Universal Treatment of Reduction for One-Loop Integrals in Projective Space

Abstract

Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language 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 with arbitrary higher powers. In this paper, we show that 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.

32 pages, 1 figure

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Cited by in corpus (4)

• Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves
• Reduction with Degenerate Gram matrix for One-loop Integrals
• Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals
• Nontrivial One-loop Recursive Reduction Relation