Work

Solving arbitrary one-loop reduction via generating function

Year: 2025

Type: article

Abstract: 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.

Source: The European Physical Journal C

DOI: 10.1140/epjc/s10052-025-13848-0

Authors: Tingfei Li, Yuekai Song, Liang Zhang

Institutions: Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Zhejiang University

Language: English

Topic: Particle physics theoretical and experimental studies

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Chinese Academy of Sciences, Fundamental Research Funds for the Central Universities

Awards: 散射振幅的新理论、新方法及其应用, G4966918070