SU(3) group structure of strange flavor hadrons

TL;DR

This paper calculates the isoscalar factors of SU(3) Clebsch-Gordan series 8x35, aiding in strange flavor hadron physics by studying SU(3) algebra, eigenvalues, and Wigner D functions for phenomenological applications.

Contribution

It extends previous SU(3) isoscalar factor calculations and applies group theory to analyze magnetic moments and sum rules in strange flavor hadron physics.

Findings

Calculated isoscalar factors for 8x35 SU(3) series.

Derived sum rules for baryon magnetic moments.

Provided practical tools for strange hadron phenomenology.

Abstract

We provide the isoscalar factors of the SU(3) Clebsch-Gordan series 8x35 which are extensions of the previous works of de Swart, McNamee and Chilton and play practical roles in current ongoing strange flavor hadron physics research. To this end, we pedagogically study the SU(3) Lie algebra, its spin symmetries, and its eigenvalues for irreducible representations. We also evaluate the values of the Wigner D functions related to the isoscalar factors; these functions are immediately applicable to strange flavor hadron phenomenology. Exploiting these SU(3) group properties associated with the spin symmetries, we investigate the decuplet-to-octet transition magnetic moments and the baryon octet and decuplet magnetic moments in the flavor symmetric limit to construct the Coleman-Glashow-type sum rules.