Chiral Properties of Baryon Interpolating Fields

Abstract

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 colour, 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 allowed baryon chiral multiplets. It turns out that the chiral multiplets of the baryons are equivalent to their Lorentz representation. For the two independent nucleon operators the only permissible chiral multiplet is the fundamental one $(\frac{1}{2},0)\oplus (0,\frac{1}{2})$. For the $\Delta$, admissible Lorentz representations are $(1,\frac{1}{2})\oplus (\frac{1}{2},1)$ and $(\frac{3}{2},0)\oplus (0,\frac{3}{2})$. In the case of the $(1,\frac{1}{2})\oplus (\frac{1}{2},1)$ chiral multiplet the $I(J)=\frac{3}{2}(\frac{3}{2})$ $\Delta$ field has one $I(J)=\frac{1}{2}(\frac{3}{2})$ chiral partner; otherwise it has none. We also consider the Abelian ($U_A(1)$) chiral transformation properties of 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's fields; in case of the $\Delta$, the $(1,\frac{1}{2})\oplus (\frac{1}{2},1)$ multiplet has Abelian axial charge -1 and the $(\frac{3}{2},0)\oplus (0,\frac{3}{2})$ multiplet has Abelian axial charge +3.

14 pages

References in corpus (3)

• Chiral Multiplets of Hadron Currents
• Predictive Ability of QCD Sum Rules for Excited Baryons
• Excited decuplet baryons from QCD sum rules

Cited by in corpus (16)

• Study of the axial U(1) anomaly at high temperature with lattice chiral fermions
• Baryon Fields with U_L(3) \times U_R(3) Chiral Symmetry: Axial Currents of Nucleons and Hyperons
• Chiral effective theory of diquarks and the U_A(1) anomaly
• Chiral extrapolation of nucleon wave function normalization constants
• Baryon Fields with U_L(3) times U_R(3) Chiral Symmetry III: Interactions with Chiral (3,3_bar)+(3_bar,3) Spinless Mesons
• Baryons with U_L(3)*U_R(3) Chiral Symmetry IV: Interactions with Chiral (8,1)+(1,8) Vector and Axial-vector Mesons and Anomalous Magnetic Moments
• Baryon fields with $U_L(3)\times U_R(3)$ chiral symmetry V: Pion-Nucleon and Kaon-Nucleon $\Sigma$ Terms
• Chiral Baryon Fields in the QCD Sum Rule
• Nucleon axial couplings and [(1/2,0) + (0,1/2)]-[(1,1/2) + (1/2,1)] chiral multiplet mixing
• Bi-local baryon interpolating fields with two flavours
• The "Closed" Chiral Symmetry and Its Application to Tetraquark
• Baryon Tri-local Interpolating Fields
• Chiral Structure of Scalar and Pseudoscalar Mesons
• Bi-Local Baryon Interpolating Fields with Three Flavours
• Structure of the Roper Resonance with Diquark Correlations
• Quartet of spin-3/2 baryons in chiral multiplet $(1,1/2)\oplus (1/2,1)$ with mirror assignment