标量胶球的有效场论：形状因子与相互作用半径
Effective field theory of scalar glueballs: Form factors and interaction radii
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中文总结 AI 辅助
本文基于杨-米尔斯胶子凝聚建立标量胶球有效场论，推导出归一化形状因子，预测基态胶球相互作用半径为0.28 fm，与格点结果吻合，并验证了f0(1710)候选态。
中文摘要 AI 辅助
我们基于杨-米尔斯胶子凝聚发展了一种规范不变的标量胶球相互作用的有效场论。从杨-米尔斯真空的相干态表述出发，我们推导了标量胶球及其与胶子相互作用的有效拉格朗日量。由此得到的满足交叉对称性的切割四胶子格林函数被投影到色单态 $J^{PC}=0^{++}$ 通道，产生了一个归一化的标量胶球形状因子，该形状因子分解为普适的运动学结构和内禀胶球函数。该形式体系预测了基态标量胶球（对应共振态 $f_0(1710)$）的无参数有效相互作用半径 $r_{\rm int}=\sqrt{6}/m_\phi=0.28$ fm，这与近期格点杨-米尔斯计算的质量半径（$r=0.263(31)$ fm）高度一致。归一化形状因子的预测动量依赖性与格点杨-米尔斯引力形状因子数据一致，其中 $f_0(1710)$ 候选态提供了最佳的整体拟合和 $r_{\rm int}$。包含第一激发态 $0^{++}$ 胶球对相互作用半径产生适度修正（$r_{\rm int}^*=0.240$ fm），同时给出稳定且运动学上稳健的形状因子修正。该框架为有效场论与第一性原理格点杨-米尔斯计算之间提供了系统性的桥梁，以研究标量胶球动力学。
英文摘要
We develop a gauge-invariant effective field theory for scalar glueball interactions based on the Yang-Mills gluon condensate. Starting from a coherent-state formulation of the Yang-Mills vacuum, we derive an effective Lagrangian for the scalar glueball and its interactions with gluons. The resulting crossing-symmetric amputated four-gluon Green's function is projected onto the color-singlet $J^{PC}=0^{++}$ channel, yielding a normalized scalar glueball form factor that factorizes into universal kinematic structures and an intrinsic glueball function. The formalism predicts a parameter-free effective interaction radius for the ground-state scalar glueball with resonance $f_0(1710)$, $r_{\rm int}=\sqrt{6}/m_ϕ=0.28$ fm, which is in excellent agreement with recent lattice Yang-Mills determinations of the mass-radius ($r=0.263(31)$ fm). The predicted momentum dependence of the normalized form factor is consistent with lattice Yang-Mills gravitational form factor data, with the $f_0(1710)$ candidate providing the best overall fit and $r_{\rm int}$. Inclusion of the first excited $0^{++}$ glueball produces modest corrections to the interaction radius ($r_{\rm int}^*=0.240$ fm) while yielding stable and kinematically robust modifications of the form factor. This framework provides a systematic bridge between effective field theory and first-principles lattice Yang-Mills calculations of scalar glueball dynamics.
发表机构
- CFisUC, Department of Physics, University of Coimbra（科英布拉大学物理系CFisUC）
- Departamento de Física, Instituto Tecnológico de Aeronáutica, DCTA（航空技术学院物理系DCTA）
- Laboratório de Computação Científica Avançada e Modelamento (Lab-CCAM)（高级计算与建模实验室(Lab-CCAM)）
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