Five-point functions and the permutation group S5

TL;DR

This paper develops a group-theoretical framework based on the permutation group S5 to analyze five-point functions and five-body wave functions, providing formulas for permutation symmetries and applications in physics.

Contribution

It introduces a systematic method to classify and manipulate five-point functions using S5 irreducible representations, with explicit formulas and practical applications.

Findings

Derived multiplet structures for five-point functions

Provided formulas for permutation symmetry operations

Applied framework to five-gluon vertex and pentaquark wave functions

Abstract

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 $f_{12345}$ 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.