发表机构
School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University; Center for High Energy Physics, Peking University（北京大学物理学院及核物理与技术国家重点实验室; 北京大学高能物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出解析性自举方法，利用泰勒展开区域有限性约束约化系数，仅需少量IBP样本或渐近展开即可确定费曼积分完整约化，并显著降低辅助质量流方法中微分方程的构建成本。
AI 中文摘要
我们提出了一种解析性自举方法，用于确定费曼积分（FIs）的约化。关键观察在于，在任何运动学点上，维度正则化的费曼积分都存在一个泰勒展开区域（解析区域），而泰勒区域的有限性强烈约束了积分约化系数，这些系数是运动学变量的有理函数。通过写出与奇点结构相容的最一般ansatz，然后仅利用少量积分约化（IBP）样本或渐近展开来固定剩余参数，即可获得完整的约化。我们在单变量和多变量情形下系统地发展了该方法，并给出了许多显式例子。有趣的是，主积分的微分方程（DEs）决定了所有这些解析性约束，反之，这些约束也有助于构建微分方程。特别地，我们表明，在辅助质量流方法中，微分方程可以以显著降低的成本构建，甚至可以在不使用IBP的情况下完全确定。
英文摘要
We propose an analyticity bootstrap method to determine the reduction of Feynman integrals (FIs). The key observation is that, at any kinematic point, a dimensionally regularized FI possesses a Taylor expansion region (analytic region), and the finiteness of the Taylor region strongly constrains the integral reduction coefficients, which are rational functions of the kinematic variables. By writing the most general ansatz compatible with the singularity structure and then fixing the remaining parameters with only a few integration-by-parts (IBP) samples or asymptotic expansions, one can obtain the full reduction. We develop the method systematically in both single-variable and multi-variable cases, with many explicit examples. Interestingly, the differential equations (DEs) of the master integrals determine all these analyticity constraints and, conversely, the constraints facilitate the construction of the DEs. In particular, we show that the DEs in the auxiliary mass flow method can be constructed at significantly reduced cost and can even be fully determined without using IBP.
Comments16 pages, 4 figures
