Phenomenological studies on decay Supported by National Natural Science Foundation of China (11575023, 11775024, 11947001, 11605150, 11805153), Natural Science Foundation of Zhejiang pvovince (LQ21A050005), Achievements of the Basic Scientific Research Business Foundation Project of Universities in Zhejiang Province and Natural Science Foundation of Ningbo (2019A610067),Chinese Physics C

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Phenomenological studies on decay Supported by National Natural Science Foundation of China (11575023, 11775024, 11947001, 11605150, 11805153), Natural Science Foundation of Zhejiang pvovince (LQ21A050005), Achievements of the Basic Scientific Research Business Foundation Project of Universities in Zhejiang Province and Natural Science Foundation of Ningbo (2019A610067)
Chinese Physics C ( IF 3.6 ) Pub Date : 2021-04-22 , DOI: 10.1088/1674-1137/abeb06
Jing-Juan Qi ₁ , Zhen-Yang Wang ₂ , Zhu-Feng Zhang ₂ , Xin-Heng Guo ₃

Affiliation

Within the quasi-two-body decay model, we study the localized CP violation and branching fraction of the four-body decay $\bar{B}^0\rightarrow [K^-\pi^+]_{S/V}[\pi^+\pi^-]_{V/S} \rightarrow K^-\pi^+\pi^-\pi^+$ when the $K^-\pi^+$ and $\pi^-\pi^+$ pair invariant masses are $0.35 \lt m_{K^-\pi^+} \lt 2.04 \; \mathrm{GeV}$ and $0 \lt m_{\pi^-\pi^+} \lt 1.06\; \mathrm{GeV}$ , with the pairs being dominated by the $\bar{K}^*_0(700)^0$ , $\bar{K}^*(892)^0$ , $\bar{K}^*(1410)^0$ , $\bar{K}^*_0(1430)$ and $\bar{K}^*(1680)^0$ , and $f_0(500)$ , $\rho^0(770)$ , $\omega(782)$ and $f_0(980)$ resonances, respectively. When dealing with the dynamical functions of these resonances, , $\rho^0(770)$ , and $\bar{K}^*_0(1430)$ are modeled with the Bugg model, Gounaris-Sakurai function, Flatt formalism and LASS lineshape, respectively, while the others are described by the relativistic Breit-Wigner function. Adopting the end point divergence parameters $\rho_A\in[0,0.5]$ and $\phi_A\in[0,2\pi]$ , our predicted results are $\mathcal{A_{CP}}(\bar{B}^0\rightarrow K^-\pi^+\pi^+\pi^-)\in[-0.365,0.447]$ and $\mathcal{B}(\bar{B}^0\rightarrow K^-\pi^+\pi^+\pi^-)\in$ $[6.11,185.32]\times10^{-8}$ , based on the hypothetical $q\bar{q}$ structures for the scalar mesons in the QCD factorization approach. Meanwhile, we calculate the CP violating asymmetries and branching fractions of the two-body decays $\bar{B}^0\rightarrow SV(VS)$ and all the individual four-body decays $\bar{B}^0\rightarrow SV(VS) \rightarrow K^-\pi^+\pi^-\pi^+$ , respectively. Our theoretical results for the two-body decays $\bar{B}^0\rightarrow \bar{K}^*(892)^0$ $f_0(980)$ , $\bar{B}^0\rightarrow \bar{K}^*_0(1430)^0$ $\omega(782)$ , $\bar{B}^0\rightarrow \bar{K}^*(892)^0f_0(980)$ , $\bar{B}^0\rightarrow$ $\bar{K}^*_0(1430)^0\rho$ , and $\bar{B}^0\rightarrow\bar{K}^*_0(1430)^0\omega$ are consistent with the available experimental data, with the remaining predictions await testing in future high precision experiments.

中文翻译：

国家自然科学基金（11575023、11775024、11947001、11605150、11805153），浙江省自然科学基金（LQ21A050005），浙江省高校基础科学研究业务基金项目和自然科学基金资助项目宁波市科学基金（2019A610067）

在准二体衰变模型中，我们研究了 $\bar{B}^0\rightarrow [K^-\pi^+]_{S/V}[\pi^+\pi^-]_{V/S} \rightarrow K^-\pi^+ \pi^-\pi^+$ 当 $K^-\pi^+$ 和 $\pi^-\pi^+$ 对不变质量为 $0.35 \lt m_{K^-\pi^+} \lt 2.04 \; \mathrm{GeV}$ 和时四体衰变的局部 CP 违反和分支分数 $0 \lt m_{\pi^-\pi^+} \lt 1.06\; \mathrm{GeV}$ ，其中对由 $\bar{K}^*_0(700)^0$ 、 $\bar{K}^*(892)^0$ 、和 $\bar{K}^*(1410)^0$ 、和、、和共振，分别。在处理这些共振的动力学函数时，分别用Bugg 模型、Gounaris-Sakurai 函数、Flatt 形式主义和 LASS 线形建模，而其他的则用相对论的 Breit-Wigner 函数来描述。采用端点散度参数和 $\bar{K}^*_0(1430)$ $\bar{K}^*(1680)^0$ $f_0(500)$ $\rho^0(770)$ $\欧米茄（782）$ $f_0(980)$ $\rho^0(770)$ $\bar{K}^*_0(1430)$ $\rho_A\in[0,0.5]$ $\phi_A\in[0,2\pi]$ ，我们的预测结果是 $\mathcal{A_{CP}}(\bar{B}^0\rightarrow K^-\pi^+\pi^+\pi^-)\in[-0.365,0.447]$ 和 $\mathcal{B}(\bar{B}^0\rightarrow K^-\pi^+\pi^+\pi^-)\in$ $[6.11,185.32]\times10^{-8}$ ，基于 $q\bar{q}$ QCD 分解方法中标量介子的假设结构。同时，我们分别计算了两体衰变 $\bar{B}^0\rightarrow SV(VS)$ 和所有单个四体衰变的CP违反不对称性和分支分数 $\bar{B}^0\rightarrow SV(VS) \rightarrow K^-\pi^+\pi^-\pi^+$ 。我们对两体衰变的理论结果 $\bar{B}^0\rightarrow \bar{K}^*(892)^0$ $f_0(980)$ , $\bar{B}^0\rightarrow \bar{K}^*_0(1430)^0$ $\欧米茄（782）$ , $\bar{B}^0\rightarrow \bar{K}^*(892)^0f_0(980)$ , $\bar{B}^0\rightarrow$ $\bar{K}^*_0(1430)^0\rho$ 和 $\bar{B}^0\rightarrow\bar{K}^*_0(1430)^0\omega$ 与可用的实验数据一致，其余预测有待未来高精度实验的检验。

更新日期：2021-04-22

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