We show that the recent MIT lattice QCD data for the pion's gravitational form factors are, in the covered momentum transfer range, fully consistent with the meson dominance principle. In particular, the 2++ component can be accurately saturated with the f2(1270) meson, whereas the 0++ component with the σ meson. To incorporate the large width of the σ, we use the dispersion relation with the spectral density obtained from analyses of the physical pion scattering data. Effects of the pion mass are estimated within Chiral Perturbation Theory and are found to be small between the lattice and the physical point. We also discuss the implications of the perturbative QCD constraints at high momentum transfers, leading to specific sum rules for the spectral densities of the gravitational form factors, and argue that these densities cannot be of definite sign.

中文翻译：

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π子和介子优势的引力形式因子


我们表明，最近 MIT 晶格 QCD 数据中，在覆盖的动量传递范围内，与介子优势原理完全一致。特别是，2++ 分量可以用 f2（1270） 介子精确饱和，而 0++ 分量可以用 σ 介子。为了合并σ的大宽度，我们使用色散关系与从物理 π 子散射数据分析中获得的光谱密度。π 子质量的影响是在手性微扰理论中估计的，并且发现晶格和物理点之间的影响很小。我们还讨论了高动量转移时扰动 QCD 约束的影响，导致了引力形式因子谱密度的特定和规则，并认为这些密度不能是确定的符号。