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arXiv · 2403.13025

GKZ hypergeometric systems of the four-loop vacuum Feynman integrals

Hai-Bin Zhang·Tai-Fu Feng
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Abstract

Basing on Mellin-Barnes representations and Miller's transformation, we present the Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of 4-loop vacuum Feynman integrals with arbitrary masses. Through the GKZ hypergeometric systems, the analytical hypergeometric solutions of 4-loop vacuum Feynman integrals with arbitrary masses can be obtained in neighborhoods of origin including infinity. The analytical expressions of Feynman integrals can be formulated as a linear combination of the fundamental solution systems in certain convergent region, which the combination coefficients can be determined by the integral at some regular singularities, the Mellin-Barnes representation of the integral, or some mathematical methods.

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Hai-Bin Zhang, Tai-Fu Feng. 2024-03-19. GKZ hypergeometric systems of the four-loop vacuum Feynman integrals. https://doi.org/10.1007/jhep03(2025)013

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