Representation Mixing forSU3andG2

Abstract

A theory whose exact invariance with respect to ${\mathrm{SU}}_3$ is broken by interactions transforming like the hypercharge generator of ${\mathrm{SU}}_3$ is studied in perturbation theory. Physical particle states corresponding to unperturbed ${\mathrm{SU}}_3$ multiplets are obtained by mixing into these multiplets possible impurities corresponding to other ${\mathrm{SU}}_3$ multiplets, these impurities being as general as the perturbation allows. The effect of symmetry breaking on various physical quantities like masses and magnetic moments can then be obtained in terms of mixing parameters, and interesting formulas follow various restrictions of their values. Similar considerations applied to $G_2$ show that many of the conclusions which made exact $G_2$ invariance unattractive remain for approximate $G_2$ invariance.