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CP-violating asymmetry in Bβˆ’β†’Ο€+Ο€βˆ’Kβˆ’B^- \to \pi^+ \pi^- K^- and Bβˆ’β†’K+Kβˆ’Kβˆ’B^- \rarr K^+ K^- K^- decays

Abstract

The recent Belle and Babar measurements of the branching ratios Bβˆ’β†’Ο€+Ο€βˆ’Kβˆ’B^- \to \pi^+ \pi^- K^- and Bβˆ’β†’K+Kβˆ’Kβˆ’B^- \to K^+ K^- K^- and BΒ±β†’Ο‡c0KΒ±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 Bβˆ’β†’Ο€+Ο€βˆ’Kβˆ’B^- \to \pi^+ \pi^- K^- and Bβˆ’β†’K+Kβˆ’Kβˆ’B^- \to K^+ K^- K^-, which results from the interference of the non resonant amplitude with the resonant amplitude BΒ±β†’Ο‡c0KΒ±B^\pm \to \chi_{c0} K^\pm β†’Ο€+Ο€βˆ’KΒ± \rarr\pi^+ \pi^- K^\pm and BΒ±β†’Ο‡c0KΒ±B^\pm \to \chi_{c0} K^\pm β†’K+Kβˆ’KΒ± \to K^+ K^- K^\pm. For γ≃58o\gamma \simeq 58^o we predict that the partial width asymmetry could reach 10% for the Bβˆ’β†’Ο€+Ο€βˆ’Kβˆ’B^- \to \pi^+ \pi^- K^- decay and 16% for the Bβˆ’β†’K+Kβˆ’Kβˆ’B^- \to K^+ K^- K^-decay.Comment: Talk given at the Quark Confinement and Hadron Spectrum V, Gargnano,Italy,10-14 September 2002, LaTeX,4 page

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