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arXiv 2005.13568hep-ph
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电磁 Dalitz 衰变 $J/ψ\rightarrowη^{(\prime)}\ell^{+}\ell^{-}$ 的 QCD 分析

QCD analysis of electromagnetic Dalitz decays $J/ψ\rightarrowη^{(\prime)}\ell^{+}\ell^{-}$

Jun-Kang He, Chao-Jie Fan

AI总结:

本文在微扰 QCD 框架下结合软波函数重叠与矢量介子主导模型,计算 $J/ψ\rightarrowη^{(\prime)}\ell^{+}\ell^{-}$ 的跃迁形状因子和分支比,电子道结果与实验吻合,并预言缪子道。

摘要:

本文在微扰 QCD 框架下研究了具有大反冲动量的电磁 Dalitz 衰变 $J/ψ\rightarrowη^{(\prime)}e^{+}e^{-}$。同时,小反冲动量区域的软贡献由软波函数的重叠描述,共振贡献则通过矢量介子主导模型进行估计。基于这一动力学图像,本文首次计算了完整运动学区域中的跃迁形状因子 $f_{ψη^{(\prime)}}(q^{2})$,并发现这些跃迁形状因子对 $η^{(\prime)}$ 分布振幅的形状不敏感。我们对归一化跃迁形状因子 $F_{ψη}(q^{2})\equiv f_{ψη}(q^{2})/f_{ψη}(0)$ 的预言与实验数据符合良好。此外,我们还发现分支比 $\mathcal{B}(J/ψ\rightarrowη^{(\prime)}e^{+}e^{-})$ 由微扰 QCD 贡献主导;由于运动学因子的抑制,共振贡献与软贡献一样小到可以忽略。综合所有这些贡献,我们得到的分支比 $\mathcal{B}(J/ψ\rightarrowη^{(\prime)}e^{+}e^{-})$ 以及比值 $R_{J/ψ}^{e}=\mathcal{B}(J/ψ\rightarrowηe^{+}e^{-})/\mathcal{B}(J/ψ\rightarrowη^{\prime}e^{+}e^{-})$ 均与实验数据很好地符合。利用所得的 $F_{ψη^{(\prime)}}(q^{2})$,我们给出了分支比 $\mathcal{B}(J/ψ\rightarrowη^{(\prime)}\mu^{+}\mu^{-})$ 及其比值 $R_{J/ψ}^\mu$ 的预言。

英文摘要:

The electromagnetic Dalitz decays $J/ψ\rightarrowη^{(\prime)}e^{+}e^{-}$ with large recoil momentum are studied in the framework of perturbative QCD. Meanwhile, the soft contributions from the small recoil momentum region are described by the overlap of soft wave functions, and the resonance contributions are estimated by the vector meson dominance model. Based on this dynamical picture, the transition form factors $f_{ψη^{(\prime)}}(q^{2})$ in full kinematic region are calculated for the first time, and we find that the transition form factors are insensitive to the shapes of $η^{(\prime)}$ distribution amplitudes. Our prediction of the normalized transition form factor $F_{ψη}(q^{2})\equiv f_{ψη}(q^{2})/f_{ψη}(0)$ agrees well with its experimental data. In addition, we also find that the branching ratios $\mathcal{B}(J/ψ\rightarrowη^{(\prime)}e^{+}e^{-})$ are dominated by the contributions of perturbative QCD, and the resonance contributions are negligibly small as well as the soft contributions due to the suppression of the kinematic factor. With all these contributions, our results of the branching ratios $\mathcal{B}(J/ψ\rightarrowη^{(\prime)}e^{+}e^{-})$ and the ratio $R_{J/ψ}^{e}=\mathcal{B}(J/ψ\rightarrowηe^{+}e^{-})/\mathcal{B}(J/ψ\rightarrowη^{\prime}e^{+}e^{-})$ are in good agreement with their experimental data. Using the obtained $F_{ψη^{(\prime)}}(q^{2})$, we give the predictions of the branching ratios $\mathcal{B}(J/ψ\rightarrowη^{(\prime)}μ^{+}μ^{-})$ and their ratio $R_{J/ψ}^μ$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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