检验$X(2370)$的味单态径向-混杂解释：胶球歧义与可区分振幅测量
Testing a Flavor-Singlet Radial-Hybrid Interpretation of the $X(2370)$: Glueball Ambiguity and Discriminating Amplitude Measurements
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中文总结 AI 辅助
本研究检验X(2370)的味单态径向-混杂解释，发现其与现有数据兼容但无法区分混合胶球构型，提出可通过特定道的相干振幅分析验证竞争衰变模式。
中文摘要 AI 辅助
赝标量$X(2370)$的本质仍未得到解决：胶球、混杂态、常规$q\bar q$以及混合构型在现有信息层面都具备合理性。我们采用$m_X=2.359\\ \mathrm{GeV}$下的道依赖单节点重叠替代模型，结合独立的味单态辐射产生因子，检验了$J^{PC}=0^{-+}$味单态径向-混杂解释。由此得到的衰变模板会自然压低$K^{*}\bar K$的衰变占比，且可根据测得的宽度进行条件归一化，不过其主导的标量和张量道仍依赖于具体模型。要重现推断出的$J/ψ\toγX$中心产生率，所需的有效单态产生振幅约为现有$N_f=2$格点锚点的固定-$V(0)$延拓值的4.4倍。在公共冗余参数筛选比较中，混杂-混合胶球的积分得分差在紧约束、基线和宽冗余设置下分别为-1.29、+0.04和+0.41；这些数值属于条件得分持平，无法作为组分测量的依据。我们指出$f_0(980)η$、$a_0(980)π$和$K_0^{*}(1430)\bar K$中的相干振幅极具信息价值。在给定的代理预测协方差下（包含两类模板的理论不确定性），它们的联合区分度与共享胶球模板的$\Deltaχ^2\simeq6.5$，与径向-$q\bar q$替代模型的$\Deltaχ^2\simeq7.6$。因此，味单态径向混杂态与当前数据兼容，但仍无法与混合胶球解释区分开来；相干振幅分析可用于检验这两种相互竞争的衰变模式。
英文摘要
The nature of the pseudoscalar $X(2370)$ remains unresolved: glueball, hybrid, conventional $q\bar q$, and mixed configurations are all viable at the level of present information. We test a flavor-singlet $J^{PC}=0^{-+}$ radial-hybrid interpretation using a channel-dependent one-node overlap surrogate at $m_X=2.359~\mathrm{GeV}$ and a separate flavor-singlet radiative production factor. The resulting decay template naturally suppresses $K^{*}\bar K$ and can be conditionally normalized to the measured width, although its dominant scalar and tensor channels remain model dependent. Reproducing the inferred central $J/ψ\toγX$ rate requires an effective singlet-production amplitude about $4.4$ times the fixed-$V(0)$ continuation of the available $N_f=2$ lattice anchor. In a common-nuisance screening comparison, the hybrid-mixed-glueball integrated-score difference is $-1.29$, $+0.04$, and $+0.41$ for tight, baseline, and wide nuisance settings, respectively; these values constitute a conditional-score tie rather than a composition measurement. We identify coherent amplitudes in $f_0(980)η$, $a_0(980)π$, and $K_0^{*}(1430)\bar K$ as particularly informative. Under the stated proxy forecast covariance, including theory uncertainty for both templates, their joint separation is $Δχ^2\simeq6.5$ from the shared glueball template and $\simeq7.6$ from the radial-$q\bar q$ surrogate. A flavor-singlet radial hybrid is therefore compatible with current data but remains indistinguishable from a mixed-glueball interpretation; a coherent amplitude analysis can test the competing decay patterns.
