Asymptotic expansion of Feynman integrals near threshold

1997/11/19 by Μ. Beneke, M. Beneke, V. A. Smirnov +1 · 42 citations
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1016/s0550-3213(98)00138-2

published as Nucl.Phys. B522 (1998) 321-344 · 24 pages, LaTeX, 4 figures included via epsf.sty

arxiv created 1997/11/19 · openalex publication_date 1998/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We present general prescriptions for the asymptotic expansion of massive multi-loop Feynman integrals near threshold. As in the case of previously known prescriptions for various limits of momenta and masses, the terms of the threshold expansion are associated with subgraphs of a given graph and are explicitly written through Taylor expansions of the corresponding integrands in certain sets of parameters. They are manifestly homogeneous in the threshold expansion parameter, so that the calculation of the given Feynman integral near the threshold reduces to the calculation of integrals of a much simpler type. The general method is illustrated by two-loop two-point and three-point diagrams. We discuss the use of the threshold expansion for problems of physical interest, such as the next-to-next-to-leading order heavy quark production cross sections close to threshold and matching calculations and power counting in non-relativistic effective theories.

Citations

• Towards systematic near-threshold calculations in perturbative QFT
• Integration by parts: The algorithm to calculate β-functions in 4 loops

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