AI 中文总结
该研究在有效场论框架下，分析单圈阶修正对光子与π介子软定理的影响，明确了对数软项与定域次领头项的修正规律，为相关理论研究提供了关键结果。
AI 中文摘要
我们研究包含单圈阶定域有效场论（EFT）修正的光子与π介子软定理。在带五维Pauli算符的有质量QED中，次领头阶软光子定理的定域解析部分会被硬积分区域重整化；而如先前已知，对数软项不会受到高维算符的修正。我们发现双软π介子定理中存在类似结构：对数贡献的系数完全由非线性σ模型（NLSM）拉氏量控制，手征EFT中四导数算符的Wilson系数则以RG方程决定的形式出现在定域次领头阶项中。
英文摘要
We study soft theorems for photons and pions with local effective field theory (EFT) corrections up to one loop order. In massive QED with a dimension-five Pauli operator, the local analytic part of the subleading soft photon theorem is renormalized by the hard integration region. On the other hand, as was previously known, the logarithmic soft terms do not receive corrections from higher-dimensional operators. We find that analogous structure appears in the double-soft pion theorem: the coefficients of logarithmic contributions are controlled entirely by the Nonlinear Sigma Model (NLSM) Lagrangian, while the Wilson coefficients of four-derivative operators in Chiral EFT appear in local subleading terms, in a form that is dictated by their RG equations.
Comments10 pages + refs, 2 figures
