发表机构
Dipartimento di Matematica e Fisica, Università del Salento; INFN Sezione di Lecce; National Centre for HPC, Big Data and Quantum Computing; CNR Nanotec（萨伦托大学数学与物理系; 意大利国家核物理研究所莱切分部; 高性能计算、大数据与量子计算国家中心; 意大利国家研究委员会纳米技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在微扰QCD框架下研究π介子引力形状因子，通过包含QCD迹反常的$TJJ$关联函数和Sudakov重求和，揭示了反常在不同形状因子中的层级作用，并识别出β函数控制的短距离机械结构贡献。
AI 中文摘要
我们在微扰QCD因子化框架下讨论了中等和大类空动量转移下的π介子引力形状因子。短距离核由单圈非阿贝尔$TJJ$关联函数补充，其中能量-动量张量与两个离壳胶子耦合。其迹部分包含QCD共形反常，并允许标量、类似膨胀子的极点解释。结合横向动量依赖的π介子波函数、Sudakov重求和以及高斯内禀横动量分布，抑制了端点和大横向分离。对π介子形状因子的投影表现出特征层级：孤立的反常在动量形状因子$4A_\pi$中抵消，在机械形状因子$D_\pi$中仍然重要，并在迹形状因子的$TJJ$修正中占主导。该结果识别出由β函数控制的短距离贡献对π介子机械结构的贡献，并阐明了微扰反常极点与相关标量部分子道之间的关系。
英文摘要
We discuss the pion gravitational form factors at intermediate and large spacelike momentum transfer in a perturbative-QCD factorization framework. The short-distance kernel is supplemented by the one-loop non-Abelian $TJJ$ correlator, where the energy--momentum tensor couples to two off-shell gluons. Its trace sector contains the QCD conformal anomaly and admits a scalar, dilaton-like pole interpretation. A transverse-momentum-dependent pion wave function, combined with Sudakov resummation and a Gaussian intrinsic-transverse-momentum profile, suppresses endpoints and large transverse separations. The projection on the pion form factors exhibits a characteristic hierarchy: the isolated anomaly cancels in the momentum form factor 4A_π$, remains important in the mechanical form factor $D_π$, and dominates the $TJJ$ correction to the trace form factor. The result identifies a beta-function-controlled short-distance contribution to pion mechanical structure and clarifies the relation between the perturbative anomaly pole and a correlated scalar partonic channel.
Comments9 pages, 2 figs
