The $S_3$ symmetry corresponding to permuting the positions of the quarks within a baryon allows us to study the 70-plet of $L=1\mathrm{}$ baryons without an explicit choice for the spatial part of the quark wave functions: given a set of operators with definite transformation properties under the spin-flavor group $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ and under this $S_3,$ the masses of the baryons can be expressed in terms of a small number of unknown parameters which are fit to the observed $L=1\mathrm{}$ baryon mass spectrum. This approach is applied to study both the quark model and chiral constituent quark model. The latter theory leads to a set of mass perturbations which more satisfactorily fits the observed $L=1\mathrm{}$ baryon mass spectrum (though we can say nothing, within our approach, about the physical reasonableness of the parameters in the fit). Predictions for the mixing angles and the unobserved baryon masses are given for both models as well as a discussion of specific baryons.

• Received 26 October 1998

DOI:https://doi.org/10.1103/PhysRevD.59.094010