CP violating phase γ and the partial widths asymmetry in B−→π+π−K− and B−→K+K−K− decays

Motivated by recent Belle measurement of the branching ratios B−→π+π−K− and B−→K+K−K− and B±→χc0K±, we investigate the CP violating asymmetry in the partial widths for the decays B−→π+π−K− and B−→K+K−K−, which results from the interference of the nonresonant decay amplitude with the resonant amplitude B±→χc0K± →π+π−K± and B±→χc0K± →K+K−K−. By taking γ≃58° we predict that the partial widths asymmetry is reaching 10% for the B−→π+π−K− decay and 16% for the B−→K+K−K− decay.