AI 中文总结
该研究提出QCD求和规则的系统优化框架，结合OPE熵等准则确定求和规则窗口，应用该框架预测了量子数J^{PC}=2^{++}的最低全粲四夸克态质量，结果与实验数据相符。
AI 中文摘要
我们提出了一种用于确定QCD拉普拉斯求和规则中求和规则窗口的系统优化框架。该方法不再主要依赖固定的收敛百分比和视觉平台选择，而是结合了OPE熵准则、局域质量平稳性，以及对拉普拉斯参数τ、连续阈tc和插值流混合角θ的关联分析。引入归一化OPE熵以量化QCD贡献在微扰与非微扰部分之间的重新分配，并划定初始工作区域。随后通过最小化质量估计量的残余变化，以及要求对连续阈和流组成具有弱敏感性，来细化该区域。作为应用，我们使用混合双夸克-反双夸克与介子-介子插值流，研究了量子数为J^PC=2^{++}的最低全粲四夸克态。优化得到θ=17.2°±0.4°，√tc=7.08±0.08 GeV，τ=0.410±0.010 GeV^{-2}，进而给出质量预测M_{c\bar{c}c\bar{c}}^{2^{++}}=(6.32±0.11) GeV。该预测态位于双J/ψ谱的近阈区域，在不确定度范围内与ATLAS报道的最低共振分量以及近期CMS出版物中参数化为BW_0的增强结构相符。所提出的框架提供了一种可复现的方法，用于识别辅助参数敏感性降低的有限区域，并将剩余依赖关系纳入最终不确定度。
英文摘要
We propose a systematic optimization framework for determining the sum rule window in QCD Laplace sum rules. Instead of relying primarily on fixed convergence percentages and visual plateau selection, the procedure combines an OPE entropy criterion, local mass stationarity, and a correlated analysis of the Laplace parameter $τ$, the continuum threshold $t_c$, and the interpolating-current mixing angle $θ$. The normalized OPE entropy is introduced to quantify the redistribution of the QCD contributions between the perturbative and nonperturbative sectors and to delimit an initial Working Region. This domain is subsequently refined by minimizing the residual variation of the mass estimator and requiring weak sensitivity to the continuum threshold and to the current composition. As an application, we study the lowest fully charmed tetraquark state with quantum numbers $J^{PC}=2^{++}$ using a mixed diquark--antidiquark and meson--meson interpolating current. The optimization selects $θ=17.2^\circ\pm0.4^\circ$, $\sqrt{t_c}=7.08\pm0.08~\mathrm{GeV}$, and $τ=0.410\pm0.010~\mathrm{GeV}^{-2}$, leading to the mass prediction $M_{c\bar c c\bar c}^{2^{++}}=(6.32\pm0.11)~\mathrm{GeV}$. The predicted state lies in the near-threshold region of the di-$J/ψ$ spectrum and is compatible, within uncertainties, with the lowest resonant component reported by ATLAS and with the enhancement parametrized as $BW_0$ in the recent CMS publication. The proposed framework provides a reproducible way of identifying finite domains of reduced auxiliary-parameter sensitivity and of incorporating the remaining dependence into the final uncertainty.
Comments13 pages and 5 figures. Presented at the 29th High-Energy Physics International Conference in QCD (QCD26), Montpellier, France
