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  • Open Access

Feynman integral reduction without integration by parts

Ziwen Wang (王子文)* and Li Lin Yang (杨李林)†

  • Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310027, China

  • *Contact author: zwenwang@zju.edu.cn
  • †Contact author: yanglilin@zju.edu.cn
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Phys. Rev. D 113, 116005 – Published 2 June, 2026

DOI: https://doi.org/10.1103/s5j9-21gz

Abstract

We present an interesting study of Feynman integral reduction that does not employ integration-by-parts identities. Our approach proceeds by studying the equivalence relations of integral contours in the Feynman parametrization. We find that the integration contour can take a more general form than that given by the Cheng-Wu theorem. We apply this idea to one-loop integrals and derive universal reduction formulas that can be used to efficiently reduce any one-loop integral. We expect that this approach can be useful in the reduction of multiloop integrals as well.

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Phys. Rev. D 113, 116005– Published 2 June, 2026
  • Received 14 October 2025
  • Accepted 28 April 2026
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