The paper develops reduction operators from resonance in GKZ systems to contract edges in Feynman graphs for one-loop, sunrise, and banana graphs, closing differential equation systems to master integrals.
Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equations can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master integrals.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
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Resonance and Differential Reduction of Feynman Integrals
The paper develops reduction operators from resonance in GKZ systems to contract edges in Feynman graphs for one-loop, sunrise, and banana graphs, closing differential equation systems to master integrals.
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Numerical analytical continuation of multivariate hypergeometric functions
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.