Study of $CP$ Violations in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}{f}_0(500)$ decays in the QCD factorization approach

Abstract

Within the QCD factorization approach, we study the $CP$ violations in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}{f}_0(500)$ decays. We find the experimental data of the localized $CP$ asymmetry in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ decays in the region $m_{K^{-}{\pi }^{+}}^2<15$ ${\mathrm{GeV}}^2$ and $0.08<m_{{\pi }^{+}{\pi }^{-}}^2<0.66$ ${\mathrm{GeV}}^2$ can be explained by the interference of two intermediate resonances, ${\rho }^0(770)$ and $f_0(500)$ when the parameters in our interference model are in the allowed ranges, i.e. the relative strong phase $\delta \in [0,1.745]\cup [3.578,6.266]$ and the end-point divergence parameters ${\rho }_S\in [2.790,5.290]$ and ${\varphi }_S\in [1.518,5.183]$. With the obtained allowed ranges for ${\rho }_S$ and ${\varphi }_S$, we obtain the predictions for the $CP$ asymmetry parameter $A_{CP}\in [-0.259,0.006]$ and the branching fraction $\mathcal{B}\in [0.585,3.230]\times 10^{-5}$ for $B^{-}\to K^{-}{f}_0(500)$ decay modes.

arXiv comment13 pages, 4 figures

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Cited by in corpus (6)

• Contributions of $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ in the three-body decays $B\to K\pi h$
• Virtual contributions from $D^{\ast }(2007{)}^0$ and $D^{\ast }(2010{)}^{\pm }$ in the $B\to D\pi h$ decays
• Study of $CP$ Violation in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}\sigma (600)$ decays in the QCD factorization approach
• Contributions of the kaon pair from $\rho (770)$ for the three-body decays $B\to DK\bar{K}$
• Study of localized $CP$ violation in $B^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}$ and the branching ratio of $B^{-}\to \sigma (600){\pi }^{-}$ in the QCD factorization approach
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays