2017/07/31 by A. V. Nesterenko
Mathematics · Physics and Astronomy · #Annihilation #Combinatorics #Electron #Energy (signal processing) #Expression (computer science) #Function (biology) #Geometry #Hadron #High-Energy Particle Collisions Research #Lambda #Loop (graph theory) #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Pi #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #hep-ex #hep-ph
paper · pdf · doi:10.1140/epjc/s10052-017-5405-5
published as Eur. Phys. J. C77, 844 (2017) · 21 pages, 8 figures, 4 tables
openalex publication_date 2017/12/01 · arxiv created 2017/12/18 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The strong corrections to the R-ratio of electron–positron annihilation into hadrons are studied at the higher-loop levels. Specifically, the derivation of a general form of the commonly employed approximate expression for the R-ratio (which constitutes its truncated re-expansion at high energies) is delineated, the appearance of the pertinent π 2 π 2 -terms is expounded, and their basic features are examined. It is demonstrated that the validity range of such approximation is strictly limited to √(s)/\varLambda > exp (π /2) ≃ 4.81 s / Λ > exp ( π / 2 ) ≃ 4.81 and that it converges rather slowly when the energy scale approaches this value. The spectral function required for the proper calculation of the R-ratio is explicitly derived and its properties at the higher-loop levels are studied. The developed method of calculation of the spectral function enables one to obtain the explicit expression for the latter at an arbitrary loop level. By making use of the derived spectral function the proper expression for the R-ratio is calculated up to the five-loop level and its properties are examined. It is shown that the loop convergence of the proper expression for the R-ratio is better than that of its commonly employed approximation. The impact of the omitted higher-order π 2 π 2 -terms on the latter is also discussed.