We present explicit formulas for the matrix elements of the $SU(6)$ generators for totally symmetric spin-flavor states, relevant for baryon spectroscopy in large $N_c$ QCD. We rely on the interplay between two different methods to calculate these matrix elements. As an outcome, general analytic formulas of the corresponding $SU(6)$ isoscalar factors are derived for arbitrary $N_c$. These results can be used to study excited states of nonstrange and strange baryons.

• Received 14 March 2006

DOI:https://doi.org/10.1103/PhysRevD.73.114025