Study of CP violations in and decays in the QCD factorization approach

Jing-Juan Qi; Xin-Heng Guo; Zhen-Yang Wang; Zhen-Hua Zhang; Jing Xu

doi:10.1140/epjc/s10052-018-6307-x

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2018) 78: 845
https://doi.org/10.1140/epjc/s10052-018-6307-x

Regular Article - Theoretical Physics

Study of CP violations in $B^-\rightarrow K^- \pi ^+\pi ^-$ and $B^-\rightarrow K^- f_0(500)$ decays in the QCD factorization approach

Jing-Juan Qi¹, Xin-Heng Guo¹^*, Zhen-Yang Wang², Zhen-Hua Zhang³^** and Jing Xu⁴

¹ College of Nuclear Science and Technology, Beijing Normal University, Beijing, 100875, China
² Physics Department, Ningbo University, Zhejiang, 315211, China
³ School of Nuclear and Technology, University of South China, Hengyang, 421001, Hunan, China
⁴ Department of Physics, Yantai University, Yantai, 264005, China

^* e-mail: xhguo@bnu.edu.cn
^** e-mail: zhangzh@usc.edu.cn

Received: 24 May 2018
Accepted: 6 October 2018
Published online: 20 October 2018

Abstract

Within the QCD factorization approach, we study the CP violations in $B^-\rightarrow K^-\pi ^+\pi ^-$ and $B^-\rightarrow K^- f_0(500)$ decays. We find the experimental data of the localized CP asymmetry in $B^-\rightarrow K^-\pi ^+\pi ^-$ 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 $\delta \in [2.124, 5.976]$ and the end-point divergence parameters $\rho _S\in [5.692, 8]$ and $\phi _S \in [0, 2\pi ]$ . With the obtained allowed ranges for $\rho _S$ and $\phi _S$ , we obtain the predictions for the CP asymmetry parameter $A_{CP} \in [-0.115, -0.151]$ and the branching fraction ${\mathcal {B}} \in [3.763, 20.014]\times 10^{-5}$ for $B^-\rightarrow K^-f_0(500)$ decay modes.