GKZ-system of the 2-loop self energy with 4 propagators

Abstract

Applying the system of linear partial differential equations derived from the Mellin-Barnes representation and the Miller transformation, we present the GKZ-system of the Feynman integral of the 2-loop self energy diagram with 4 propagators. The codimension of the derived GKZ-system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. In total 536 hypergeometric functions are obtained in the neighborhoods of the origin and infinity, in which 30 linearly independent hypergeometric functions whose convergent regions have nonempty intersection constitute a fundamental solution system in a proper subset of the whole parameter space.

latex, 306 pages, including 1 figure + 254 pages of supplementary material, accepted for publication in the European Physical Journal C. arXiv admin note: text overlap with arXiv:2206.04224

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Cited by in corpus (4)

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• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• From equations in coordinate space to Picard-Fuchs and back
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals