2021/02/28 by Valery E. Lyubovitskij, Fabian Wunder, Alexey S. Zhevlakov
Mathematics · Physics and Astronomy · #Algebra over a field #Algorithm #Black Holes and Theoretical Physics #Combinatorics #Covariant transformation #Formalism (music) #Geometry #Integral equation #Invariant (physics) #Loop (graph theory) #Mathematical analysis #Mathematical physics #Mathematics #Order of integration (calculus) #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Recurrence relation #Recursion (computer science) #Scalar (mathematics) #Slater integrals #Volume integral #hep-ph
paper · pdf · doi:10.1007/jhep06(2021)066
published as JHEP 06 (2021) 066 · 134 pages, 8 figures
openalex publication_date 2021/06/09 · arxiv created 2021/06/10 · arxiv updated 2021/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract We discuss new ideas for consideration of loop diagrams and angular integrals in D -dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε -expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.