An improved moment QCD sum rule

Abstract

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.