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arXiv 2204.01092hep-ph
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用微扰QCD方法研究$B_{(s)}^0 \to ϕϕ\to (K^+K^-)(K^+K^-)$衰变

Study of $B_{(s)}^0 \to ϕϕ\to (K^+K^-)(K^+K^-)$ decays in the perturbative QCD approach

Da-Cheng Yan, Zhou Rui, Zhen-Jun Xiao, Ya Li

备注：
21 pages,2 figures,7 tables;some numerical results updated. arXiv admin note: text overlap with arXiv:2107.10684
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摘要：

本文对微扰QCD（PQCD）方法中的企鹅主导过程$B_{(s)}^0 \to ϕϕ\to (K^+K^-)(K^+K^-)$进行了详细的分析。除了占主导地位的$P$波共振，标量背景$f_0(980) \to K^+K^-$也占。通过将PQCD因子化公式拟合到三体和四体$B$衰变的分支比中，改进了$KK$两介子分布振幅的Gegenbauer矩。我们从相应的四体衰变模中提取了二体$B_{(s)}^0 \to ϕϕ$衰变的分支比，并计算了相关的极化分数和两个相对相位$ϕ_{\parallel,\perp}$，这与以前的理论预测是一致的。PQCD预测的“真正的”三重积不对称性（TPAs）是零，这是预期在标准模型中由于消失的弱相位差，并支持目前的数据报告的CDF和LHCb合作。第一次预测了衰变$B^0_s \to ϕϕ\to (K^+K^-)(K^+K^-)$的一个大的“假”TPA $\mathcal{A}_\text{T-fake}^1=30.4\%$，这表明存在重要的末态相互作用。稀有衰变通道$B^0 \to ϕϕ\to (K^+K^-)(K^+K^-)$的TPAs也进行了预测，并可以在不久的将来进行测试。

英文摘要：

In this work, we make a detailed analysis on the penguin-dominant processes $B_{(s)}^0 \to ϕϕ\to (K^+K^-)(K^+K^-)$ in the perturbative QCD (PQCD) approach. In addition to the dominant $P$-wave resonance, the scalar background $f_0(980) \to K^+K^-$ is also accounted for. We improve the Gegenbauer moments in $KK$ two-meson distribution amplitudes by fitting the PQCD factorization formulas to measured branching ratios of three-body and four-body $B$ decays. We extract the branching ratios of two-body $B_{(s)}^0 \to ϕϕ$ decays from the corresponding four-body decay modes and calculate the relevant polarization fractions together with two relative phases $ϕ_{\parallel,\perp}$, which are consistent with the previous theoretical predictions. The PQCD predictions for the "true" triple product asymmetries (TPAs) are zero which are expected in the standard model due to the vanishing weak phase difference, and support the current data reported by the CDF and LHCb Collaborations. A large "fake" TPA $\mathcal{A}_\text{T-fake}^1=30.4\%$ of the decay $B^0_s \to ϕϕ\to (K^+K^-)(K^+K^-)$ is predicted for the first time, which indicates the presence of the significant final-state interactions. The TPAs of the rare decay channel $B^0 \to ϕϕ\to (K^+K^-)(K^+K^-)$ are also predicted and can be tested in the near future.

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