论文标题
QCD Sum-Rule分析的近代领先顺序（NLO）扰动效应：标量 - 等距通道中的案例研究
Next-to-Leading Order (NLO) Perturbative Effects in QCD Sum-Rule Analyses of Light Tetraquark Systems: A Case Study in the Scalar-Isoscalar Channel
论文作者
论文摘要
QCD Sum-rule质量预测四夸克状态提供了有关实验观察到的异国情调介子的解释和内部结构的见解。但是，在领先顺序（LO）上进行了绝大多数Tetraquark QCD Sum-Rule分析，这引发了有关高环校正的基本理论不确定性的问题。在标量（$ j^{pc} = 0^{++} $）中系统地检查了近代领先顺序（NLO）扰动效应的影响，Isoscalar Light-Quark Tetraquark系统已经进行了全面的LO和sum-rule分析，并且先前已经计算出与易裂剂的NLO扰动校正。将标量 - 等级态作为详细的案例研究来说明LO和NLO分析之间的差异，这表明在单个Laplace Sum-Rules中的NLO效应在数值上具有重要意义，并且在提高Sum-rule分析的可靠性方面具有重要作用，从而通过扩大Borel窗口来提高总和规则分析的可靠性。但是，发现总和对NLO效应的比率不太敏感，具有取消从NLO校正出现的异常维度的附加优势。基于这些总和比率的NLO质量预测非常健壮，尽管基础相关器的扰动收敛缓慢。质量预测$ 0.52 \，\ text {gev} <m_σ<0.77 \，\ \ text {gev} $对于最轻的标量 - 等距$σ$ state与$ f_0（500）$的四quark解释非常吻合Tetraquark Current与手性拉格朗日分析中发现的模式一致。研究了$σ$共振宽度的效果，以针对不同型号，包括受手性拉格朗日启发的共振形状。
QCD sum-rule mass predictions for tetraquark states provide insights on the interpretations and internal structure of experimentally-observed exotic mesons. However, the overwhelming majority of tetraquark QCD sum-rule analyses have been performed at leading order (LO), which raises questions about the underlying theoretical uncertainties from higher-loop corrections. The impact of next-to-leading order (NLO) perturbative effects are systematically examined in scalar ($J^{PC}=0^{++}$) isoscalar light-quark tetraquark systems where comprehensive LO sum-rule analyses have been performed and NLO perturbative corrections to the correlators have previously been calculated. Using the scalar-isoscalar state as a detailed case study to illustrate the differences between LO and NLO analyses, it is shown that NLO effects in individual Laplace sum-rules are numerically significant and have an important role in improving the reliability of the sum-rule analyses by widening the Borel window. However, ratios of sum-rules are found to be less sensitive to NLO effects with the additional advantage of cancelling the anomalous dimension that emerges from the NLO corrections. NLO mass predictions based on these sum-rule ratios are thus remarkably robust despite the slow perturbative convergence of the underlying correlator. The mass predictions $0.52\,\text{GeV}< m_σ< 0.77\,\text{GeV}$ for the lightest scalar-isoscalar $σ$ state are in good agreement with the four-quark interpretation of the $f_0(500)$, and the relative coupling strengths of the $f_{0}(980)$ and $f_0(500)$ to the tetraquark current agree with the pattern found in chiral Lagrangian analyses. Effects of the $σ$ resonance width are studied for different models, including resonance shapes inspired by chiral Lagrangians.
