  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 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 SU(3) x SU(2) 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 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
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.
