发表机构
Bogoliubov Lab. Theor. Phys., JINR; Gomel State Technical University（约飞联合核子研究所鲍里索夫理论物理实验室; 戈梅利国立技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对由真空极化插入费曼图引起的轻子反常磁矩电磁修正，提出基于Mellin-Barnes变换与PSLQ算法的解析计算方法，并利用函数方程实现超几何函数解析延拓，从而获得高阶辐射修正的显式表达式。
AI 中文摘要
本文详细展示并考察了我们在轻子反常磁矩 $a_L$ 的电磁修正解析计算中所使用的数学方法与途径，该修正由一类特殊的、插入真空极化算符的费曼图所引起。所发展的方法本质上基于对有质量粒子传播子应用Mellin--Barnes变换，随后利用PSLQ算法来求解由此产生的函数方程。函数方程也被用于将特定类型的超几何函数解析延拓到其参数的整个复平面。研究表明，这些方法能够获得相当高阶的辐射修正的显式表达式。
英文摘要
The mathematical methods and approaches used in our analytical calculations of electromagnetic corrections to the leptonic anomaly $a_L$, which is caused by a special class of Feynman diagrams with insertions of the vacuum polarization operator, are presented and examined in detail. The developed methods are essentially based on the Mellin--Barnes transform for the propagators of massive particles with subsequent application of the PSLQ algorithm to solve the emerging functional equations. Functional equations are also used in the procedure of analytic continuation of a particular type of hypergeometric functions to the entire complex plane of their parameters. It is shown that these approaches make it possible to obtain explicit expressions for radiative corrections of rather high orders.
Comments8 pages (twocolumn), 18th Int. Conf. Foundations & Advances in Nonlinear Science (21.09-25.09.2026, Minsk, Belarus)
