2025/02/24 by Gernot Eichmann, Eichmann, Gernot, Torres, Raul D.
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Coding theory and cryptography #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2502.17225
openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Five-point functions and five-body wave functions play an important role in many areas of nuclear and particle physics, e.g., in 2 -> 3 scattering processes, in the five-gluon vertex, or in the study of pentaquarks. In this work we consider the permutation group S5 to facilitate the description of such objects. We work out the multiplets transforming under irreducible representations of S5 and provide compact formulas allowing one to cast the permutations of an object f12345 into combinations with definite permutation symmetry. We also give the explicit expressions for the irreducible multiplet products. We consider several practical applications as examples: We arrange the four-momenta and Lorentz invariants of a five-point function into the multiplet structure, we work out the color tensors of the five-gluon vertex in the multiplet notation, and we discuss applications for five-body wave functions like those of pentaquarks.