Universal treatment of the reduction for one-loop integrals in a projective space

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.

Automated summary

This paper presents a universal treatment for the reduction problem of one-loop integrals, including degenerated cases, using the language of projective space and Feynman parametrization. The method can also handle propagators with arbitrary higher powers.