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- W4294553411 abstract "We study multivariate Mellin transforms of Laurent polynomials by considering special toric compactifications which make their singular structure apparent. This gives a precise description of their convergence domain, refining results of Nilsson, Passare, Berkesch and Forsgaa rd. We also reformulate the geometric sector decomposition approach of Kaneko and Ueda in terms of these compactifications. Specializing to the case of Feynman integrals in the parametric representation, we construct multiple such compactifications given by certain systems of subgraphs. As particular cases, we recover the sector decompositions of Hepp, Speer and Smirnov, as well as the iterated blow-up constructions of Brown and Bloch-Esnault-Kreimer. A fundamental role is played by the Newton polytope of the product of the Symanzik polynomials, which we show to be a generalized permutahedron for generic kinematics. As an application, we review two approaches to dimensional regularization of Feynman integrals, based on sector decomposition and on analytic continuation." @default.
- W4294553411 created "2022-09-04" @default.
- W4294553411 creator A5045573431 @default.
- W4294553411 date "2018-06-04" @default.
- W4294553411 modified "2023-10-17" @default.
- W4294553411 title "Toric geometry and regularization of Feynman integrals" @default.
- W4294553411 doi "https://doi.org/10.48550/arxiv.1806.01086" @default.
- W4294553411 hasPublicationYear "2018" @default.
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