发表机构
Bethe Center for Theoretical Physics, Universität Bonn; Institute of Physics, Johannes Gutenberg University Mainz（波恩大学贝特理论物理中心; 美因茨约翰内斯·古腾堡大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文探讨椭圆费曼积分中有理基的选择，提出基于前导奇点椭圆推广的基，并发现非对角块的ε依赖性具有普遍结构，在解耦变换下保持不变。
AI 中文摘要
将多圈散射振幅表示为多值超越函数的线性组合，并带有依赖于过程的理性系数，长期以来被认为是有利的。通常，这些超越函数满足一个具有耦合齐次块的微分方程组。当这些耦合块可以通过代数基变换被移除时，有理基与代数基之间的关系是普遍且极小的。在此，我们探讨当解耦需要涉及完全椭圆积分的变换时，是否存在类似的普遍且极小的关系。我们详细阐述了参考文献 arXiv:2504.20897 中提出的方法，在该方法中，我们建议使用基于前导奇点的椭圆推广构建的基可能为这个问题提供答案。我们将此分析扩展到通过此构造获得的基所满足的有理微分方程的非对角块。我们发现，这些块的 $\epsilon$ 依赖性可以组织成一个普遍结构，该结构在用于以迭代积分表达解的解耦变换下得以保持。
英文摘要
Representing multi-loop scattering amplitudes as linear combinations of multivalued transcendental functions with process-dependent rational coefficients has long been understood to be advantageous. In general, these transcendental functions satisfy a system of differential equations with coupled homogeneous blocks. When these coupled blocks can be removed through algebraic basis transformations, the relation between the rational and algebraic bases is universal and minimal. Here, we ask whether an analogous universal and minimal relation exists when decoupling requires transformations involving complete elliptic integrals. We elaborate on the method proposed in ref. arXiv:2504.20897, in which we suggested that a basis constructed using an elliptic generalization of leading singularities may provide an answer to this question. We extend this analysis to the off-diagonal blocks of the rational differential equations satisfied by the bases obtained through this construction. We find that the $ε$ dependence of these blocks can be organized into a universal structure that is preserved under the decoupling transformation used to express the solutions in terms of iterated integrals.
Comments27 pages
