CPviolation in the partial width asymmetries forB−→π+π−K−andB−→K+K−K−decays

Abstract

We investigate the possibility of observing CP asymmetries in partial widths for the decays ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{K}^{\ensuremath{-}}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{K}^{\ensuremath{-}}$ produced by the interference of the nonresonant decay amplitude with resonant amplitudes. The resonant states that subsequently decay into ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{+}{K}^{\ensuremath{-}}$ or ${K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ are charmonium $\overline{c}c$ states with ${J}^{P}{=0}^{+}{,1}^{\ensuremath{-}}{,1}^{+}$ or the $\ensuremath{\varphi}(1020)$ meson. We find that the largest partial width asymmetry comes from the ${\ensuremath{\chi}}_{c0}$ resonance, while the resonance $\ensuremath{\psi}(2S)$ gives a partial width asymmetry of the order 10%.