Abstract
We show that the Lee-Pomeransky parametric representation of Feynman integrals can be understood as a solution of a certain Gel’fand-Kapranov-Zelevinsky (GKZ) system. In order to define such GKZ system, we consider the polynomial obtained from the Symanzik polynomials g = \( \mathcal{U} \) + \( \mathcal{F} \) as having indeterminate coefficients. Noncompact integration cycles can be determined from the coamoeba — the argument mapping — of the algebraic variety associated with g. In general, we add a deformation to g in order to define integrals of generic graphs as linear combinations of their canonical series. We evaluate several Feynman integrals with arbitrary non-integer powers in the propagators using the canonical series algorithm.
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de la Cruz, L. Feynman integrals as A-hypergeometric functions. J. High Energ. Phys. 2019, 123 (2019). https://doi.org/10.1007/JHEP12(2019)123
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DOI: https://doi.org/10.1007/JHEP12(2019)123