Hepp and Speer Sectors within Modern Strategies of Sector Decomposition

TL;DR

This paper revisits Hepp and Speer sectors, integrating them into modern sector decomposition strategies for analyzing Feynman integrals, and demonstrates their compatibility within current frameworks.

Contribution

It shows how Speer sectors are incorporated into recent iterative sector decomposition methods for Feynman integrals.

Findings

Speer sectors are reproduced within modern strategies

Hepp and Speer sectors are applicable to Euclidean momenta

The paper bridges classical and contemporary sector decomposition approaches

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.