Fierz identities follow from permutations of quark indices and thus determine which chiral multiplets of baryon fields are Pauli allowed and which are not. In a previous paper we investigate the Fierz identities of baryon fields with two light flavors and find that all bilocal fields that can be constructed from three quarks are Pauli allowed. That does not mean that all possible chiral multiplets exist; however, some chiral multiplets do not appear among structures with a given spin in the local limit, say $J=1/2$. One such chiral multiplet is the [$(\mathbf{6},\mathbf{3})\oplus (\mathbf{3},\mathbf{6})$], which is necessary for a successful chiral mixing phenomenology. In the present paper we extend those methods to three light flavors, i.e., to $S{U}_F(3)$ symmetry and explicitly construct all three necessary chiral $S{U}_L(3)\times S{U}_R(3)$ multiplets, viz. [$(\mathbf{6},\mathbf{3})\oplus (\mathbf{3},\mathbf{6})$], $[(\mathbf{3},\overline{\mathbf{3}})\oplus (\overline{\mathbf{3}},\mathbf{3})]$, and [$(\overline{\mathbf{3}},\mathbf{3})\oplus (\mathbf{3},\overline{\mathbf{3}})$] that are necessary for a phenomenologically successful chiral mixing. We complete this analysis by considering some bilocal baryon fields that are sufficient for the construction of the “missing” spin-$1/2$ baryon interpolating fields. Bilocal baryon fields have definite total angular momentum only in the local limit. The physical significance of these results lies in the fact that they show that there is no need for higher Fock space components, such as the $q^4\overline{q}$, in the baryon chiral mixing framework, for the purpose of fitting the observed axial couplings and magnetic moments: all of the sufficient “mirror components” exist as bilocal fields.

• Received 14 November 2012

DOI:https://doi.org/10.1103/PhysRevD.88.036013