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arXiv 1807.02641hep-phhep-ex
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准二体衰变$B_{(s)}\to P f_2(1270)\to Pππ$的微扰QCD方法

Quasi-two-body decays $B_{(s)}\to P f_2(1270)\to Pππ$ in the perturbative QCD approach

Ya Li, Ai-Jun Ma, Zhou Rui, Wen-Fei Wang, Zhen-Jun Xiao

备注：
15 pages,3 figures
发表信息：
Phys. Rev. D 98, 056019 (2018)
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摘要：

本文用微扰QCD因式分解方法计算了具有二π分布振幅$Φ_{ππ}^{\rm D}$的准二体衰变$B_{(s)}\to P f_2(1270)\to Pππ$的$CP$平均分支比和直接$CP$破坏不对称性，其中$P$代表轻赝标介子$K, π, η$和$η^{\prime}$ .采用相对论性的Breit-Wigner公式描述$D$波共振$f_2(1270)$的类时形状因子$F_π$，其中包含了共振区π介子之间的末态相互作用.通过测定$D$波的2 π分布振幅的Gegenbauer矩，可以使理论结果与实验数据相一致。所考虑的衰减模式的衰减速率通常为$10^{-9}$至$ 10^{-6}$的量级。积分的直接$CP$不对称性的充电模式同意{ \it BABAR}和Belle测量。作为副产品，我们从相应的准二体衰变模式中提取了$B_{(s)}\to Pf_2(1270)$的分支比，这仍然需要在正在进行的和即将进行的实验中进行实验测试。

英文摘要：

In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P f_2(1270)\to Pππ$ with the two-pion distribution amplitude $Φ_{ππ}^{\rm D}$ by using the perturbative QCD factorization approach, where $P$ represents a light pseudoscalar meson $K, π, η$ and $η^{\prime}$. The relativistic Breit-Wigner formula for the $D$-wave resonance $f_2(1270)$ is adopted to parameterize the timelike form factor $F_π$, which contains the final state interactions between the pions in the resonant regions. The consistency of theoretical results with data can be achieved by determining the Gegenbauer moments of the $D$-wave two-pion distribution amplitudes. The decay rates for the considered decay modes are generally in the order of $10^{-9}$ to $ 10^{-6}$. The integrated direct $CP$ asymmetries for the charged modes agree with the {\it BABAR} and Belle measurements. As a by-product, we extract the branching ratios of $B_{(s)}\to Pf_2(1270)$ from the corresponding quasi-two-body decay modes, which still need experimental tests at the ongoing and forthcoming experiments.

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