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Solving arbitrary one-loop reduction via generating function
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DOI：10.1140/epjc/s10052-025-13848-0.png)
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Abstract
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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.
Keywords:
ALGEBRAIC REDUCTION
FEYNMAN DIAGRAMS
AMPLITUDES
INTEGRALS
UNITARITY
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4.8
Papers:
1.8W
Citations:
4.7W
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