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arXiv 1607.08313hep-phhep-ex
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$B$介子无粲三体衰变中的直接CP破坏

Direct CP Violation in Charmless Three-body Decays of $B$ Mesons

Hai-Yang Cheng, Chun-Khiang Chua, Zhi-Qing Zhang

摘要:

在一个基于因子分解方法的简单模型框架下研究了$B$介子无粲三体强子衰变中的直接CP破坏。重介子的三体衰变同时受到共振和非共振的贡献。树主导和企鹅主导的三体衰变的主要非共振贡献分别来自$b\to u$树过渡和$b\to s$企鹅过渡。前者可以在重介子手征微扰理论的框架下进行计算,而后者则由标量密度$\langle M_1M_2|\bar q_1 q_2|0\rangle$的矩阵元决定。强相位存在于有效Wilson系数、共振传播子和标量密度矩阵元中。为了适应在$B^-\to K^-π^+π^-$中观察到的分支分数和CP不对称性,矩阵元素$\langle Kπ|\bar sq|0\rangle$应该具有额外的强相位,这可能来自于某种功率校正,例如终态相互作用。我们计算了包容性和区域CP不对称性,发现非共振CP破坏通常是远远大于共振的,干扰效应一般是相当显着的。如果在$K^+K^-K^-$模式中关闭非共振贡献,则当面对实验时,由于共振而导致的CP不对称性的预测将在符号上是错误的。在我们对$B^-\to π^-π^+π^-$的研究中,我们发现${\cal A}_{C\!P}(ρ^0π^-)$应该是正的,以便解释在这种衰变中观察到的CP不对称性。然而,所有的理论都预测在$B^-\to ρ^0π^-$中有一个大的和负的CP破坏。CP-不对称Dalitz分布的测量对理论模型提出了非常严格的约束。我们在一些(大的)不变质量区域中检查违反的幅度和符号来测试我们的模型。

英文摘要:

Direct CP violation in charmless three-body hadronic decays of $B$ mesons is studied within the framework of a simple model based on the factorization approach. Three-body decays of heavy mesons receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated and penguin-dominated three-body decays arise from the $b\to u$ tree transition and $b\to s$ penguin transition, respectively. The former can be evaluated in the framework of heavy meson chiral perturbation theory with some modification, while the latter is governed by the matrix element of the scalar density $\langle M_1M_2|\bar q_1 q_2|0\rangle$. Strong phases in this work reside in effective Wilson coefficients, propagators of resonances and the matrix element of scalar density. In order to accommodate the branching fraction and CP asymmetries observed in $B^-\to K^-π^+π^-$, the matrix element $\langle Kπ|\bar sq|0\rangle$ should have an additional strong phase, which might arise from some sort of power corrections such as final-state interactions. We calculate inclusive and regional CP asymmetries and find that nonresonant CP violation is usually much larger than the resonant one and that the interference effect is generally quite significant. If nonresonant contributions are turned off in the $K^+K^-K^-$ mode, the predicted CP asymmetries due to resonances will be wrong in sign when confronted with experiment. In our study of $B^-\to π^-π^+π^-$, we find that ${\cal A}_{C\!P}(ρ^0π^-)$ should be positive in order to account for CP asymmetries observed in this decay. However, all theories predict a large and negative CP violation in $B^-\to ρ^0π^-$. Measurements of CP-asymmetry Dalitz distributions put very stringent constraints on the theoretical models. We check the magnitude and the sign of violation in some (large) invariant mass regions to test our model.

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