Comments: Talk given at the Quark Confinement and Hadron Spectrum V, Gargnano,Italy,10-14 September 2002, LaTeX,4 pages