On the status of expansion by regions

Abstract

We discuss the status of expansion by regions, i.e. a well-known strategy to obtain an expansion of a given multiloop Feynman integral in a given limit where some kinematic invariants and/or masses have certain scaling measured in powers of a given small parameter. Using the Lee-Pomeransky parametric representation, we formulate the corresponding prescriptions in a simple geometrical language and make a conjecture that they hold even in a much more general case. We prove this conjecture in some partial cases and illustrate them in a simple example.

arXiv commentPublished version: presentation improved, Section 7 deleted

References in corpus (17)

• Asymptotic expansion of Feynman integrals near threshold
• An automatized algorithm to compute infrared divergent multi-loop integrals
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• FIESTA 4: optimized Feynman integral calculations with GPU support
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• Numerical evaluation of multi-loop integrals by sector decomposition
• Sector Decomposition
• Resolution of singularities for multi-loop integrals
• Expansion by regions: revealing potential and Glauber regions automatically
• SecDec: A general program for sector decomposition
• Problems of the Strategy of Regions
• Geometric approach to asymptotic expansion of Feynman integrals
• Critical points and number of master integrals
• Foundation and generalization of the expansion by regions
• Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
• Unveiling Regions in multi-scale Feynman Integrals using Singularities and Power Geometry
• Hepp and Speer Sectors within Modern Strategies of Sector Decomposition

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