AI 中文总结
该研究针对重夸克偶素共振，结合极点定义与pNRQCD匹配提出其复杂色电极化率的计算方法，通过ψ(3770)极点的单阈值模型给出了留数因子，为相关研究提供了归一化方案。
AI 中文摘要
对于稳定的致密夸克偶素，色电极化率由通过虚色八重态的两次E1跃迁产生；而不稳定夸克偶素由孤立复极点定义，我们通过该极点的二次位移定义其极化率。结合共振性质的标准极点留数定义与pNRQCD匹配表明，完整的双场顶点由全逆传播子的能量导数归一化，其分子包含八重态E1-E1传播、衰变道的场依赖及局域硬匹配项，且无重复计数；稳定态结果以其标准符号和色因子被复现。一个校准到ψ(3770)极点的最小单阈值模型，在其指定的场约定下给出留数因子0.800-0.336i，这说明存在潜在显著的归一化效应，但并非模型无关的极点可观测量，绝对极化率仍需夸克偶素和道响应输入。
英文摘要
For a stable compact quarkonium, chromoelectric polarizability is generated by two E1 transitions through virtual color-octet states. An unstable quarkonium is instead defined by an isolated complex pole. We define its polarizability by the quadratic displacement of that pole. Combining the standard pole-residue definition of resonance properties with pNRQCD matching shows that the complete two-field vertex is normalized by the energy derivative of the full inverse propagator. Its numerator contains octet E1-E1 propagation, the field dependence of decay channels, and local hard matching terms, without double counting. The stable-state result is recovered with its standard sign and color factor. A minimal single-threshold model calibrated to the Psi(3770) pole gives, within its specified field convention, the residue factor 0.800-0.336i. This illustrates a potentially sizable normalization effect but is not a model-independent pole observable. The absolute polarizability still requires quarkonium and channel response inputs.
Comments16 pages
