Analytic computing methods for precision calculations in quantum field theory

2018/06/08 by J. Blümlein, Johannes Blümlein, Carsten Schneider
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Computation #Computer science #Current (fluid) #Effective field theory #Field (mathematics) #Function (biology) #Loop (graph theory) #Massless particle #Observable #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum field theory #Quantum gravity #Quantum mechanics #Scale (ratio) #Statistical physics #Theoretical physics #Thermal quantum field theory #hep-ph #hep-th #math-ph #math.MP

paper · pdf · doi:10.1142/s0217751x18300156

published as Int.J.Mod.Phys. A33 (2018) no.17, 1830015 · 29 pages LATEX

openalex publication_date 2018/06/08 · arxiv created 2018/09/08 · arxiv updated 2018/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

An overview is presented on the current status of main mathematical computation methods for the multiloop corrections to single-scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present, massless single-scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero-scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods.

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