A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
Hepp and Speer Sectors within Modern Strategies of Sector Decomposition
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abstract
Hepp and Speer sectors were successfully used in the sixties and seventies for proving mathematical theorems on analytically or/and dimensionally regularized and renormalized Feynman integrals at Euclidean external momenta. We describe them within recently developed strategies of introducing iterative sector decompositions. We show that Speer sectors are reproduced within one of the existing strategies.
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New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.