Hypergeometric Series Representations of Feynman Integrals by GKZ 
Hypergeometric Systems

Klausen , René Pascal

doi:10.1007/JHEP04(2020)121

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Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems

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Klausen , René Pascal
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Klausen, R. P. (2020). Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems. Journal of High Energy Physics, 2020(4): 121. doi:10.1007/JHEP04(2020)121.

Cite as: https://hdl.handle.net/21.11116/0000-0006-5207-6

Abstract

We show that almost all Feynman integrals as well as their coefficients in a
Laurent series in dimensional regularization can be written in terms of Horn
hypergeometric functions. By applying the results of
Gelfand-Kapranov-Zelevinsky (GKZ) we derive a formula for a class of
hypergeometric series representations of Feynman integrals, which can be
obtained by triangulations of the Newton polytope $\Delta_G$ corresponding to
the Lee-Pomeransky polynomial $G$. Those series can be of higher dimension, but
converge fast for convenient kinematics, which also allows numerical
applications. Further, we discuss possible difficulties which can arise in a
practical usage of this approach and give strategies to solve them.