Recently, a nice work about the understanding of one-loop integrals has been given by Arkani-Hamed and Yuan [arXiv:1712.09991] using the language of the projective space associated to their Feynman parametrization. We find this language is also very suitable to deal with the reduction problem of one-loop integrals with general tensor structures as well as propagators having arbitrary higher powers. In this paper, we show how to combine Feynman parametrization and embedding formalism to give a universal treatment of reductions for general one-loop integrals, even including the degenerated cases, such as the vanishing Gram determinant. Results from this method can be written in a compact and symmetric form.

• Received 19 May 2022
• Accepted 13 September 2022

DOI:https://doi.org/10.1103/PhysRevD.106.056025

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Published by the American Physical Society