Tensor reduction of two-loop vacuum diagrams and projectors for expanding three-point functions

1995/11/07 by A. I. Davydychev, A.I. Davydychev, J. B. Tausk +1 · 23 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cartesian tensor #Momentum (technical analysis) #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics #Reduction (mathematics) #Scalar (mathematics) #Tensor (intrinsic definition) #Tensor calculus #Tensor field #hep-ph #hep-th

paper · pdf · doi:10.1016/0550-3213(96)00033-8

published in Nuclear Physics B 465(3), 507-520 (Elsevier BV) · 13 pages, plain latex, no figures

arxiv created 1995/11/07 · openalex publication_date 1996/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators (projectors) extracting the coefficients of the momentum expansion of massive scalar three-point functions (with any number of loops), so the solution to the latter problem is also given.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Reduction of general two-loop self-energies to standard scalar integrals
• Regularization and renormalization of gauge fields
• New results for two-loop off-shell three-point diagrams
• Dimensional renorinalization : The number of dimensions as a regularizing parameter