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Fierz identities follow from permutations of quark indices and thus determinewhich chiral multiplets of baryon fields are Pauli-allowed, and which are not.In a previous paper we have investigated the Fierz identities of baryon fieldswith two light flavours and found that all bilocal fields that can beconstructed from three quarks are Pauli-allowed. That does not mean that allpossible chiral multiplets exist, however: some chiral multiplets do not appearamong structures with a given spin in the local limit, say J = 1/2. One suchchiral multiplet is the [(6,3)+(3,6)], which is necessary for a successfulchiral mixing phenomenology. In the present paper we extend those methods tothree light flavors, i.e. to SU_F(3) symmetry and explicitly construct allthree necessary chiral SU_L(3)*SU_R(3) multiplets, viz. [(6,3)+(3,6)],[(3,3_bar)+(3_bar,3)] and [(3_bar,3)+(3,3_bar)] that are necessary for aphenomenologically successful chiral mixing. We complete this analysis byconsidering some bi-local baryon fields that are sufficient for theconstruction of the "missing" spin 1/2 baryon interpolating fields. Bi-localbaryon fields have definite total angular momentum only in the local limit. Thephysical significance of these results lies in the fact that they show thatthere is no need for higher Fock space components, such as the (q^4 q_bar), inthe baryon chiral mixing framework, for the purpose of fitting the observedaxial couplings and magnetic moments: all of the sufficient "mirror components"exist as bi-local fields.

Bi-Local Baryon Interpolating Fields with Three Flavours