https://doi.org/10.1140/epjc/s10052-025-13848-0
Regular Article - Theoretical Physics
Solving arbitrary one-loop reduction via generating function
1
Zhejiang Institute of Modern Physics, Zhejiang University, 310027, Hangzhou, People’s Republic of China
2
Kavli Institute for Theoretical Sciences (KITS), University of Chinese Academy of Sciences, 100190, Beijing, China
Received:
15
November
2024
Accepted:
20
January
2025
Published online:
4
February
2025
Recently, the concept of generating function has been employed in one-loop reduction. For one-loop integrals encompassing arbitrary tensor ranks and higher-pole contributions, the generating function can be decomposed into a tensor part and a higher-pole part. While the tensor component has been thoroughly addressed in recent studies, there remains a lack of satisfactory investigations regarding the higher-pole part. In this work, we completely solve the problem. We first establish the partial differential equations governing the higher-pole generating function. Based on these equations, we derive an integration recursion relation and solve it iteratively. This approach enables us to explore the analytical structure of higher-pole reduction and provides a valuable tool for generating reduction coefficients efficiently.
© The Author(s) 2025
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