Hepp and Speer Sectors within Modern Strategies of Sector Decomposition

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.

LaTeX, 12 pages with 3 figures

References in corpus (12)

• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Sector Decomposition
• Resolution of singularities for multi-loop integrals
• Fermionic contributions to the three-loop static potential
• Single Scale Tadpoles and O(GF mt^2 as^3) Corrections to the rho Parameter
• Two-Loop QCD Corrections to the Heavy-to-Light Quark Decay
• Fermionic Corrections to the Heavy-Quark Pair Production in the Quark-Antiquark Channel
• NNLO corrections to inclusive semileptonic B decays in the shape-function region
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions
• Blowing up Feynman integrals
• $\mathcal{O}(\alpha {\alpha }_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold

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