Wave-function mixing of flavor-degenerate baryons

There are two baryons at the center of an octet weight diagram of S${\mathrm{U}\left(3\right)\mathrm{}}_{\mathrm{flavor}}$ both of which contain the same quarks. We call these baryons "flavor degenerate." We discuss the symmetry of the wave functions of these baryons in terms of a quark-ordering principle and a mixing angle. We explore the consequences of the mixing on predictions of the masses and magnetic moments of flavor-degenerate baryons, including baryons containing heavy quarks. We obtain a simple approximate expression for the mixing angles in terms of the quark masses. The mixing angles turn out to be rather small, but still change some of the calculated magnetic moments substantially. The effect of mixing on the baryon masses is much smaller.