Algebraic-numerical evaluation of Feynman diagrams: two-loop self-energies

2001/12/01 by Giampiero Passarino, G. Passarino, Sandro Uccirati +1 · 2 citations
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Quantum and Classical Electrodynamics #advanced mathematical theories #hep-ph

paper · pdf · doi:10.1016/s0550-3213(02)00138-4

published as Nucl.Phys. B629 (2002) 97-187 · 92 pages(Latex), 4 figures

arxiv created 2001/12/01 · openalex publication_date 2002/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A recently proposed scheme for numerical evaluation of Feynman diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F. V. Tkachov and it is based on the so-called generalized Bernstein functional relation. On-shell derivatives of self-energies are also considered and their infrared properties analyzed to prove that the method which is aimed to a numerical evaluation of massive diagrams can handle the infrared problem within the scheme of dimensional regularization. Particular care is devoted to study the general massive diagrams around their leading and non-leading Landau singularities.

Citations

• Differential Equations for Two-Loop Four-Point Functions
• Analytic two-loop results for self-energy- and vertex-type diagrams with one non-zero mass

Cited by

• Two-loop vertices in quantum field theory: infrared convergent scalar configurations
• The two loop crossed ladder vertex diagram with two massive exchanges