通过非淬火粲偶素谱学对$R$值数据的重新分析澄清$\psi(4160)$令人困惑的质量位移
Clarifying the puzzling mass shift of the $ψ(4160)$ via a reanalysis of $R$-value data with unquenched charmonium spectroscopy
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- Lanzhou University（兰州大学）
- Institute of Modern Physics of CAS（中国科学院近代物理研究所）
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中文总结 AI 辅助
通过非淬火粲偶素谱重新分析BESII R值数据，证明ψ(4160)质量无需上移，4.19 GeV增强源于邻近态相干，并给出64个等价解及其现象学评估。
中文摘要 AI 辅助
长期以来，提取的$\psi(4160)$质量在后续分析中从约$4.16$~GeV上移至$4.19$~GeV，这一现象在粲偶素谱学中仍是一个令人困惑的问题。在我们先前的研究中，该问题通过非淬火粲偶素框架下的$B^+\to K^+\mu^+\mu^-$过程进行了探讨，发现较低质量的$\psi(4160)$赋值与数据相容。在此，我们重新审视在历史上提取较高$\psi(4160)$质量中起重要作用的BESII $R$值数据，并提供独立检验。与包含$\psi(4040)$、$\psi(4160)$和$\psi(4415)$的传统淬火图像不同，非淬火矢量粲偶素谱包含六个态：$\psi(4040)$、$\psi(4160)$、$\psi(4220)$、$\psi(4380)$、$\psi(4415)$和$\psi(4500)$。将这些态与近阈值的$\psi(3770)$一起纳入，我们发现BESII $R$值线形在整个能量范围内可以被很好地重现，同时保留较低质量的$\psi(4160)$赋值。$4.19$~GeV附近的增强源于邻近的$\psi(4040)$、$\psi(4160)$和$\psi(4220)$振幅之间的相干相互作用，而非要求$\psi(4160)$质量本身向上位移。额外的高能态也自然地描述了$4.4$~GeV区域的线形结构。我们进一步表明，七共振相干振幅包含六个复零点，产生$2^6=64$个数学上等价的解，这些解具有相同的线形但二电子宽度和相对相位显著不同。将这些解与现有实验信息和代表性的非淬火粲偶素预言进行比较，我们对其现象学一致性进行了定性评估，并突出显示了几个与当前信息似乎更相容的解。
英文摘要
The long-standing upward shift of the extracted $ψ(4160)$ mass, from about $4.16$~GeV to $4.19$~GeV in later analyses, remains a puzzling issue in charmonium spectroscopy. In our previous study, this problem was investigated through the $B^+\to K^+μ^+μ^-$ process within an unquenched charmonium framework, where the lower-mass $ψ(4160)$ assignment was found to be compatible with the data. Here we revisit the BESII $R$-value data, which played an important role in the historical extraction of the higher $ψ(4160)$ mass, and provide an independent examination. In contrast to the conventional quenched picture with $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$, the unquenched vector-charmonium spectrum contains six states: $ψ(4040)$, $ψ(4160)$, $ψ(4220)$, $ψ(4380)$, $ψ(4415)$, and $ψ(4500)$. Including these states together with the near-threshold $ψ(3770)$, we find that the BESII $R$-value line shape can be well reproduced over the full energy range while retaining the lower-mass $ψ(4160)$ assignment. The enhancement around $4.19$~GeV then arises from the coherent interplay among the nearby $ψ(4040)$, $ψ(4160)$, and $ψ(4220)$ amplitudes, rather than requiring an upward shift of the $ψ(4160)$ mass itself. The additional higher states also naturally describe the line-shape structure in the $4.4$~GeV region. We further show that the seven-resonance coherent amplitude contains six complex zeros, yielding $2^6=64$ mathematically equivalent solutions with identical line shapes but substantially different di-electron widths and relative phases. Comparing these solutions with available experimental information and representative unquenched charmonium predictions, we provide a qualitative assessment of their phenomenological consistency and highlight several solutions that appear more compatible with present information.
