Chiral properties of baryon interpolating fields
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We study the chiral transformation properties of all possible local (non-derivative) interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We derive and use the relations/identities among the baryon operators with identical quantum numbers that follow from the combined color, Dirac and isospin Fierz transformations. These relations reduce the number of independent baryon operators with any given spin and isospin. The Fierz identities also effectively restrict the allowed baryon chiral multiplets. It turns out that the non-derivative baryons chiral multiplets have the same dimensionality as their Lorentz representations. For the two independent nucleon operators the only permissible chiral multiplet is the fundamental one, (1/2, 0) circle plus (0, 1/2). For the Delta, admissible Lorentz representations are (1, 1/2) circle plus (1/2, 1) and (3/2, 0) circle plus (0, 3/2). In the case of the (1, 1/2) circle plus (1/2, 1) chir...al multiplet, the I (J) = 3/2 (3/2) Delta field has one I (J) = 1/2 (3/2) chiral partner; otherwise it has none. We also consider the Abelian (U(A)(1)) chiral transformation properties of the fields and show that each baryon comes in two varieties: (1) with Abelian axial charge + 3; and (2) with Abelian axial charge -1. In case of the nucleon these are the two Ioffe fields; in case of the Delta, the (1, 1/2) circle plus (1/2, 1) multiplet has an Abelian axial charge -1 and the (3/2, 0) circle plus (0, 3/2) multiplet has an Abelian axial charge +3.