AI 中文总结
研究针对 QCD 求和规则中拉普拉斯和矩量求和规则的缺点，提出改进的矩量求和规则框架，纳入夸克 - 强子对偶性并对非物理参数设条件，能确定对偶参数和基态质量、提取电流耦合，应用于四夸克系统验证了方案有效性，增强了 QCD 求和规则的稳健性和可靠性。
AI 中文摘要
QCD 求和规则是强子物理中最重要的非微扰工具之一，拉普拉斯求和规则（LSR）和矩量求和规则（MSR）是最常用的两种形式。然而，这两种方法都有显著缺点，如 LSR 依赖主观标准，传统 MSR 无法提取内插流的耦合常数，且两种方法得到的基态质量常不一致。本文提出改进的矩量求和规则（IMSR）框架，明确纳入夸克 - 强子对偶性，对非物理参数施加严格依赖条件，能唯一确定对偶参数最优值和基态质量，还能同时提取电流耦合。将 IMSR 应用于赝标量 $ud\Bar{d}\Bar{s}$ 四夸克系统，结果与之前的 LSR 分析高度一致，验证了该方案的有效性，大大增强了 QCD 求和规则的稳健性和可靠性，有效消除了长期困扰传统形式的主观性。
英文摘要
QCD sum rules are among the most important non-perturbative tools in hadron physics, with the Laplace sum rule (LSR) and moment sum rule (MSR) being the two most commonly used formulations. Despite their widespread application, both approaches have significant shortcomings: the LSR relies on subjective criteria -- namely OPE convergence and pole dominance -- to constrain the parameter space, while the conventional MSR cannot extract the coupling constant of the interpolating current. More critically, the ground-state masses obtained from these two methods are often inconsistent. In this work, we propose an improved moment sum rule (IMSR) framework that resolves these issues simultaneously. Our method explicitly incorporates quark-hadron duality, which introduces the approximation condition on the OPE side and provides a natural a posteriori constraint on the parameters. We impose rigorous dependence conditions on the unphysical parameters $(Q^2_0,n)$ to quantify and control their influence. As a result, our framework uniquely determines both the optimal value of the duality parameter and the ground-state mass, without invoking any ad hoc or subjective criteria. It also allows for the simultaneous extraction of the current coupling. Applying the IMSR to a pseudoscalar $ud\Bar{d}\Bar{s}$ tetraquark system, the results are in excellent agreement with our previous LSR analyses, validating the effectiveness of the proposed scheme. The IMSR method substantially enhances the robustness and reliability of QCD sum rules, effectively eliminating the subjectivity that has long plagued conventional formulations.
Comments21 pages, 8 figures
