CP violating phase $\gamma$ and the partial widths asymmetry in $B^{-}\to {\pi }^{+}{\pi }^{-}{K}^{-}$ and $B^{-}\to K^{+}{K}^{-}{K}^{-}$ decays

Motivated by recent Belle measurement of the branching ratios $B^- \to \pi^+ \pi^- K^-$and$B^- \to K^+ K^- K^-$and$B^\pm \to \chi_{c0} K^\pm$, we investigate 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 nonresonant decay amplitude with the resonant amplitude $B^{\pm }\to {\chi }_{c0}{K}^{\pm }$ $\to {\pi }^{+}{\pi }^{-}{K}^{\pm }$ and $B^\pm \to \chi_{c0} K^\pm$ $\to K^{+}{K}^{-}{K}^{-}$. By taking $\gamma \simeq {58}^o$ we predict that the partial widths asymmetry is reaching 10% for the $B^{-}\to {\pi }^{+}{\pi }^{-}{K}^{-}$ decay and 16% for the $B^{-}\to K^{+}{K}^{-}{K}^{-}$decay.