SU(3) Clebsch-Gordan coefficients at large $N_c$

TL;DR

This paper shows that many SU(3) Clebsch-Gordan coefficients used in hadronic physics are special cases of Hecht's 1965 formulas, with extensions for multiplicity two to improve large N_c analyses.

Contribution

It clarifies the connection between previous SU(3) Clebsch-Gordan calculations and Hecht's analytic formulas, providing a unified framework for large N_c studies.

Findings

Many SU(3) Clebsch-Gordan coefficients are special cases of Hecht's formulas.

Hecht's alternative for multiplicity two provides correct 1/N_c corrections.

The work aids in accurate large N_c hadronic physics calculations.

Abstract

It is argued that several papers where SU(3) Clebsch-Gordan coefficients were calculated in order to describe properties of hadronic systems are, up to a phase convention, particular cases of analytic formulae derived by Hecht in 1965 in the context of nuclear physics. This is valid for irreducible representations with multiplicity one in the corresponding Clebsch-Gordan series. For multiplicity two, Hecht has proposed an alternative which can provide correct $1/N_c$ sub-leading orders in large $N_c$ studies.