AI 中文总结
本研究针对重夸克偶素径向激发阶梯是否有限截断的问题，用高斯展开法求解屏蔽Godfrey--Isgur哈密顿量，首次定量给出粲偶素和底偶素的径向激发上限，且该判据可通过未来实验数据检验。
AI 中文摘要
强子谱学中一个根本性的开放问题是，夸克偶素的径向激发阶梯是否会在有限能级处截断——这种可能性将挑战传统的夸克-反夸克束缚态图像，并为非微扰强相互作用提供决定性线索。利用新观测到的高质量强子态，我们通过高斯展开法求解粲偶素和底偶素的屏蔽Godfrey--Isgur哈密顿量来研究这一问题。计算得到的能谱在4.74 GeV（c\bar{c}）和11.67 GeV（b\bar{b}）处趋于饱和，而均方根半径增长至约10 fm——比禁闭尺度高一个数量级——此时相邻质量差降至10 MeV以下。结合由质量-半径解耦起始定义的基于阈值的质量差判据，以及额外的诊断方法，我们确定粲偶素的实际径向上限为n≈8–10，底偶素为n≈12–13。超出这些极限时，传统的q\bar{q}描述不再适用。这项工作首次定量确定了这些上限，且所提出的判据可通过BESIII、Belle II和LHCb即将获得的高统计数据直接检验。
英文摘要
A fundamental open question in hadron spectroscopy is whether the radial excitation ladder of quarkonia truncates at a finite level---a possibility that would challenge the conventional quark-antiquark bound-state picture and offer decisive clues to the nonperturbative strong interaction. Taking advantage of the newly observed high-mass hadronic states, we address this issue by solving a screened Godfrey--Isgur Hamiltonian for charmonium and bottomonium using the Gaussian expansion method. The calculated spectra saturate at $4.74\,\mathrm{GeV}$ ($c\bar{c}$) and $11.67\,\mathrm{GeV}$ ($b\bar{b}$), while root-mean-square radii grow to $\sim10\,\mathrm{fm}$---an order of magnitude above the confinement scale---where adjacent mass gaps drop below $10\,\mathrm{MeV}$. Combining a threshold-based mass-gap criterion, defined by the onset of mass--radius decoupling, with additional diagnostics, we locate the operational upper radial limits at $n\approx8$--$10$ for charmonium and $n\approx12$--$13$ for bottomonium. Beyond these limits, the conventional $q\bar{q}$ description ceases to apply. This work provides the first quantitative determination of these upper limits, and the proposed criterion is directly testable with forthcoming high-statistics data from BESIII, Belle II, and LHCb.
CommentsManuscript (5 pages) combined with Supplemental Material (16 pages)
